src/HOL/Tools/ATP/atp_translate.ML
author blanchet
Mon Jun 27 14:56:28 2011 +0200 (2011-06-27)
changeset 43572 ae612a423dad
parent 43501 0e422a84d0b2
child 43622 80673841372b
permissions -rw-r--r--
added "sound" option to force Sledgehammer to be pedantically sound
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(*  Title:      HOL/Tools/ATP/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 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 connective = ATP_Problem.connective
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  type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
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  type format = ATP_Problem.format
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  type formula_kind = ATP_Problem.formula_kind
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  type 'a problem = 'a ATP_Problem.problem
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  datatype locality =
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    General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
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    Chained
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  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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  datatype type_level =
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    All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
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    No_Types
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  datatype type_heaviness = Heavyweight | Lightweight
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  datatype type_sys =
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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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  val bound_var_prefix : string
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  val schematic_var_prefix : string
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  val fixed_var_prefix : string
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  val tvar_prefix : string
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  val tfree_prefix : string
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  val const_prefix : string
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  val type_const_prefix : string
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  val class_prefix : string
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  val skolem_const_prefix : string
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  val old_skolem_const_prefix : string
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  val new_skolem_const_prefix : string
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  val type_decl_prefix : string
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  val sym_decl_prefix : string
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  val preds_sym_formula_prefix : string
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  val lightweight_tags_sym_formula_prefix : string
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val helper_prefix : string
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  val class_rel_clause_prefix : string
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  val arity_clause_prefix : string
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  val tfree_clause_prefix : string
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  val typed_helper_suffix : string
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  val untyped_helper_suffix : string
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  val type_tag_idempotence_helper_name : string
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  val predicator_name : string
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  val app_op_name : string
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  val type_tag_name : string
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  val type_pred_name : string
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  val simple_type_prefix : string
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  val prefixed_predicator_name : string
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  val prefixed_app_op_name : string
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  val prefixed_type_tag_name : string
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  val ascii_of : string -> string
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  val unascii_of : string -> string
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  val strip_prefix_and_unascii : string -> string -> string option
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  val proxy_table : (string * (string * (thm * (string * string)))) list
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  val proxify_const : string -> (string * string) option
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  val invert_const : string -> string
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  val unproxify_const : string -> string
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  val new_skolem_var_name_from_const : string -> string
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  val num_type_args : theory -> string -> int
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  val atp_irrelevant_consts : string list
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  val atp_schematic_consts_of : term -> typ list Symtab.table
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  val is_locality_global : locality -> bool
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  val type_sys_from_string : string -> type_sys
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  val polymorphism_of_type_sys : type_sys -> polymorphism
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  val level_of_type_sys : type_sys -> type_level
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  val is_type_sys_virtually_sound : type_sys -> bool
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  val is_type_sys_fairly_sound : type_sys -> bool
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  val choose_format : format list -> type_sys -> format * type_sys
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  val mk_aconns :
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    connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
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  val unmangled_const : string -> string * string fo_term list
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  val unmangled_const_name : string -> string
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  val helper_table : ((string * bool) * thm list) list
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  val factsN : string
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  val prepare_atp_problem :
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    Proof.context -> format -> formula_kind -> formula_kind -> type_sys -> bool
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    -> bool -> bool -> bool -> term list -> term
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    -> ((string * locality) * term) list
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    -> string problem * string Symtab.table * int * int
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       * (string * locality) list vector * int list * int Symtab.table
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  val atp_problem_weights : string problem -> (string * real) list
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end;
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structure ATP_Translate : ATP_TRANSLATE =
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struct
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open ATP_Util
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open ATP_Problem
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type name = string * string
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(* experimental *)
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val generate_useful_info = false
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fun useful_isabelle_info s =
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  if generate_useful_info then
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    SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
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  else
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    NONE
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val intro_info = useful_isabelle_info "intro"
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val elim_info = useful_isabelle_info "elim"
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val simp_info = useful_isabelle_info "simp"
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val bound_var_prefix = "B_"
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val schematic_var_prefix = "V_"
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val fixed_var_prefix = "v_"
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val tvar_prefix = "T_"
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val tfree_prefix = "t_"
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val const_prefix = "c_"
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val type_const_prefix = "tc_"
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val class_prefix = "cl_"
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val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
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val old_skolem_const_prefix = skolem_const_prefix ^ "o"
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val new_skolem_const_prefix = skolem_const_prefix ^ "n"
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val type_decl_prefix = "ty_"
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val sym_decl_prefix = "sy_"
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val preds_sym_formula_prefix = "psy_"
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val lightweight_tags_sym_formula_prefix = "tsy_"
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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 = "clar_"
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val arity_clause_prefix = "arity_"
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val tfree_clause_prefix = "tfree_"
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val typed_helper_suffix = "_T"
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val untyped_helper_suffix = "_U"
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val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
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val predicator_name = "hBOOL"
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val app_op_name = "hAPP"
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val type_tag_name = "ti"
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val type_pred_name = "is"
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val simple_type_prefix = "ty_"
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val prefixed_predicator_name = const_prefix ^ predicator_name
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val prefixed_app_op_name = const_prefix ^ app_op_name
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val prefixed_type_tag_name = const_prefix ^ type_tag_name
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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(*Escaping of special characters.
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  Alphanumeric characters are left unchanged.
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  The character _ goes to __
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  Characters in the range ASCII space to / go to _A to _P, respectively.
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  Other characters go to _nnn where nnn is the decimal ASCII code.*)
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val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
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fun stringN_of_int 0 _ = ""
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  | stringN_of_int k n =
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    stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
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fun ascii_of_char c =
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  if Char.isAlphaNum c then
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    String.str c
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  else if c = #"_" then
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    "__"
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  else if #" " <= c andalso c <= #"/" then
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    "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
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  else
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    (* fixed width, in case more digits follow *)
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    "_" ^ stringN_of_int 3 (Char.ord c)
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val ascii_of = String.translate ascii_of_char
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(** Remove ASCII armoring from names in proof files **)
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(* We don't raise error exceptions because this code can run inside a worker
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   thread. Also, the errors are impossible. *)
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val unascii_of =
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  let
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    fun un rcs [] = String.implode(rev rcs)
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      | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
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        (* Three types of _ escapes: __, _A to _P, _nnn *)
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      | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
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      | un rcs (#"_" :: c :: cs) =
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        if #"A" <= c andalso c<= #"P" then
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          (* translation of #" " to #"/" *)
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          un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
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        else
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          let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
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            case Int.fromString (String.implode digits) of
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              SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
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            | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
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          end
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      | un rcs (c :: cs) = un (c :: rcs) cs
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  in un [] o String.explode end
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(* If string s has the prefix s1, return the result of deleting it,
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   un-ASCII'd. *)
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fun strip_prefix_and_unascii s1 s =
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  if String.isPrefix s1 s then
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    SOME (unascii_of (String.extract (s, size s1, NONE)))
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  else
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    NONE
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val proxy_table =
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  [("c_False", (@{const_name False}, (@{thm fFalse_def},
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       ("fFalse", @{const_name ATP.fFalse})))),
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   ("c_True", (@{const_name True}, (@{thm fTrue_def},
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       ("fTrue", @{const_name ATP.fTrue})))),
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   ("c_Not", (@{const_name Not}, (@{thm fNot_def},
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       ("fNot", @{const_name ATP.fNot})))),
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   ("c_conj", (@{const_name conj}, (@{thm fconj_def},
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       ("fconj", @{const_name ATP.fconj})))),
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   ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
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       ("fdisj", @{const_name ATP.fdisj})))),
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   ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
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       ("fimplies", @{const_name ATP.fimplies})))),
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   ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
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       ("fequal", @{const_name ATP.fequal}))))]
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val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
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(* Readable names for the more common symbolic functions. Do not mess with the
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   table unless you know what you are doing. *)
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val const_trans_table =
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  [(@{type_name Product_Type.prod}, "prod"),
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   (@{type_name Sum_Type.sum}, "sum"),
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   (@{const_name False}, "False"),
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   (@{const_name True}, "True"),
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   (@{const_name Not}, "Not"),
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   (@{const_name conj}, "conj"),
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   (@{const_name disj}, "disj"),
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   (@{const_name implies}, "implies"),
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   (@{const_name HOL.eq}, "equal"),
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   (@{const_name If}, "If"),
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   (@{const_name Set.member}, "member"),
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   (@{const_name Meson.COMBI}, "COMBI"),
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   (@{const_name Meson.COMBK}, "COMBK"),
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   (@{const_name Meson.COMBB}, "COMBB"),
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   (@{const_name Meson.COMBC}, "COMBC"),
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   (@{const_name Meson.COMBS}, "COMBS")]
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  |> Symtab.make
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  |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
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(* Invert the table of translations between Isabelle and ATPs. *)
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val const_trans_table_inv =
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  const_trans_table |> Symtab.dest |> map swap |> Symtab.make
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val const_trans_table_unprox =
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  Symtab.empty
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  |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
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val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
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val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
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fun lookup_const c =
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  case Symtab.lookup const_trans_table c of
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    SOME c' => c'
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  | NONE => ascii_of c
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(*Remove the initial ' character from a type variable, if it is present*)
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fun trim_type_var s =
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  if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
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  else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
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fun ascii_of_indexname (v,0) = ascii_of v
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  | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
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fun make_bound_var x = bound_var_prefix ^ ascii_of x
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fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
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fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
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fun make_schematic_type_var (x,i) =
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      tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
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fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
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(* HOL.eq MUST BE "equal" because it's built into ATPs. *)
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fun make_fixed_const @{const_name HOL.eq} = "equal"
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  | make_fixed_const c = const_prefix ^ lookup_const c
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fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
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fun make_type_class clas = class_prefix ^ ascii_of clas
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fun new_skolem_var_name_from_const s =
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  let val ss = s |> space_explode Long_Name.separator in
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    nth ss (length ss - 2)
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  end
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(* The number of type arguments of a constant, zero if it's monomorphic. For
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   (instances of) Skolem pseudoconstants, this information is encoded in the
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   constant name. *)
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fun num_type_args thy s =
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  if String.isPrefix skolem_const_prefix s then
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    s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
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  else
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    (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
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(* These are either simplified away by "Meson.presimplify" (most of the time) or
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   handled specially via "fFalse", "fTrue", ..., "fequal". *)
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val atp_irrelevant_consts =
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  [@{const_name False}, @{const_name True}, @{const_name Not},
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   @{const_name conj}, @{const_name disj}, @{const_name implies},
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   @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
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val atp_monomorph_bad_consts =
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  atp_irrelevant_consts @
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  (* These are ignored anyway by the relevance filter (unless they appear in
blanchet@43248
   320
     higher-order places) but not by the monomorphizer. *)
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   321
  [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
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   322
   @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
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   323
   @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
blanchet@43248
   324
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   325
fun add_schematic_const (x as (_, T)) =
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   326
  Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
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   327
val add_schematic_consts_of =
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   328
  Term.fold_aterms (fn Const (x as (s, _)) =>
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   329
                       not (member (op =) atp_monomorph_bad_consts s)
blanchet@43258
   330
                       ? add_schematic_const x
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   331
                      | _ => I)
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   332
fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
blanchet@43248
   333
blanchet@43085
   334
(** Definitions and functions for FOL clauses and formulas for TPTP **)
blanchet@43085
   335
blanchet@43085
   336
(* The first component is the type class; the second is a "TVar" or "TFree". *)
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   337
datatype type_literal =
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   338
  TyLitVar of name * name |
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   339
  TyLitFree of name * name
blanchet@43085
   340
blanchet@43085
   341
blanchet@43085
   342
(** Isabelle arities **)
blanchet@43085
   343
blanchet@43085
   344
datatype arity_literal =
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   345
  TConsLit of name * name * name list |
blanchet@43085
   346
  TVarLit of name * name
blanchet@43085
   347
blanchet@43085
   348
fun gen_TVars 0 = []
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   349
  | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
blanchet@43085
   350
blanchet@43263
   351
val type_class = the_single @{sort type}
blanchet@43263
   352
blanchet@43263
   353
fun add_packed_sort tvar =
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   354
  fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
blanchet@43085
   355
blanchet@43086
   356
type arity_clause =
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   357
  {name : string,
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   358
   prem_lits : arity_literal list,
blanchet@43496
   359
   concl_lits : arity_literal}
blanchet@43085
   360
blanchet@43085
   361
(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
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   362
fun make_axiom_arity_clause (tcons, name, (cls, args)) =
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   363
  let
blanchet@43085
   364
    val tvars = gen_TVars (length args)
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   365
    val tvars_srts = ListPair.zip (tvars, args)
blanchet@43085
   366
  in
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   367
    {name = name,
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   368
     prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
blanchet@43086
   369
     concl_lits = TConsLit (`make_type_class cls,
blanchet@43086
   370
                            `make_fixed_type_const tcons,
blanchet@43086
   371
                            tvars ~~ tvars)}
blanchet@43085
   372
  end
blanchet@43085
   373
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   374
fun arity_clause _ _ (_, []) = []
blanchet@43495
   375
  | arity_clause seen n (tcons, ("HOL.type", _) :: ars) =  (* ignore *)
blanchet@43495
   376
    arity_clause seen n (tcons, ars)
blanchet@43495
   377
  | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
blanchet@43495
   378
    if member (op =) seen class then
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   379
      (* multiple arities for the same (tycon, class) pair *)
blanchet@43495
   380
      make_axiom_arity_clause (tcons,
blanchet@43495
   381
          lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
blanchet@43495
   382
          ar) ::
blanchet@43495
   383
      arity_clause seen (n + 1) (tcons, ars)
blanchet@43495
   384
    else
blanchet@43495
   385
      make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
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   386
                               ascii_of class, ar) ::
blanchet@43495
   387
      arity_clause (class :: seen) n (tcons, ars)
blanchet@43085
   388
blanchet@43085
   389
fun multi_arity_clause [] = []
blanchet@43085
   390
  | multi_arity_clause ((tcons, ars) :: tc_arlists) =
blanchet@43085
   391
      arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
blanchet@43085
   392
blanchet@43085
   393
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
blanchet@43085
   394
  provided its arguments have the corresponding sorts.*)
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   395
fun type_class_pairs thy tycons classes =
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   396
  let
blanchet@43093
   397
    val alg = Sign.classes_of thy
blanchet@43093
   398
    fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
blanchet@43093
   399
    fun add_class tycon class =
blanchet@43093
   400
      cons (class, domain_sorts tycon class)
blanchet@43093
   401
      handle Sorts.CLASS_ERROR _ => I
blanchet@43093
   402
    fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
blanchet@43093
   403
  in map try_classes tycons end
blanchet@43085
   404
blanchet@43085
   405
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
blanchet@43085
   406
fun iter_type_class_pairs _ _ [] = ([], [])
blanchet@43085
   407
  | iter_type_class_pairs thy tycons classes =
blanchet@43263
   408
      let
blanchet@43263
   409
        fun maybe_insert_class s =
blanchet@43263
   410
          (s <> type_class andalso not (member (op =) classes s))
blanchet@43263
   411
          ? insert (op =) s
blanchet@43263
   412
        val cpairs = type_class_pairs thy tycons classes
blanchet@43263
   413
        val newclasses =
blanchet@43263
   414
          [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
blanchet@43263
   415
        val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
blanchet@43266
   416
      in (classes' @ classes, union (op =) cpairs' cpairs) end
blanchet@43085
   417
blanchet@43085
   418
fun make_arity_clauses thy tycons =
blanchet@43085
   419
  iter_type_class_pairs thy tycons ##> multi_arity_clause
blanchet@43085
   420
blanchet@43085
   421
blanchet@43085
   422
(** Isabelle class relations **)
blanchet@43085
   423
blanchet@43086
   424
type class_rel_clause =
blanchet@43496
   425
  {name : string,
blanchet@43496
   426
   subclass : name,
blanchet@43496
   427
   superclass : name}
blanchet@43085
   428
blanchet@43085
   429
(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
blanchet@43085
   430
fun class_pairs _ [] _ = []
blanchet@43085
   431
  | class_pairs thy subs supers =
blanchet@43085
   432
      let
blanchet@43085
   433
        val class_less = Sorts.class_less (Sign.classes_of thy)
blanchet@43085
   434
        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
blanchet@43085
   435
        fun add_supers sub = fold (add_super sub) supers
blanchet@43085
   436
      in fold add_supers subs [] end
blanchet@43085
   437
blanchet@43085
   438
fun make_class_rel_clause (sub,super) =
blanchet@43086
   439
  {name = sub ^ "_" ^ super,
blanchet@43086
   440
   subclass = `make_type_class sub,
blanchet@43086
   441
   superclass = `make_type_class super}
blanchet@43085
   442
blanchet@43085
   443
fun make_class_rel_clauses thy subs supers =
blanchet@43093
   444
  map make_class_rel_clause (class_pairs thy subs supers)
blanchet@43085
   445
blanchet@43085
   446
datatype combterm =
blanchet@43085
   447
  CombConst of name * typ * typ list |
blanchet@43085
   448
  CombVar of name * typ |
blanchet@43085
   449
  CombApp of combterm * combterm
blanchet@43085
   450
blanchet@43085
   451
fun combtyp_of (CombConst (_, T, _)) = T
blanchet@43085
   452
  | combtyp_of (CombVar (_, T)) = T
blanchet@43085
   453
  | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
blanchet@43085
   454
blanchet@43085
   455
(*gets the head of a combinator application, along with the list of arguments*)
blanchet@43085
   456
fun strip_combterm_comb u =
blanchet@43496
   457
  let
blanchet@43496
   458
    fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
blanchet@43496
   459
      | stripc x = x
blanchet@43496
   460
  in stripc (u, []) end
blanchet@43085
   461
blanchet@43085
   462
fun atyps_of T = fold_atyps (insert (op =)) T []
blanchet@43085
   463
blanchet@43085
   464
fun new_skolem_const_name s num_T_args =
blanchet@43085
   465
  [new_skolem_const_prefix, s, string_of_int num_T_args]
blanchet@43085
   466
  |> space_implode Long_Name.separator
blanchet@43085
   467
blanchet@43085
   468
(* Converts a term (with combinators) into a combterm. Also accumulates sort
blanchet@43085
   469
   infomation. *)
blanchet@43085
   470
fun combterm_from_term thy bs (P $ Q) =
blanchet@43085
   471
    let
blanchet@43085
   472
      val (P', P_atomics_Ts) = combterm_from_term thy bs P
blanchet@43085
   473
      val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
blanchet@43085
   474
    in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
blanchet@43085
   475
  | combterm_from_term thy _ (Const (c, T)) =
blanchet@43085
   476
    let
blanchet@43085
   477
      val tvar_list =
blanchet@43085
   478
        (if String.isPrefix old_skolem_const_prefix c then
blanchet@43085
   479
           [] |> Term.add_tvarsT T |> map TVar
blanchet@43085
   480
         else
blanchet@43085
   481
           (c, T) |> Sign.const_typargs thy)
blanchet@43085
   482
      val c' = CombConst (`make_fixed_const c, T, tvar_list)
blanchet@43085
   483
    in (c', atyps_of T) end
blanchet@43085
   484
  | combterm_from_term _ _ (Free (v, T)) =
blanchet@43085
   485
    (CombConst (`make_fixed_var v, T, []), atyps_of T)
blanchet@43085
   486
  | combterm_from_term _ _ (Var (v as (s, _), T)) =
blanchet@43085
   487
    (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
blanchet@43085
   488
       let
blanchet@43085
   489
         val Ts = T |> strip_type |> swap |> op ::
blanchet@43085
   490
         val s' = new_skolem_const_name s (length Ts)
blanchet@43085
   491
       in CombConst (`make_fixed_const s', T, Ts) end
blanchet@43085
   492
     else
blanchet@43085
   493
       CombVar ((make_schematic_var v, s), T), atyps_of T)
blanchet@43085
   494
  | combterm_from_term _ bs (Bound j) =
blanchet@43085
   495
    nth bs j
blanchet@43085
   496
    |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
blanchet@43085
   497
  | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
blanchet@43085
   498
blanchet@43421
   499
datatype locality =
blanchet@43421
   500
  General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
blanchet@43421
   501
  Chained
blanchet@43085
   502
blanchet@43085
   503
(* (quasi-)underapproximation of the truth *)
blanchet@43085
   504
fun is_locality_global Local = false
blanchet@43085
   505
  | is_locality_global Assum = false
blanchet@43085
   506
  | is_locality_global Chained = false
blanchet@43085
   507
  | is_locality_global _ = true
blanchet@43085
   508
blanchet@42613
   509
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
   510
datatype type_level =
blanchet@43362
   511
  All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
blanchet@43362
   512
  No_Types
blanchet@43128
   513
datatype type_heaviness = Heavyweight | Lightweight
blanchet@42613
   514
blanchet@43102
   515
datatype type_sys =
blanchet@42722
   516
  Simple_Types of type_level |
blanchet@42837
   517
  Preds of polymorphism * type_level * type_heaviness |
blanchet@42837
   518
  Tags of polymorphism * type_level * type_heaviness
blanchet@42613
   519
blanchet@42689
   520
fun try_unsuffixes ss s =
blanchet@42689
   521
  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
blanchet@42689
   522
blanchet@42613
   523
fun type_sys_from_string s =
blanchet@42722
   524
  (case try (unprefix "poly_") s of
blanchet@42722
   525
     SOME s => (SOME Polymorphic, s)
blanchet@42613
   526
   | NONE =>
blanchet@42613
   527
     case try (unprefix "mono_") s of
blanchet@42722
   528
       SOME s => (SOME Monomorphic, s)
blanchet@42722
   529
     | NONE =>
blanchet@42722
   530
       case try (unprefix "mangled_") s of
blanchet@42722
   531
         SOME s => (SOME Mangled_Monomorphic, s)
blanchet@42722
   532
       | NONE => (NONE, s))
blanchet@42613
   533
  ||> (fn s =>
blanchet@42689
   534
          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
blanchet@42689
   535
          case try_unsuffixes ["?", "_query"] s of
blanchet@43362
   536
            SOME s => (Noninf_Nonmono_Types, s)
blanchet@42613
   537
          | NONE =>
blanchet@42689
   538
            case try_unsuffixes ["!", "_bang"] s of
blanchet@43362
   539
              SOME s => (Fin_Nonmono_Types, s)
blanchet@42613
   540
            | NONE => (All_Types, s))
blanchet@42828
   541
  ||> apsnd (fn s =>
blanchet@42837
   542
                case try (unsuffix "_heavy") s of
blanchet@43128
   543
                  SOME s => (Heavyweight, s)
blanchet@43128
   544
                | NONE => (Lightweight, s))
blanchet@42837
   545
  |> (fn (poly, (level, (heaviness, core))) =>
blanchet@42837
   546
         case (core, (poly, level, heaviness)) of
blanchet@43128
   547
           ("simple", (NONE, _, Lightweight)) => Simple_Types level
blanchet@42854
   548
         | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
blanchet@42886
   549
         | ("tags", (SOME Polymorphic, _, _)) =>
blanchet@43361
   550
           Tags (Polymorphic, level, heaviness)
blanchet@42854
   551
         | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
blanchet@43128
   552
         | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
blanchet@43128
   553
           Preds (poly, Const_Arg_Types, Lightweight)
blanchet@43128
   554
         | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
blanchet@43128
   555
           Preds (Polymorphic, No_Types, Lightweight)
blanchet@42753
   556
         | _ => raise Same.SAME)
blanchet@42753
   557
  handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
blanchet@42613
   558
blanchet@42722
   559
fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
blanchet@42828
   560
  | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
blanchet@42828
   561
  | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
blanchet@42613
   562
blanchet@42722
   563
fun level_of_type_sys (Simple_Types level) = level
blanchet@42828
   564
  | level_of_type_sys (Preds (_, level, _)) = level
blanchet@42828
   565
  | level_of_type_sys (Tags (_, level, _)) = level
blanchet@42828
   566
blanchet@43128
   567
fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
blanchet@42837
   568
  | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
blanchet@42837
   569
  | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
blanchet@42831
   570
blanchet@42687
   571
fun is_type_level_virtually_sound level =
blanchet@43362
   572
  level = All_Types orelse level = Noninf_Nonmono_Types
blanchet@42613
   573
val is_type_sys_virtually_sound =
blanchet@42613
   574
  is_type_level_virtually_sound o level_of_type_sys
blanchet@42613
   575
blanchet@42613
   576
fun is_type_level_fairly_sound level =
blanchet@43362
   577
  is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
blanchet@42613
   578
val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
blanchet@42613
   579
blanchet@42994
   580
fun is_setting_higher_order THF (Simple_Types _) = true
blanchet@42994
   581
  | is_setting_higher_order _ _ = false
blanchet@42994
   582
blanchet@43101
   583
fun choose_format formats (Simple_Types level) =
blanchet@43101
   584
    if member (op =) formats THF then (THF, Simple_Types level)
blanchet@43101
   585
    else if member (op =) formats TFF then (TFF, Simple_Types level)
blanchet@43128
   586
    else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
blanchet@43101
   587
  | choose_format formats type_sys =
blanchet@43101
   588
    (case hd formats of
blanchet@43101
   589
       CNF_UEQ =>
blanchet@43101
   590
       (CNF_UEQ, case type_sys of
blanchet@43101
   591
                   Preds stuff =>
blanchet@43289
   592
                   (if is_type_sys_fairly_sound type_sys then Tags else Preds)
blanchet@43101
   593
                       stuff
blanchet@43101
   594
                 | _ => type_sys)
blanchet@43101
   595
     | format => (format, type_sys))
blanchet@43101
   596
blanchet@40114
   597
type translated_formula =
blanchet@43496
   598
  {name : string,
blanchet@43496
   599
   locality : locality,
blanchet@43496
   600
   kind : formula_kind,
blanchet@43496
   601
   combformula : (name, typ, combterm) formula,
blanchet@43496
   602
   atomic_types : typ list}
blanchet@38282
   603
blanchet@42640
   604
fun update_combformula f ({name, locality, kind, combformula, atomic_types}
blanchet@42640
   605
                          : translated_formula) =
blanchet@42640
   606
  {name = name, locality = locality, kind = kind, combformula = f combformula,
blanchet@42562
   607
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   608
blanchet@42558
   609
fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
blanchet@42558
   610
blanchet@43064
   611
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@43064
   612
blanchet@43064
   613
fun insert_type ctxt get_T x xs =
blanchet@43064
   614
  let val T = get_T x in
blanchet@43064
   615
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@43064
   616
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@43064
   617
  end
blanchet@42677
   618
blanchet@42753
   619
(* The Booleans indicate whether all type arguments should be kept. *)
blanchet@42753
   620
datatype type_arg_policy =
blanchet@42753
   621
  Explicit_Type_Args of bool |
blanchet@42753
   622
  Mangled_Type_Args of bool |
blanchet@42753
   623
  No_Type_Args
blanchet@41136
   624
blanchet@42836
   625
fun should_drop_arg_type_args (Simple_Types _) =
blanchet@42836
   626
    false (* since TFF doesn't support overloading *)
blanchet@42836
   627
  | should_drop_arg_type_args type_sys =
blanchet@42836
   628
    level_of_type_sys type_sys = All_Types andalso
blanchet@43128
   629
    heaviness_of_type_sys type_sys = Heavyweight
blanchet@42831
   630
blanchet@43128
   631
fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
blanchet@43105
   632
  | general_type_arg_policy type_sys =
blanchet@43105
   633
    if level_of_type_sys type_sys = No_Types then
blanchet@43105
   634
      No_Type_Args
blanchet@43105
   635
    else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
blanchet@43105
   636
      Mangled_Type_Args (should_drop_arg_type_args type_sys)
blanchet@43105
   637
    else
blanchet@43105
   638
      Explicit_Type_Args (should_drop_arg_type_args type_sys)
blanchet@42563
   639
blanchet@42951
   640
fun type_arg_policy type_sys s =
blanchet@42951
   641
  if s = @{const_name HOL.eq} orelse
blanchet@42966
   642
     (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
blanchet@42951
   643
    No_Type_Args
blanchet@43105
   644
  else if s = type_tag_name then
blanchet@43105
   645
    Explicit_Type_Args false
blanchet@42951
   646
  else
blanchet@42951
   647
    general_type_arg_policy type_sys
blanchet@42227
   648
blanchet@43085
   649
(*Make literals for sorted type variables*)
blanchet@43263
   650
fun generic_add_sorts_on_type (_, []) = I
blanchet@43263
   651
  | generic_add_sorts_on_type ((x, i), s :: ss) =
blanchet@43263
   652
    generic_add_sorts_on_type ((x, i), ss)
blanchet@43263
   653
    #> (if s = the_single @{sort HOL.type} then
blanchet@43093
   654
          I
blanchet@43093
   655
        else if i = ~1 then
blanchet@43263
   656
          insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
blanchet@43093
   657
        else
blanchet@43263
   658
          insert (op =) (TyLitVar (`make_type_class s,
blanchet@43263
   659
                                   (make_schematic_type_var (x, i), x))))
blanchet@43263
   660
fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
blanchet@43263
   661
  | add_sorts_on_tfree _ = I
blanchet@43263
   662
fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
blanchet@43263
   663
  | add_sorts_on_tvar _ = I
blanchet@43085
   664
blanchet@43263
   665
fun type_literals_for_types type_sys add_sorts_on_typ Ts =
blanchet@43263
   666
  [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
blanchet@41137
   667
blanchet@42534
   668
fun mk_aconns c phis =
blanchet@42534
   669
  let val (phis', phi') = split_last phis in
blanchet@42534
   670
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   671
  end
blanchet@38282
   672
fun mk_ahorn [] phi = phi
blanchet@42534
   673
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   674
fun mk_aquant _ [] phi = phi
blanchet@42522
   675
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   676
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   677
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   678
blanchet@42522
   679
fun close_universally atom_vars phi =
blanchet@41145
   680
  let
blanchet@41145
   681
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   682
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   683
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   684
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   685
        union (op =) (atom_vars tm []
blanchet@42526
   686
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   687
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   688
blanchet@42531
   689
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
blanchet@42522
   690
  | combterm_vars (CombConst _) = I
blanchet@42574
   691
  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
blanchet@42674
   692
fun close_combformula_universally phi = close_universally combterm_vars phi
blanchet@42522
   693
blanchet@42522
   694
fun term_vars (ATerm (name as (s, _), tms)) =
blanchet@42998
   695
  is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
blanchet@42674
   696
fun close_formula_universally phi = close_universally term_vars phi
blanchet@41145
   697
blanchet@42994
   698
val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
blanchet@42994
   699
val homo_infinite_type = Type (homo_infinite_type_name, [])
blanchet@42994
   700
blanchet@43178
   701
fun fo_term_from_typ format type_sys =
blanchet@42994
   702
  let
blanchet@42994
   703
    fun term (Type (s, Ts)) =
blanchet@43178
   704
      ATerm (case (is_setting_higher_order format type_sys, s) of
blanchet@42994
   705
               (true, @{type_name bool}) => `I tptp_bool_type
blanchet@42994
   706
             | (true, @{type_name fun}) => `I tptp_fun_type
blanchet@43178
   707
             | _ => if s = homo_infinite_type_name andalso
blanchet@43178
   708
                       (format = TFF orelse format = THF) then
blanchet@43178
   709
                      `I tptp_individual_type
blanchet@43178
   710
                    else
blanchet@43178
   711
                      `make_fixed_type_const s,
blanchet@42994
   712
             map term Ts)
blanchet@42994
   713
    | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
blanchet@42994
   714
    | term (TVar ((x as (s, _)), _)) =
blanchet@42994
   715
      ATerm ((make_schematic_type_var x, s), [])
blanchet@42994
   716
  in term end
blanchet@42562
   717
blanchet@43401
   718
fun fo_term_for_type_arg format type_sys T =
blanchet@43401
   719
  if T = dummyT then NONE else SOME (fo_term_from_typ format type_sys T)
blanchet@43401
   720
blanchet@42562
   721
(* This shouldn't clash with anything else. *)
blanchet@42542
   722
val mangled_type_sep = "\000"
blanchet@42542
   723
blanchet@42562
   724
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   725
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42761
   726
    f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
blanchet@42761
   727
    ^ ")"
blanchet@42542
   728
blanchet@42998
   729
val bool_atype = AType (`I tptp_bool_type)
blanchet@42998
   730
blanchet@43085
   731
fun make_simple_type s =
blanchet@43085
   732
  if s = tptp_bool_type orelse s = tptp_fun_type orelse
blanchet@43085
   733
     s = tptp_individual_type then
blanchet@43085
   734
    s
blanchet@43085
   735
  else
blanchet@43085
   736
    simple_type_prefix ^ ascii_of s
blanchet@43085
   737
blanchet@43178
   738
fun ho_type_from_fo_term format type_sys pred_sym ary =
blanchet@42963
   739
  let
blanchet@42963
   740
    fun to_atype ty =
blanchet@42963
   741
      AType ((make_simple_type (generic_mangled_type_name fst ty),
blanchet@42963
   742
              generic_mangled_type_name snd ty))
blanchet@42963
   743
    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
blanchet@42998
   744
    fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
blanchet@42994
   745
      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
blanchet@42994
   746
    fun to_ho (ty as ATerm ((s, _), tys)) =
blanchet@42994
   747
      if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
blanchet@43178
   748
  in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
blanchet@42963
   749
blanchet@43178
   750
fun mangled_type format type_sys pred_sym ary =
blanchet@43178
   751
  ho_type_from_fo_term format type_sys pred_sym ary
blanchet@43178
   752
  o fo_term_from_typ format type_sys
blanchet@42963
   753
blanchet@43178
   754
fun mangled_const_name format type_sys T_args (s, s') =
blanchet@42963
   755
  let
blanchet@43401
   756
    val ty_args = T_args |> map_filter (fo_term_for_type_arg format type_sys)
blanchet@42963
   757
    fun type_suffix f g =
blanchet@42963
   758
      fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42963
   759
                o generic_mangled_type_name f) ty_args ""
blanchet@42963
   760
  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@42542
   761
blanchet@42542
   762
val parse_mangled_ident =
blanchet@42542
   763
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   764
blanchet@42542
   765
fun parse_mangled_type x =
blanchet@42542
   766
  (parse_mangled_ident
blanchet@42542
   767
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   768
                    [] >> ATerm) x
blanchet@42542
   769
and parse_mangled_types x =
blanchet@42542
   770
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   771
blanchet@42542
   772
fun unmangled_type s =
blanchet@42542
   773
  s |> suffix ")" |> raw_explode
blanchet@42542
   774
    |> Scan.finite Symbol.stopper
blanchet@42542
   775
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   776
                                                quote s)) parse_mangled_type))
blanchet@42542
   777
    |> fst
blanchet@42542
   778
blanchet@42561
   779
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   780
fun unmangled_const s =
blanchet@42542
   781
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   782
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   783
  end
blanchet@42542
   784
blanchet@43017
   785
fun introduce_proxies format type_sys =
blanchet@42568
   786
  let
blanchet@43017
   787
    fun intro top_level (CombApp (tm1, tm2)) =
blanchet@43017
   788
        CombApp (intro top_level tm1, intro false tm2)
blanchet@43017
   789
      | intro top_level (CombConst (name as (s, _), T, T_args)) =
blanchet@42570
   790
        (case proxify_const s of
blanchet@43159
   791
           SOME proxy_base =>
blanchet@43000
   792
           if top_level orelse is_setting_higher_order format type_sys then
blanchet@43000
   793
             case (top_level, s) of
blanchet@43000
   794
               (_, "c_False") => (`I tptp_false, [])
blanchet@43000
   795
             | (_, "c_True") => (`I tptp_true, [])
blanchet@43000
   796
             | (false, "c_Not") => (`I tptp_not, [])
blanchet@43000
   797
             | (false, "c_conj") => (`I tptp_and, [])
blanchet@43000
   798
             | (false, "c_disj") => (`I tptp_or, [])
blanchet@43000
   799
             | (false, "c_implies") => (`I tptp_implies, [])
blanchet@43000
   800
             | (false, s) =>
blanchet@43017
   801
               if is_tptp_equal s then (`I tptp_equal, [])
blanchet@43017
   802
               else (proxy_base |>> prefix const_prefix, T_args)
blanchet@43000
   803
             | _ => (name, [])
blanchet@42569
   804
           else
blanchet@42574
   805
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   806
          | NONE => (name, T_args))
blanchet@42574
   807
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@43017
   808
      | intro _ tm = tm
blanchet@43017
   809
  in intro true end
blanchet@42568
   810
blanchet@42994
   811
fun combformula_from_prop thy format type_sys eq_as_iff =
blanchet@38282
   812
  let
blanchet@42568
   813
    fun do_term bs t atomic_types =
blanchet@41140
   814
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42994
   815
      |>> (introduce_proxies format type_sys #> AAtom)
blanchet@42568
   816
      ||> union (op =) atomic_types
blanchet@38282
   817
    fun do_quant bs q s T t' =
wenzelm@43324
   818
      let val s = singleton (Name.variant_list (map fst bs)) s in
blanchet@38518
   819
        do_formula ((s, T) :: bs) t'
blanchet@42562
   820
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   821
      end
blanchet@38282
   822
    and do_conn bs c t1 t2 =
blanchet@43198
   823
      do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
blanchet@38282
   824
    and do_formula bs t =
blanchet@38282
   825
      case t of
blanchet@43096
   826
        @{const Trueprop} $ t1 => do_formula bs t1
blanchet@43096
   827
      | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   828
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   829
        do_quant bs AForall s T t'
blanchet@38282
   830
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   831
        do_quant bs AExists s T t'
haftmann@38795
   832
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   833
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   834
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   835
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   836
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   837
      | _ => do_term bs t
blanchet@38282
   838
  in do_formula [] end
blanchet@38282
   839
blanchet@43264
   840
fun presimplify_term _ [] t = t
blanchet@43264
   841
  | presimplify_term ctxt presimp_consts t =
blanchet@43264
   842
    t |> exists_Const (member (op =) presimp_consts o fst) t
blanchet@43264
   843
         ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@43264
   844
            #> Meson.presimplify ctxt
blanchet@43264
   845
            #> prop_of)
blanchet@38282
   846
wenzelm@41491
   847
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   848
fun conceal_bounds Ts t =
blanchet@38282
   849
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   850
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   851
fun reveal_bounds Ts =
blanchet@38282
   852
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   853
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   854
blanchet@43265
   855
fun is_fun_equality (@{const_name HOL.eq},
blanchet@43265
   856
                     Type (_, [Type (@{type_name fun}, _), _])) = true
blanchet@43265
   857
  | is_fun_equality _ = false
blanchet@43265
   858
blanchet@42747
   859
fun extensionalize_term ctxt t =
blanchet@43265
   860
  if exists_Const is_fun_equality t then
blanchet@43265
   861
    let val thy = Proof_Context.theory_of ctxt in
blanchet@43265
   862
      t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@43265
   863
        |> prop_of |> Logic.dest_equals |> snd
blanchet@43265
   864
    end
blanchet@43265
   865
  else
blanchet@43265
   866
    t
blanchet@38608
   867
blanchet@38282
   868
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   869
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   870
    if Meson.is_fol_term thy t then
blanchet@38491
   871
      t
blanchet@38491
   872
    else
blanchet@38491
   873
      let
blanchet@38491
   874
        fun aux Ts t =
blanchet@38491
   875
          case t of
blanchet@38491
   876
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   877
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   878
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   879
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   880
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   881
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   882
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   883
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   884
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   885
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   886
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   887
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   888
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   889
              $ t1 $ t2 =>
blanchet@38491
   890
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   891
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   892
                   t
blanchet@38491
   893
                 else
blanchet@38491
   894
                   t |> conceal_bounds Ts
blanchet@38491
   895
                     |> Envir.eta_contract
blanchet@38491
   896
                     |> cterm_of thy
blanchet@39890
   897
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   898
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   899
                     |> reveal_bounds Ts
blanchet@39370
   900
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   901
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   902
      handle THM _ =>
blanchet@38491
   903
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   904
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   905
             else HOLogic.true_const
blanchet@38491
   906
  end
blanchet@38282
   907
blanchet@38282
   908
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   909
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   910
fun freeze_term t =
blanchet@38282
   911
  let
blanchet@38282
   912
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   913
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   914
      | aux (Var ((s, i), T)) =
blanchet@38282
   915
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   916
      | aux t = t
blanchet@38282
   917
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   918
blanchet@43264
   919
fun preprocess_prop ctxt presimp_consts kind t =
blanchet@38282
   920
  let
wenzelm@42361
   921
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   922
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   923
              |> transform_elim_prop
blanchet@41211
   924
              |> Object_Logic.atomize_term thy
blanchet@42563
   925
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@43096
   926
  in
blanchet@43096
   927
    t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@43096
   928
      |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
blanchet@43096
   929
      |> extensionalize_term ctxt
blanchet@43264
   930
      |> presimplify_term ctxt presimp_consts
blanchet@43120
   931
      |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@43096
   932
      |> introduce_combinators_in_term ctxt kind
blanchet@43096
   933
  end
blanchet@43096
   934
blanchet@43096
   935
(* making fact and conjecture formulas *)
blanchet@43096
   936
fun make_formula thy format type_sys eq_as_iff name loc kind t =
blanchet@43096
   937
  let
blanchet@42962
   938
    val (combformula, atomic_types) =
blanchet@42994
   939
      combformula_from_prop thy format type_sys eq_as_iff t []
blanchet@38282
   940
  in
blanchet@42640
   941
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   942
     atomic_types = atomic_types}
blanchet@38282
   943
  end
blanchet@38282
   944
blanchet@43295
   945
fun make_fact ctxt format type_sys eq_as_iff preproc presimp_consts
blanchet@42994
   946
              ((name, loc), t) =
blanchet@43096
   947
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43295
   948
    case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
blanchet@43295
   949
           |> make_formula thy format type_sys (eq_as_iff andalso format <> CNF)
blanchet@43295
   950
                           name loc Axiom of
blanchet@43295
   951
      formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
blanchet@43096
   952
      if s = tptp_true then NONE else SOME formula
blanchet@43295
   953
    | formula => SOME formula
blanchet@43096
   954
  end
blanchet@42561
   955
blanchet@43264
   956
fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
blanchet@43096
   957
  let
blanchet@43096
   958
    val thy = Proof_Context.theory_of ctxt
blanchet@43096
   959
    val last = length ts - 1
blanchet@43096
   960
  in
blanchet@42709
   961
    map2 (fn j => fn t =>
blanchet@42709
   962
             let
blanchet@42709
   963
               val (kind, maybe_negate) =
blanchet@42709
   964
                 if j = last then
blanchet@42709
   965
                   (Conjecture, I)
blanchet@42709
   966
                 else
blanchet@42709
   967
                   (prem_kind,
blanchet@42709
   968
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   969
                    else I)
blanchet@42709
   970
              in
blanchet@43264
   971
                t |> preproc ?
blanchet@43264
   972
                     (preprocess_prop ctxt presimp_consts kind #> freeze_term)
blanchet@43193
   973
                  |> make_formula thy format type_sys (format <> CNF)
blanchet@43293
   974
                                  (string_of_int j) Local kind
blanchet@42962
   975
                  |> maybe_negate
blanchet@42709
   976
              end)
blanchet@38613
   977
         (0 upto last) ts
blanchet@38613
   978
  end
blanchet@38282
   979
blanchet@42682
   980
(** Finite and infinite type inference **)
blanchet@42682
   981
blanchet@42886
   982
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   983
  | deep_freeze_atyp T = T
blanchet@42886
   984
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   985
blanchet@42682
   986
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   987
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   988
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   989
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   990
blanchet@42886
   991
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   992
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   993
  | should_encode_type _ _ All_Types _ = true
blanchet@43572
   994
  | should_encode_type ctxt _ Fin_Nonmono_Types T =
blanchet@43572
   995
    is_type_surely_finite ctxt false T
blanchet@42682
   996
  | should_encode_type _ _ _ _ = false
blanchet@42682
   997
blanchet@42837
   998
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   999
                             should_predicate_on_var T =
blanchet@43128
  1000
    (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
blanchet@42878
  1001
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
  1002
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
  1003
blanchet@42836
  1004
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
  1005
    String.isPrefix bound_var_prefix s
blanchet@42836
  1006
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
  1007
  | is_var_or_bound_var _ = false
blanchet@42836
  1008
blanchet@43361
  1009
datatype tag_site =
blanchet@43361
  1010
  Top_Level of bool option |
blanchet@43361
  1011
  Eq_Arg of bool option |
blanchet@43361
  1012
  Elsewhere
blanchet@42829
  1013
blanchet@43361
  1014
fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
blanchet@43361
  1015
  | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
blanchet@43361
  1016
                         u T =
blanchet@42837
  1017
    (case heaviness of
blanchet@43128
  1018
       Heavyweight => should_encode_type ctxt nonmono_Ts level T
blanchet@43128
  1019
     | Lightweight =>
blanchet@42836
  1020
       case (site, is_var_or_bound_var u) of
blanchet@43361
  1021
         (Eq_Arg pos, true) =>
blanchet@43361
  1022
         (* The first disjunct prevents a subtle soundness issue explained in
blanchet@43361
  1023
            Blanchette's Ph.D. thesis. See also
blanchet@43361
  1024
            "formula_lines_for_lightweight_tags_sym_decl". *)
blanchet@43361
  1025
         (pos <> SOME false andalso poly = Polymorphic andalso
blanchet@43361
  1026
          level <> All_Types andalso heaviness = Lightweight andalso
blanchet@43361
  1027
          exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
blanchet@43361
  1028
         should_encode_type ctxt nonmono_Ts level T
blanchet@42829
  1029
       | _ => false)
blanchet@42829
  1030
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
  1031
blanchet@42994
  1032
fun homogenized_type ctxt nonmono_Ts level =
blanchet@42994
  1033
  let
blanchet@42994
  1034
    val should_encode = should_encode_type ctxt nonmono_Ts level
blanchet@42994
  1035
    fun homo 0 T = if should_encode T then T else homo_infinite_type
blanchet@42994
  1036
      | homo ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@42994
  1037
        homo 0 T1 --> homo (ary - 1) T2
blanchet@42994
  1038
      | homo _ _ = raise Fail "expected function type"
blanchet@42994
  1039
  in homo end
blanchet@42682
  1040
blanchet@42573
  1041
(** "hBOOL" and "hAPP" **)
blanchet@41313
  1042
blanchet@42574
  1043
type sym_info =
blanchet@43064
  1044
  {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
blanchet@42563
  1045
blanchet@43064
  1046
fun add_combterm_syms_to_table ctxt explicit_apply =
blanchet@42558
  1047
  let
blanchet@43064
  1048
    fun consider_var_arity const_T var_T max_ary =
blanchet@43064
  1049
      let
blanchet@43064
  1050
        fun iter ary T =
blanchet@43210
  1051
          if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
blanchet@43210
  1052
             type_instance ctxt (T, var_T) then
blanchet@43210
  1053
            ary
blanchet@43210
  1054
          else
blanchet@43210
  1055
            iter (ary + 1) (range_type T)
blanchet@43064
  1056
      in iter 0 const_T end
blanchet@43201
  1057
    fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@43201
  1058
      if explicit_apply = NONE andalso
blanchet@43201
  1059
         (can dest_funT T orelse T = @{typ bool}) then
blanchet@43201
  1060
        let
blanchet@43201
  1061
          val bool_vars' = bool_vars orelse body_type T = @{typ bool}
blanchet@43201
  1062
          fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
blanchet@43201
  1063
            {pred_sym = pred_sym andalso not bool_vars',
blanchet@43213
  1064
             min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
blanchet@43201
  1065
             max_ary = max_ary, types = types}
blanchet@43201
  1066
          val fun_var_Ts' =
blanchet@43201
  1067
            fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
blanchet@43201
  1068
        in
blanchet@43201
  1069
          if bool_vars' = bool_vars andalso
blanchet@43201
  1070
             pointer_eq (fun_var_Ts', fun_var_Ts) then
blanchet@43201
  1071
            accum
blanchet@43167
  1072
          else
blanchet@43213
  1073
            ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
blanchet@43201
  1074
        end
blanchet@43201
  1075
      else
blanchet@43201
  1076
        accum
blanchet@43201
  1077
    fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@43201
  1078
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
  1079
        (case head of
blanchet@42563
  1080
           CombConst ((s, _), T, _) =>
blanchet@42558
  1081
           if String.isPrefix bound_var_prefix s then
blanchet@43201
  1082
             add_var_or_bound_var T accum
blanchet@42558
  1083
           else
blanchet@43139
  1084
             let val ary = length args in
blanchet@43201
  1085
               ((bool_vars, fun_var_Ts),
blanchet@43064
  1086
                case Symtab.lookup sym_tab s of
blanchet@43064
  1087
                  SOME {pred_sym, min_ary, max_ary, types} =>
blanchet@43064
  1088
                  let
blanchet@43201
  1089
                    val pred_sym =
blanchet@43201
  1090
                      pred_sym andalso top_level andalso not bool_vars
blanchet@43064
  1091
                    val types' = types |> insert_type ctxt I T
blanchet@43064
  1092
                    val min_ary =
blanchet@43064
  1093
                      if is_some explicit_apply orelse
blanchet@43064
  1094
                         pointer_eq (types', types) then
blanchet@43064
  1095
                        min_ary
blanchet@43064
  1096
                      else
blanchet@43201
  1097
                        fold (consider_var_arity T) fun_var_Ts min_ary
blanchet@43064
  1098
                  in
blanchet@43201
  1099
                    Symtab.update (s, {pred_sym = pred_sym,
blanchet@43064
  1100
                                       min_ary = Int.min (ary, min_ary),
blanchet@43064
  1101
                                       max_ary = Int.max (ary, max_ary),
blanchet@43064
  1102
                                       types = types'})
blanchet@43064
  1103
                                  sym_tab
blanchet@43064
  1104
                  end
blanchet@43064
  1105
                | NONE =>
blanchet@43064
  1106
                  let
blanchet@43201
  1107
                    val pred_sym = top_level andalso not bool_vars
blanchet@43064
  1108
                    val min_ary =
blanchet@43064
  1109
                      case explicit_apply of
blanchet@43064
  1110
                        SOME true => 0
blanchet@43064
  1111
                      | SOME false => ary
blanchet@43201
  1112
                      | NONE => fold (consider_var_arity T) fun_var_Ts ary
blanchet@43064
  1113
                  in
blanchet@43201
  1114
                    Symtab.update_new (s, {pred_sym = pred_sym,
blanchet@43064
  1115
                                           min_ary = min_ary, max_ary = ary,
blanchet@43064
  1116
                                           types = [T]})
blanchet@43064
  1117
                                      sym_tab
blanchet@43064
  1118
                  end)
blanchet@43064
  1119
             end
blanchet@43201
  1120
         | CombVar (_, T) => add_var_or_bound_var T accum
blanchet@43064
  1121
         | _ => accum)
blanchet@43064
  1122
        |> fold (add false) args
blanchet@42558
  1123
      end
blanchet@43064
  1124
  in add true end
blanchet@43064
  1125
fun add_fact_syms_to_table ctxt explicit_apply =
blanchet@43064
  1126
  fact_lift (formula_fold NONE
blanchet@43064
  1127
                          (K (add_combterm_syms_to_table ctxt explicit_apply)))
blanchet@38282
  1128
blanchet@43139
  1129
val default_sym_tab_entries : (string * sym_info) list =
blanchet@43174
  1130
  (prefixed_predicator_name,
blanchet@43139
  1131
   {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
blanchet@42568
  1132
  ([tptp_false, tptp_true]
blanchet@43139
  1133
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
blanchet@43139
  1134
  ([tptp_equal, tptp_old_equal]
blanchet@43139
  1135
   |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
blanchet@41140
  1136
blanchet@43064
  1137
fun sym_table_for_facts ctxt explicit_apply facts =
blanchet@43201
  1138
  ((false, []), Symtab.empty)
blanchet@43201
  1139
  |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
blanchet@43139
  1140
  |> fold Symtab.update default_sym_tab_entries
blanchet@38282
  1141
blanchet@42558
  1142
fun min_arity_of sym_tab s =
blanchet@42558
  1143
  case Symtab.lookup sym_tab s of
blanchet@42574
  1144
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
  1145
  | NONE =>
blanchet@42558
  1146
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
  1147
      SOME s =>
blanchet@42570
  1148
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
  1149
        if s = predicator_name then 1
blanchet@42966
  1150
        else if s = app_op_name then 2
blanchet@42966
  1151
        else if s = type_pred_name then 1
blanchet@42557
  1152
        else 0
blanchet@42547
  1153
      end
blanchet@42544
  1154
    | NONE => 0
blanchet@38282
  1155
blanchet@38282
  1156
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
  1157
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
  1158
   type instantiations). If false, the constant always receives all of its
blanchet@38282
  1159
   arguments and is used as a predicate. *)
blanchet@42558
  1160
fun is_pred_sym sym_tab s =
blanchet@42558
  1161
  case Symtab.lookup sym_tab s of
blanchet@42574
  1162
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
  1163
    pred_sym andalso min_ary = max_ary
blanchet@42558
  1164
  | NONE => false
blanchet@38282
  1165
blanchet@42568
  1166
val predicator_combconst =
blanchet@42966
  1167
  CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
blanchet@42568
  1168
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
  1169
blanchet@42568
  1170
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
  1171
  case strip_combterm_comb tm of
blanchet@42542
  1172
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
  1173
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
  1174
  | _ => predicator tm
blanchet@42542
  1175
blanchet@42544
  1176
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
  1177
blanchet@43130
  1178
val app_op = `make_fixed_const app_op_name
blanchet@43130
  1179
blanchet@42544
  1180
fun explicit_app arg head =
blanchet@42544
  1181
  let
blanchet@42562
  1182
    val head_T = combtyp_of head
blanchet@42693
  1183
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
  1184
    val explicit_app =
blanchet@43130
  1185
      CombConst (app_op, head_T --> head_T, [arg_T, res_T])
blanchet@42544
  1186
  in list_app explicit_app [head, arg] end
blanchet@42544
  1187
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
  1188
blanchet@42565
  1189
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
  1190
  let
blanchet@42544
  1191
    fun aux tm =
blanchet@42544
  1192
      case strip_combterm_comb tm of
blanchet@42544
  1193
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
  1194
        args |> map aux
blanchet@42557
  1195
             |> chop (min_arity_of sym_tab s)
blanchet@42544
  1196
             |>> list_app head
blanchet@42544
  1197
             |-> list_explicit_app
blanchet@42544
  1198
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
  1199
  in aux end
blanchet@38282
  1200
blanchet@42753
  1201
fun chop_fun 0 T = ([], T)
blanchet@42753
  1202
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
  1203
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
  1204
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
  1205
blanchet@42780
  1206
fun filter_type_args _ _ _ [] = []
blanchet@42780
  1207
  | filter_type_args thy s arity T_args =
blanchet@42834
  1208
    let
blanchet@42834
  1209
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42966
  1210
      val U = if s = app_op_name then
blanchet@42834
  1211
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
  1212
              else
blanchet@42834
  1213
                s |> Sign.the_const_type thy
blanchet@42834
  1214
    in
blanchet@42781
  1215
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
  1216
        [] => []
blanchet@42781
  1217
      | res_U_vars =>
blanchet@42781
  1218
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
  1219
          U_args ~~ T_args
blanchet@43401
  1220
          |> map (fn (U, T) =>
blanchet@43401
  1221
                     if member (op =) res_U_vars (dest_TVar U) then T
blanchet@43401
  1222
                     else dummyT)
blanchet@42781
  1223
        end
blanchet@42780
  1224
    end
blanchet@42780
  1225
    handle TYPE _ => T_args
blanchet@42753
  1226
blanchet@43179
  1227
fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
blanchet@42753
  1228
  let
blanchet@42753
  1229
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
  1230
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
  1231
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
  1232
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@43179
  1233
        (case strip_prefix_and_unascii const_prefix s of
blanchet@43179
  1234
           NONE => (name, T_args)
blanchet@43179
  1235
         | SOME s'' =>
blanchet@43179
  1236
           let
blanchet@43179
  1237
             val s'' = invert_const s''
blanchet@43179
  1238
             fun filtered_T_args false = T_args
blanchet@43179
  1239
               | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@43179
  1240
           in
blanchet@43179
  1241
             case type_arg_policy type_sys s'' of
blanchet@43179
  1242
               Explicit_Type_Args drop_args =>
blanchet@43179
  1243
               (name, filtered_T_args drop_args)
blanchet@43179
  1244
             | Mangled_Type_Args drop_args =>
blanchet@43179
  1245
               (mangled_const_name format type_sys (filtered_T_args drop_args)
blanchet@43179
  1246
                                   name, [])
blanchet@43179
  1247
             | No_Type_Args => (name, [])
blanchet@43179
  1248
           end)
blanchet@43179
  1249
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42753
  1250
      | aux _ tm = tm
blanchet@42753
  1251
  in aux 0 end
blanchet@42573
  1252
blanchet@43179
  1253
fun repair_combterm ctxt format type_sys sym_tab =
blanchet@42994
  1254
  not (is_setting_higher_order format type_sys)
blanchet@42994
  1255
  ? (introduce_explicit_apps_in_combterm sym_tab
blanchet@42994
  1256
     #> introduce_predicators_in_combterm sym_tab)
blanchet@43179
  1257
  #> enforce_type_arg_policy_in_combterm ctxt format type_sys
blanchet@43179
  1258
fun repair_fact ctxt format type_sys sym_tab =
blanchet@42701
  1259
  update_combformula (formula_map
blanchet@43179
  1260
      (repair_combterm ctxt format type_sys sym_tab))
blanchet@42573
  1261
blanchet@42573
  1262
(** Helper facts **)
blanchet@42573
  1263
blanchet@43194
  1264
(* The Boolean indicates that a fairly sound type encoding is needed. *)
blanchet@43085
  1265
val helper_table =
blanchet@43194
  1266
  [(("COMBI", false), @{thms Meson.COMBI_def}),
blanchet@43194
  1267
   (("COMBK", false), @{thms Meson.COMBK_def}),
blanchet@43194
  1268
   (("COMBB", false), @{thms Meson.COMBB_def}),
blanchet@43194
  1269
   (("COMBC", false), @{thms Meson.COMBC_def}),
blanchet@43194
  1270
   (("COMBS", false), @{thms Meson.COMBS_def}),
blanchet@43194
  1271
   (("fequal", true),
blanchet@43085
  1272
    (* This is a lie: Higher-order equality doesn't need a sound type encoding.
blanchet@43085
  1273
       However, this is done so for backward compatibility: Including the
blanchet@43085
  1274
       equality helpers by default in Metis breaks a few existing proofs. *)
blanchet@43194
  1275
    @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
blanchet@43194
  1276
           fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
blanchet@43194
  1277
   (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
blanchet@43194
  1278
   (("fFalse", true), @{thms True_or_False}),
blanchet@43194
  1279
   (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
blanchet@43194
  1280
   (("fTrue", true), @{thms True_or_False}),
blanchet@43194
  1281
   (("fNot", false),
blanchet@43194
  1282
    @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
blanchet@43194
  1283
           fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
blanchet@43194
  1284
   (("fconj", false),
blanchet@43194
  1285
    @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
blanchet@43194
  1286
        by (unfold fconj_def) fast+}),
blanchet@43194
  1287
   (("fdisj", false),
blanchet@43194
  1288
    @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
blanchet@43194
  1289
        by (unfold fdisj_def) fast+}),
blanchet@43194
  1290
   (("fimplies", false),
blanchet@43210
  1291
    @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
blanchet@43194
  1292
        by (unfold fimplies_def) fast+}),
blanchet@43194
  1293
   (("If", true), @{thms if_True if_False True_or_False})]
blanchet@43194
  1294
  |> map (apsnd (map zero_var_indexes))
blanchet@43085
  1295
blanchet@43130
  1296
val type_tag = `make_fixed_const type_tag_name
blanchet@43130
  1297
blanchet@43159
  1298
fun type_tag_idempotence_fact () =
blanchet@42573
  1299
  let
blanchet@42573
  1300
    fun var s = ATerm (`I s, [])
blanchet@43159
  1301
    fun tag tm = ATerm (type_tag, [var "T", tm])
blanchet@43207
  1302
    val tagged_a = tag (var "A")
blanchet@42573
  1303
  in
blanchet@43159
  1304
    Formula (type_tag_idempotence_helper_name, Axiom,
blanchet@43207
  1305
             AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
blanchet@42879
  1306
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
  1307
  end
blanchet@42573
  1308
blanchet@43159
  1309
fun should_specialize_helper type_sys t =
blanchet@43159
  1310
  case general_type_arg_policy type_sys of
blanchet@43159
  1311
    Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
blanchet@43159
  1312
  | _ => false
blanchet@43159
  1313
blanchet@43064
  1314
fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
blanchet@42573
  1315
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
  1316
    SOME mangled_s =>
blanchet@42573
  1317
    let
blanchet@42573
  1318
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
  1319
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@43159
  1320
      fun dub_and_inst needs_fairly_sound (th, j) =
blanchet@43159
  1321
        ((unmangled_s ^ "_" ^ string_of_int j ^
blanchet@43159
  1322
          (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
blanchet@42893
  1323
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
  1324
           else untyped_helper_suffix),
blanchet@43421
  1325
          Helper),
blanchet@42573
  1326
         let val t = th |> prop_of in
blanchet@43159
  1327
           t |> should_specialize_helper type_sys t
blanchet@43064
  1328
                ? (case types of
blanchet@43064
  1329
                     [T] => specialize_type thy (invert_const unmangled_s, T)
blanchet@43064
  1330
                   | _ => I)
blanchet@42573
  1331
         end)
blanchet@43159
  1332
      val make_facts =
blanchet@43295
  1333
        map_filter (make_fact ctxt format type_sys false false [])
blanchet@42893
  1334
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
  1335
    in
blanchet@43085
  1336
      helper_table
blanchet@43194
  1337
      |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
blanchet@43159
  1338
                  if helper_s <> unmangled_s orelse
blanchet@42894
  1339
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
  1340
                    []
blanchet@42573
  1341
                  else
blanchet@42573
  1342
                    ths ~~ (1 upto length ths)
blanchet@43159
  1343
                    |> map (dub_and_inst needs_fairly_sound)
blanchet@43159
  1344
                    |> make_facts)
blanchet@42573
  1345
    end
blanchet@42573
  1346
  | NONE => []
blanchet@42962
  1347
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
blanchet@42962
  1348
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
blanchet@42962
  1349
                  []
blanchet@42573
  1350
blanchet@43085
  1351
(***************************************************************)
blanchet@43085
  1352
(* Type Classes Present in the Axiom or Conjecture Clauses     *)
blanchet@43085
  1353
(***************************************************************)
blanchet@43085
  1354
blanchet@43085
  1355
fun set_insert (x, s) = Symtab.update (x, ()) s
blanchet@43085
  1356
blanchet@43085
  1357
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
blanchet@43085
  1358
blanchet@43085
  1359
(* Remove this trivial type class (FIXME: similar code elsewhere) *)
blanchet@43085
  1360
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
blanchet@43085
  1361
blanchet@43093
  1362
fun classes_of_terms get_Ts =
blanchet@43121
  1363
  map (map snd o get_Ts)
blanchet@43093
  1364
  #> List.foldl add_classes Symtab.empty
blanchet@43093
  1365
  #> delete_type #> Symtab.keys
blanchet@43085
  1366
blanchet@43093
  1367
val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
blanchet@43093
  1368
val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
blanchet@43085
  1369
blanchet@43085
  1370
(*fold type constructors*)
blanchet@43189
  1371
fun fold_type_constrs f (Type (a, Ts)) x =
blanchet@43189
  1372
    fold (fold_type_constrs f) Ts (f (a,x))
blanchet@43189
  1373
  | fold_type_constrs _ _ x = x
blanchet@43085
  1374
blanchet@43085
  1375
(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
blanchet@43189
  1376
fun add_type_constrs_in_term thy =
blanchet@43085
  1377
  let
blanchet@43188
  1378
    fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
blanchet@43181
  1379
      | add (t $ u) = add t #> add u
blanchet@43188
  1380
      | add (Const (x as (s, _))) =
blanchet@43188
  1381
        if String.isPrefix skolem_const_prefix s then I
blanchet@43189
  1382
        else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
blanchet@43181
  1383
      | add (Abs (_, _, u)) = add u
blanchet@43181
  1384
      | add _ = I
blanchet@43181
  1385
  in add end
blanchet@43085
  1386
blanchet@43189
  1387
fun type_constrs_of_terms thy ts =
blanchet@43189
  1388
  Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
blanchet@43085
  1389
blanchet@43096
  1390
fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
blanchet@43214
  1391
                       facts =
blanchet@42573
  1392
  let
blanchet@42573
  1393
    val thy = Proof_Context.theory_of ctxt
blanchet@43222
  1394
    val fact_ts = facts |> map snd
blanchet@43264
  1395
    val presimp_consts = Meson.presimplified_consts ctxt
blanchet@43295
  1396
    val make_fact = make_fact ctxt format type_sys true preproc presimp_consts
blanchet@42573
  1397
    val (facts, fact_names) =
blanchet@43264
  1398
      facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
blanchet@43214
  1399
            |> map_filter (try (apfst the))
blanchet@43214
  1400
            |> ListPair.unzip
blanchet@42573
  1401
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
  1402
       boost an ATP's performance (for some reason). *)
blanchet@43192
  1403
    val hyp_ts =
blanchet@43192
  1404
      hyp_ts
blanchet@43192
  1405
      |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
blanchet@42573
  1406
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
  1407
    val all_ts = goal_t :: fact_ts
blanchet@42573
  1408
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
  1409
    val supers = tvar_classes_of_terms all_ts
blanchet@43189
  1410
    val tycons = type_constrs_of_terms thy all_ts
blanchet@42994
  1411
    val conjs =
blanchet@43096
  1412
      hyp_ts @ [concl_t]
blanchet@43264
  1413
      |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
blanchet@42573
  1414
    val (supers', arity_clauses) =
blanchet@42589
  1415
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
  1416
      else make_arity_clauses thy tycons supers
blanchet@42573
  1417
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
  1418
  in
blanchet@42573
  1419
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
  1420
  end
blanchet@42573
  1421
blanchet@42573
  1422
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
  1423
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
  1424
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
  1425
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
  1426
blanchet@42573
  1427
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
  1428
blanchet@43130
  1429
val type_pred = `make_fixed_const type_pred_name
blanchet@43130
  1430
blanchet@43179
  1431
fun type_pred_combterm ctxt format type_sys T tm =
blanchet@43179
  1432
  CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
blanchet@43179
  1433
           |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
blanchet@42573
  1434
blanchet@43421
  1435
fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@43421
  1436
  | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@43000
  1437
    accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
blanchet@43493
  1438
fun should_predicate_on_var_in_formula pos phi (SOME true) name =
blanchet@43421
  1439
    formula_fold pos (is_var_positively_naked_in_term name) phi false
blanchet@43493
  1440
  | should_predicate_on_var_in_formula _ _ _ _ = true
blanchet@42834
  1441
blanchet@43178
  1442
fun mk_const_aterm format type_sys x T_args args =
blanchet@43401
  1443
  ATerm (x, map_filter (fo_term_for_type_arg format type_sys) T_args @ args)
blanchet@42994
  1444
blanchet@43361
  1445
fun tag_with_type ctxt format nonmono_Ts type_sys pos T tm =
blanchet@43130
  1446
  CombConst (type_tag, T --> T, [T])
blanchet@43179
  1447
  |> enforce_type_arg_policy_in_combterm ctxt format type_sys
blanchet@43361
  1448
  |> term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
blanchet@42829
  1449
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42962
  1450
and term_from_combterm ctxt format nonmono_Ts type_sys =
blanchet@42573
  1451
  let
blanchet@42962
  1452
    fun aux site u =
blanchet@42962
  1453
      let
blanchet@42962
  1454
        val (head, args) = strip_combterm_comb u
blanchet@42962
  1455
        val (x as (s, _), T_args) =
blanchet@42962
  1456
          case head of
blanchet@42962
  1457
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42962
  1458
          | CombVar (name, _) => (name, [])
blanchet@42962
  1459
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@43361
  1460
        val (pos, arg_site) =
blanchet@43361
  1461
          case site of
blanchet@43361
  1462
            Top_Level pos =>
blanchet@43361
  1463
            (pos, if is_tptp_equal s then Eq_Arg pos else Elsewhere)
blanchet@43361
  1464
          | Eq_Arg pos => (pos, Elsewhere)
blanchet@43361
  1465
          | Elsewhere => (NONE, Elsewhere)
blanchet@43178
  1466
        val t = mk_const_aterm format type_sys x T_args
blanchet@43178
  1467
                    (map (aux arg_site) args)
blanchet@42962
  1468
        val T = combtyp_of u
blanchet@42962
  1469
      in
blanchet@42962
  1470
        t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@43361
  1471
                tag_with_type ctxt format nonmono_Ts type_sys pos T
blanchet@42962
  1472
              else
blanchet@42962
  1473
                I)
blanchet@42962
  1474
      end
blanchet@42962
  1475
  in aux end
blanchet@42962
  1476
and formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42962
  1477
                             should_predicate_on_var =
blanchet@42829
  1478
  let
blanchet@43361
  1479
    fun do_term pos =
blanchet@43361
  1480
      term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
blanchet@42573
  1481
    val do_bound_type =
blanchet@42682
  1482
      case type_sys of
blanchet@42722
  1483
        Simple_Types level =>
blanchet@42994
  1484
        homogenized_type ctxt nonmono_Ts level 0
blanchet@43178
  1485
        #> mangled_type format type_sys false 0 #> SOME
blanchet@42682
  1486
      | _ => K NONE
blanchet@42878
  1487
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
  1488
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
  1489
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
  1490
        CombVar (name, T)
blanchet@43179
  1491
        |> type_pred_combterm ctxt format type_sys T
blanchet@43361
  1492
        |> do_term pos |> AAtom |> SOME
blanchet@42573
  1493
      else
blanchet@42573
  1494
        NONE
blanchet@42878
  1495
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
  1496
        let
blanchet@42878
  1497
          val phi = phi |> do_formula pos
blanchet@42878
  1498
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
  1499
        in
blanchet@42834
  1500
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
  1501
                                        | SOME T => do_bound_type T)),
blanchet@42834
  1502
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
  1503
                      (map_filter
blanchet@42834
  1504
                           (fn (_, NONE) => NONE
blanchet@42834
  1505
                             | (s, SOME T) =>
blanchet@42878
  1506
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
  1507
                           xs)
blanchet@42834
  1508
                      phi)
blanchet@42834
  1509
        end
blanchet@42878
  1510
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@43361
  1511
      | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
blanchet@43493
  1512
  in do_formula end
blanchet@42573
  1513
blanchet@43098
  1514
fun bound_tvars type_sys Ts =
blanchet@42727
  1515
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@43263
  1516
                (type_literals_for_types type_sys add_sorts_on_tvar Ts))
blanchet@42727
  1517
blanchet@42573
  1518
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
  1519
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
  1520
   the remote provers might care. *)
blanchet@43501
  1521
fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
blanchet@43501
  1522
        type_sys (j, {name, locality, kind, combformula, atomic_types}) =
blanchet@43501
  1523
  (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
blanchet@43493
  1524
   kind,
blanchet@43493
  1525
   combformula
blanchet@43493
  1526
   |> close_combformula_universally
blanchet@43493
  1527
   |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@43493
  1528
                               should_predicate_on_var_in_formula
blanchet@43501
  1529
                               (if pos then SOME true else NONE)
blanchet@43493
  1530
   |> bound_tvars type_sys atomic_types
blanchet@43493
  1531
   |> close_formula_universally,
blanchet@43493
  1532
   NONE,
blanchet@43493
  1533
   case locality of
blanchet@43493
  1534
     Intro => intro_info
blanchet@43493
  1535
   | Elim => elim_info
blanchet@43493
  1536
   | Simp => simp_info
blanchet@43493
  1537
   | _ => NONE)
blanchet@43493
  1538
  |> Formula
blanchet@42573
  1539
blanchet@43086
  1540
fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
blanchet@43086
  1541
                                       : class_rel_clause) =
blanchet@42573
  1542
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
  1543
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
  1544
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
  1545
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
  1546
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
  1547
  end
blanchet@42573
  1548
blanchet@42573
  1549
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
  1550
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
  1551
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
  1552
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
  1553
blanchet@43086
  1554
fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
blanchet@43086
  1555
                                   : arity_clause) =
blanchet@43495
  1556
  Formula (arity_clause_prefix ^ name, Axiom,
blanchet@42573
  1557
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
  1558
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
  1559
                    (formula_from_fo_literal
blanchet@42895
  1560
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
  1561
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
  1562
blanchet@42962
  1563
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
blanchet@43098
  1564
        ({name, kind, combformula, atomic_types, ...} : translated_formula) =
blanchet@42577
  1565
  Formula (conjecture_prefix ^ name, kind,
blanchet@42962
  1566
           formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@43493
  1567
               should_predicate_on_var_in_formula (SOME false)
blanchet@42939
  1568
               (close_combformula_universally combformula)
blanchet@43098
  1569
           |> bound_tvars type_sys atomic_types
blanchet@42573
  1570
           |> close_formula_universally, NONE, NONE)
blanchet@42573
  1571
blanchet@43098
  1572
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@43263
  1573
  atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
blanchet@42573
  1574
               |> map fo_literal_from_type_literal
blanchet@42573
  1575
blanchet@42573
  1576
fun formula_line_for_free_type j lit =
blanchet@43085
  1577
  Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
  1578
           formula_from_fo_literal lit, NONE, NONE)
blanchet@43098
  1579
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
  1580
  let
blanchet@43098
  1581
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
  1582
    val lits = fold (union (op =)) litss []
blanchet@42573
  1583
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
  1584
blanchet@42573
  1585
(** Symbol declarations **)
blanchet@42544
  1586
blanchet@42574
  1587
fun should_declare_sym type_sys pred_sym s =
blanchet@42998
  1588
  is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
blanchet@42894
  1589
  (case type_sys of
blanchet@42894
  1590
     Simple_Types _ => true
blanchet@43128
  1591
   | Tags (_, _, Lightweight) => true
blanchet@42894
  1592
   | _ => not pred_sym)
blanchet@38282
  1593
blanchet@42886
  1594
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
  1595
  let
blanchet@42698
  1596
    fun add_combterm in_conj tm =
blanchet@42574
  1597
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
  1598
        (case head of
blanchet@42574
  1599
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
  1600
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
  1601
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
  1602
               Symtab.map_default (s, [])
blanchet@42886
  1603
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1604
                                         in_conj))
blanchet@42574
  1605
             else
blanchet@42574
  1606
               I
blanchet@42574
  1607
           end
blanchet@42574
  1608
         | _ => I)
blanchet@42698
  1609
        #> fold (add_combterm in_conj) args
blanchet@42574
  1610
      end
blanchet@42698
  1611
    fun add_fact in_conj =
blanchet@42834
  1612
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
  1613
  in
blanchet@42698
  1614
    Symtab.empty
blanchet@42698
  1615
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
  1616
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
  1617
  end
blanchet@42533
  1618
blanchet@42685
  1619
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1620
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@43572
  1621
fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
blanchet@43572
  1622
  | add_combterm_nonmonotonic_types ctxt level sound locality _
blanchet@43179
  1623
        (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
blanchet@43179
  1624
                           tm2)) =
blanchet@43000
  1625
    (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1626
     (case level of
blanchet@43362
  1627
        Noninf_Nonmono_Types =>
blanchet@43293
  1628
        not (is_locality_global locality) orelse
blanchet@43572
  1629
        not (is_type_surely_infinite ctxt sound T)
blanchet@43572
  1630
      | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
blanchet@42886
  1631
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@43572
  1632
  | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
blanchet@43572
  1633
fun add_fact_nonmonotonic_types ctxt level sound
blanchet@43572
  1634
        ({kind, locality, combformula, ...} : translated_formula) =
blanchet@42834
  1635
  formula_fold (SOME (kind <> Conjecture))
blanchet@43572
  1636
               (add_combterm_nonmonotonic_types ctxt level sound locality)
blanchet@43572
  1637
               combformula
blanchet@43572
  1638
fun nonmonotonic_types_for_facts ctxt type_sys sound facts =
blanchet@42829
  1639
  let val level = level_of_type_sys type_sys in
blanchet@43362
  1640
    if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
blanchet@43572
  1641
      [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
blanchet@42886
  1642
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1643
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1644
            nonmonotonic types not being empty. *)
blanchet@42886
  1645
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1646
    else
blanchet@42886
  1647
      []
blanchet@42829
  1648
  end
blanchet@42677
  1649
blanchet@42994
  1650
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
blanchet@42994
  1651
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  1652
  let
blanchet@43178
  1653
    val (T_arg_Ts, level) =
blanchet@42994
  1654
      case type_sys of
blanchet@43178
  1655
        Simple_Types level => ([], level)
blanchet@43178
  1656
      | _ => (replicate (length T_args) homo_infinite_type, No_Types)
blanchet@42994
  1657
  in
blanchet@42998
  1658
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@42994
  1659
          (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
blanchet@43178
  1660
          |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
blanchet@42994
  1661
  end
blanchet@42579
  1662
blanchet@43125
  1663
fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
blanchet@43401
  1664
        poly_nonmono_Ts type_sys n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1665
  let
blanchet@42709
  1666
    val (kind, maybe_negate) =
blanchet@42709
  1667
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1668
      else (Axiom, I)
blanchet@42753
  1669
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@43399
  1670
    val num_args = length arg_Ts
blanchet@42579
  1671
    val bound_names =
blanchet@43399
  1672
      1 upto num_args |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1673
    val bounds =
blanchet@42579
  1674
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@43401
  1675
    val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
blanchet@43401
  1676
    fun should_keep_arg_type T =
blanchet@43401
  1677
      sym_needs_arg_types orelse
blanchet@43401
  1678
      not (should_predicate_on_type ctxt nonmono_Ts type_sys (K false) T)
blanchet@42579
  1679
    val bound_Ts =
blanchet@43401
  1680
      arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
blanchet@42579
  1681
  in
blanchet@43125
  1682
    Formula (preds_sym_formula_prefix ^ s ^
blanchet@42709
  1683
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1684
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1685
             |> fold (curry (CombApp o swap)) bounds
blanchet@43179
  1686
             |> type_pred_combterm ctxt format type_sys res_T
blanchet@42963
  1687
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@43401
  1688
             |> formula_from_combformula ctxt format poly_nonmono_Ts type_sys
blanchet@43493
  1689
                                         (K (K (K (K true)))) (SOME true)
blanchet@43098
  1690
             |> n > 1 ? bound_tvars type_sys (atyps_of T)
blanchet@42709
  1691
             |> close_formula_universally
blanchet@42709
  1692
             |> maybe_negate,
blanchet@42879
  1693
             intro_info, NONE)
blanchet@42579
  1694
  end
blanchet@42579
  1695
blanchet@43129
  1696
fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
blanchet@43401
  1697
        poly_nonmono_Ts type_sys n s
blanchet@43401
  1698
        (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1699
  let
blanchet@42829
  1700
    val ident_base =
blanchet@43129
  1701
      lightweight_tags_sym_formula_prefix ^ s ^
blanchet@43125
  1702
      (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1703
    val (kind, maybe_negate) =
blanchet@42852
  1704
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1705
      else (Axiom, I)
blanchet@42829
  1706
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1707
    val bound_names =
blanchet@42829
  1708
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1709
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@43178
  1710
    val cst = mk_const_aterm format type_sys (s, s') T_args
blanchet@42830
  1711
    val atomic_Ts = atyps_of T
blanchet@42834
  1712
    fun eq tms =
blanchet@42834
  1713
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@43000
  1714
       else AAtom (ATerm (`I tptp_equal, tms)))
blanchet@43098
  1715
      |> bound_tvars type_sys atomic_Ts
blanchet@42830
  1716
      |> close_formula_universally
blanchet@42852
  1717
      |> maybe_negate
blanchet@43361
  1718
    (* See also "should_tag_with_type". *)
blanchet@43361
  1719
    fun should_encode T =
blanchet@43401
  1720
      should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
blanchet@43361
  1721
      (case type_sys of
blanchet@43361
  1722
         Tags (Polymorphic, level, Lightweight) =>
blanchet@43361
  1723
         level <> All_Types andalso Monomorph.typ_has_tvars T
blanchet@43361
  1724
       | _ => false)
blanchet@43401
  1725
    val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_sys NONE
blanchet@42829
  1726
    val add_formula_for_res =
blanchet@42829
  1727
      if should_encode res_T then
blanchet@42852
  1728
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42994
  1729
                       eq [tag_with res_T (cst bounds), cst bounds],
blanchet@42879
  1730
                       simp_info, NONE))
blanchet@42829
  1731
      else
blanchet@42829
  1732
        I
blanchet@42829
  1733
    fun add_formula_for_arg k =
blanchet@42829
  1734
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1735
        if should_encode arg_T then
blanchet@42829
  1736
          case chop k bounds of
blanchet@42829
  1737
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1738
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42994
  1739
                           eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
blanchet@42994
  1740
                               cst bounds],
blanchet@42879
  1741
                           simp_info, NONE))
blanchet@42829
  1742
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1743
        else
blanchet@42829
  1744
          I
blanchet@42829
  1745
      end
blanchet@42829
  1746
  in
blanchet@42834
  1747
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1748
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1749
  end
blanchet@42829
  1750
blanchet@42836
  1751
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1752
blanchet@43401
  1753
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
blanchet@43401
  1754
                                poly_nonmono_Ts type_sys (s, decls) =
blanchet@42998
  1755
  case type_sys of
blanchet@42998
  1756
    Simple_Types _ =>
blanchet@42998
  1757
    decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
blanchet@42998
  1758
  | Preds _ =>
blanchet@42998
  1759
    let
blanchet@42998
  1760
      val decls =
blanchet@42998
  1761
        case decls of
blanchet@42998
  1762
          decl :: (decls' as _ :: _) =>
blanchet@42998
  1763
          let val T = result_type_of_decl decl in
blanchet@42998
  1764
            if forall (curry (type_instance ctxt o swap) T
blanchet@42998
  1765
                       o result_type_of_decl) decls' then
blanchet@42998
  1766
              [decl]
blanchet@42998
  1767
            else
blanchet@42998
  1768
              decls
blanchet@42998
  1769
          end
blanchet@42998
  1770
        | _ => decls
blanchet@42998
  1771
      val n = length decls
blanchet@42998
  1772
      val decls =
blanchet@43401
  1773
        decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_sys
blanchet@43401
  1774
                                                  (K true)
blanchet@43401
  1775
                         o result_type_of_decl)
blanchet@42998
  1776
    in
blanchet@42998
  1777
      (0 upto length decls - 1, decls)
blanchet@43125
  1778
      |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
blanchet@43401
  1779
                   nonmono_Ts poly_nonmono_Ts type_sys n s)
blanchet@42998
  1780
    end
blanchet@42998
  1781
  | Tags (_, _, heaviness) =>
blanchet@42998
  1782
    (case heaviness of
blanchet@43128
  1783
       Heavyweight => []
blanchet@43128
  1784
     | Lightweight =>
blanchet@42998
  1785
       let val n = length decls in
blanchet@42998
  1786
         (0 upto n - 1 ~~ decls)
blanchet@43129
  1787
         |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
blanchet@43401
  1788
                      conj_sym_kind poly_nonmono_Ts type_sys n s)
blanchet@42998
  1789
       end)
blanchet@42579
  1790
blanchet@42956
  1791
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@43401
  1792
                                     poly_nonmono_Ts type_sys sym_decl_tab =
blanchet@42998
  1793
  sym_decl_tab
blanchet@42998
  1794
  |> Symtab.dest
blanchet@42998
  1795
  |> sort_wrt fst
blanchet@42998
  1796
  |> rpair []
blanchet@42998
  1797
  |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
blanchet@43401
  1798
                             nonmono_Ts poly_nonmono_Ts type_sys)
blanchet@42543
  1799
blanchet@43185
  1800
fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
blanchet@43185
  1801
    poly <> Mangled_Monomorphic andalso
blanchet@43185
  1802
    ((level = All_Types andalso heaviness = Lightweight) orelse
blanchet@43362
  1803
     level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
blanchet@43159
  1804
  | needs_type_tag_idempotence _ = false
blanchet@42831
  1805
blanchet@42939
  1806
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1807
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1808
    if heading = needle then j
blanchet@42939
  1809
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1810
blanchet@42998
  1811
val implicit_declsN = "Should-be-implicit typings"
blanchet@42998
  1812
val explicit_declsN = "Explicit typings"
blanchet@41157
  1813
val factsN = "Relevant facts"
blanchet@41157
  1814
val class_relsN = "Class relationships"
blanchet@42543
  1815
val aritiesN = "Arities"
blanchet@41157
  1816
val helpersN = "Helper facts"
blanchet@41157
  1817
val conjsN = "Conjectures"
blanchet@41313
  1818
val free_typesN = "Type variables"
blanchet@41157
  1819
blanchet@43259
  1820
val explicit_apply = NONE (* for experimental purposes *)
blanchet@43259
  1821
blanchet@43572
  1822
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys sound
blanchet@43493
  1823
        exporter readable_names preproc hyp_ts concl_t facts =
blanchet@38282
  1824
  let
blanchet@43101
  1825
    val (format, type_sys) = choose_format [format] type_sys
blanchet@41313
  1826
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@43096
  1827
      translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
blanchet@43096
  1828
                         facts
blanchet@43064
  1829
    val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
blanchet@43572
  1830
    val nonmono_Ts =
blanchet@43572
  1831
      conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys sound
blanchet@43179
  1832
    val repair = repair_fact ctxt format type_sys sym_tab
blanchet@42682
  1833
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@43064
  1834
    val repaired_sym_tab =
blanchet@43064
  1835
      conjs @ facts |> sym_table_for_facts ctxt (SOME false)
blanchet@42573
  1836
    val helpers =
blanchet@42962
  1837
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
blanchet@42962
  1838
                       |> map repair
blanchet@43401
  1839
    val poly_nonmono_Ts =
blanchet@43213
  1840
      if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
blanchet@42894
  1841
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1842
        nonmono_Ts
blanchet@42894
  1843
      else
blanchet@42894
  1844
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1845
    val sym_decl_lines =
blanchet@42731
  1846
      (conjs, helpers @ facts)
blanchet@42886
  1847
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@43401
  1848
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@43401
  1849
                                               poly_nonmono_Ts type_sys
blanchet@42881
  1850
    val helper_lines =
blanchet@42956
  1851
      0 upto length helpers - 1 ~~ helpers
blanchet@43501
  1852
      |> map (formula_line_for_fact ctxt format helper_prefix I false true
blanchet@43401
  1853
                                    poly_nonmono_Ts type_sys)
blanchet@43159
  1854
      |> (if needs_type_tag_idempotence type_sys then
blanchet@43159
  1855
            cons (type_tag_idempotence_fact ())
blanchet@43159
  1856
          else
blanchet@43159
  1857
            I)
blanchet@42522
  1858
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@43039
  1859
       FLOTTER hack. *)
blanchet@38282
  1860
    val problem =
blanchet@42998
  1861
      [(explicit_declsN, sym_decl_lines),
blanchet@42956
  1862
       (factsN,
blanchet@43501
  1863
        map (formula_line_for_fact ctxt format fact_prefix ascii_of
blanchet@43501
  1864
                                   (not exporter) (not exporter) nonmono_Ts
blanchet@43501
  1865
                                   type_sys)
blanchet@42956
  1866
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1867
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1868
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1869
       (helpersN, helper_lines),
blanchet@42962
  1870
       (conjsN,
blanchet@42962
  1871
        map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
blanchet@42962
  1872
            conjs),
blanchet@43098
  1873
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1874
    val problem =
blanchet@42561
  1875
      problem
blanchet@43092
  1876
      |> (case format of
blanchet@43092
  1877
            CNF => ensure_cnf_problem
blanchet@43092
  1878
          | CNF_UEQ => filter_cnf_ueq_problem
blanchet@43092
  1879
          | _ => I)
blanchet@42998
  1880
      |> (if is_format_typed format then
blanchet@42998
  1881
            declare_undeclared_syms_in_atp_problem type_decl_prefix
blanchet@42998
  1882
                                                   implicit_declsN
blanchet@42998
  1883
          else
blanchet@42998
  1884
            I)
blanchet@43092
  1885
    val (problem, pool) = problem |> nice_atp_problem readable_names
blanchet@42881
  1886
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1887
    val typed_helpers =
blanchet@42881
  1888
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1889
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1890
                     else NONE)
blanchet@42881
  1891
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1892
                  ~~ helpers)
blanchet@42778
  1893
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1894
      if min_ary > 0 then
blanchet@42755
  1895
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1896
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1897
        | NONE => I
blanchet@42755
  1898
      else
blanchet@42755
  1899
        I
blanchet@38282
  1900
  in
blanchet@38282
  1901
    (problem,
blanchet@38282
  1902
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1903
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1904
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1905
     fact_names |> Vector.fromList,
blanchet@42881
  1906
     typed_helpers,
blanchet@42755
  1907
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1908
  end
blanchet@38282
  1909
blanchet@41313
  1910
(* FUDGE *)
blanchet@41313
  1911
val conj_weight = 0.0
blanchet@41770
  1912
val hyp_weight = 0.1
blanchet@41770
  1913
val fact_min_weight = 0.2
blanchet@41313
  1914
val fact_max_weight = 1.0
blanchet@42608
  1915
val type_info_default_weight = 0.8
blanchet@41313
  1916
blanchet@41313
  1917
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42998
  1918
  is_tptp_user_symbol s ? Symtab.default (s, weight)
blanchet@41313
  1919
  #> fold (add_term_weights weight) tms
blanchet@42577
  1920
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1921
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1922
  | add_problem_line_weights _ _ = I
blanchet@41313
  1923
blanchet@41313
  1924
fun add_conjectures_weights [] = I
blanchet@41313
  1925
  | add_conjectures_weights conjs =
blanchet@41313
  1926
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1927
      add_problem_line_weights conj_weight conj
blanchet@41313
  1928
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1929
    end
blanchet@41313
  1930
blanchet@41313
  1931
fun add_facts_weights facts =
blanchet@41313
  1932
  let
blanchet@41313
  1933
    val num_facts = length facts
blanchet@41313
  1934
    fun weight_of j =
blanchet@41313
  1935
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1936
                        / Real.fromInt num_facts
blanchet@41313
  1937
  in
blanchet@41313
  1938
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1939
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1940
  end
blanchet@41313
  1941
blanchet@41313
  1942
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1943
fun atp_problem_weights problem =
blanchet@42608
  1944
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1945
    Symtab.empty
blanchet@42608
  1946
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1947
    |> add_facts_weights (get factsN)
blanchet@42608
  1948
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42998
  1949
            [explicit_declsN, class_relsN, aritiesN]
blanchet@42608
  1950
    |> Symtab.dest
blanchet@42608
  1951
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1952
  end
blanchet@41313
  1953
blanchet@38282
  1954
end;