src/HOL/Tools/ATP/atp_translate.ML
author blanchet
Wed Jul 20 00:37:42 2011 +0200 (2011-07-20)
changeset 43907 073ab5379842
parent 43906 14d34bd434b8
child 43936 127749bbc639
permissions -rw-r--r--
pass type arguments to lambda-lifted Frees, to account for polymorphism
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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 Metis and Sledgehammer.
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*)
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signature ATP_TRANSLATE =
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sig
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  type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_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 order = First_Order | Higher_Order
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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_enc =
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    Simple_Types of order * 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 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_enc_from_string : string -> type_enc
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  val is_type_enc_higher_order : type_enc -> bool
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  val polymorphism_of_type_enc : type_enc -> polymorphism
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  val level_of_type_enc : type_enc -> type_level
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  val is_type_enc_virtually_sound : type_enc -> bool
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  val is_type_enc_fairly_sound : type_enc -> bool
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  val choose_format : format list -> type_enc -> format * type_enc
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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, 'b) ho_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 conceal_lambdas : Proof.context -> term -> term
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  val introduce_combinators : Proof.context -> term -> term
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  val prepare_atp_problem :
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    Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
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    -> bool -> (term list -> term list * term list) -> bool -> bool -> term list
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    -> term -> ((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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val generate_info = false (* experimental *)
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fun isabelle_info s =
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  if generate_info then SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
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  else NONE
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val introN = "intro"
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val elimN = "elim"
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val simpN = "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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(* TODO: Use a more descriptive prefix in "SMT_Translate.lift_lambdas". *)
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val lambda_lifted_prefix = Name.uu
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val skolem_const_prefix = "ATP" ^ 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 lambda_fact_prefix = "ATP.lambda_"
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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 atp_weak_prefix = "ATP:"
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val concealed_lambda_prefix = atp_weak_prefix ^ "lambda_"
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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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   ("c_All", (@{const_name All}, (@{thm fAll_def},
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       ("fAll", @{const_name ATP.fAll})))),
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   ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
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       ("fEx", @{const_name ATP.fEx}))))]
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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 All}, "All"),
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   (@{const_name Ex}, "Ex"),
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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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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 (unprefix "'" x, i))
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fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
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(* "HOL.eq" is mapped to the ATP's equality. *)
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fun make_fixed_const @{const_name HOL.eq} = tptp_old_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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(* 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
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     higher-order places) but not by the monomorphizer. *)
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  [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
blanchet@43248
   318
   @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
blanchet@43248
   319
   @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
blanchet@43248
   320
blanchet@43258
   321
fun add_schematic_const (x as (_, T)) =
blanchet@43258
   322
  Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
blanchet@43258
   323
val add_schematic_consts_of =
blanchet@43258
   324
  Term.fold_aterms (fn Const (x as (s, _)) =>
blanchet@43258
   325
                       not (member (op =) atp_monomorph_bad_consts s)
blanchet@43258
   326
                       ? add_schematic_const x
blanchet@43258
   327
                      | _ => I)
blanchet@43258
   328
fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
blanchet@43248
   329
blanchet@43085
   330
(** Definitions and functions for FOL clauses and formulas for TPTP **)
blanchet@43085
   331
blanchet@43085
   332
(* The first component is the type class; the second is a "TVar" or "TFree". *)
blanchet@43085
   333
datatype type_literal =
blanchet@43085
   334
  TyLitVar of name * name |
blanchet@43085
   335
  TyLitFree of name * name
blanchet@43085
   336
blanchet@43085
   337
blanchet@43085
   338
(** Isabelle arities **)
blanchet@43085
   339
blanchet@43085
   340
datatype arity_literal =
blanchet@43085
   341
  TConsLit of name * name * name list |
blanchet@43085
   342
  TVarLit of name * name
blanchet@43085
   343
blanchet@43085
   344
fun gen_TVars 0 = []
blanchet@43093
   345
  | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
blanchet@43085
   346
blanchet@43263
   347
val type_class = the_single @{sort type}
blanchet@43263
   348
blanchet@43263
   349
fun add_packed_sort tvar =
blanchet@43263
   350
  fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
blanchet@43085
   351
blanchet@43086
   352
type arity_clause =
blanchet@43496
   353
  {name : string,
blanchet@43496
   354
   prem_lits : arity_literal list,
blanchet@43496
   355
   concl_lits : arity_literal}
blanchet@43085
   356
blanchet@43085
   357
(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
blanchet@43085
   358
fun make_axiom_arity_clause (tcons, name, (cls, args)) =
blanchet@43085
   359
  let
blanchet@43085
   360
    val tvars = gen_TVars (length args)
blanchet@43085
   361
    val tvars_srts = ListPair.zip (tvars, args)
blanchet@43085
   362
  in
blanchet@43086
   363
    {name = name,
blanchet@43263
   364
     prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
blanchet@43086
   365
     concl_lits = TConsLit (`make_type_class cls,
blanchet@43086
   366
                            `make_fixed_type_const tcons,
blanchet@43086
   367
                            tvars ~~ tvars)}
blanchet@43085
   368
  end
blanchet@43085
   369
blanchet@43085
   370
fun arity_clause _ _ (_, []) = []
blanchet@43495
   371
  | arity_clause seen n (tcons, ("HOL.type", _) :: ars) =  (* ignore *)
blanchet@43495
   372
    arity_clause seen n (tcons, ars)
blanchet@43495
   373
  | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
blanchet@43495
   374
    if member (op =) seen class then
blanchet@43495
   375
      (* multiple arities for the same (tycon, class) pair *)
blanchet@43495
   376
      make_axiom_arity_clause (tcons,
blanchet@43495
   377
          lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
blanchet@43495
   378
          ar) ::
blanchet@43495
   379
      arity_clause seen (n + 1) (tcons, ars)
blanchet@43495
   380
    else
blanchet@43495
   381
      make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
blanchet@43495
   382
                               ascii_of class, ar) ::
blanchet@43495
   383
      arity_clause (class :: seen) n (tcons, ars)
blanchet@43085
   384
blanchet@43085
   385
fun multi_arity_clause [] = []
blanchet@43085
   386
  | multi_arity_clause ((tcons, ars) :: tc_arlists) =
blanchet@43085
   387
      arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
blanchet@43085
   388
blanchet@43622
   389
(* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
blanchet@43622
   390
   theory thy provided its arguments have the corresponding sorts. *)
blanchet@43085
   391
fun type_class_pairs thy tycons classes =
blanchet@43093
   392
  let
blanchet@43093
   393
    val alg = Sign.classes_of thy
blanchet@43093
   394
    fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
blanchet@43093
   395
    fun add_class tycon class =
blanchet@43093
   396
      cons (class, domain_sorts tycon class)
blanchet@43093
   397
      handle Sorts.CLASS_ERROR _ => I
blanchet@43093
   398
    fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
blanchet@43093
   399
  in map try_classes tycons end
blanchet@43085
   400
blanchet@43085
   401
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
blanchet@43085
   402
fun iter_type_class_pairs _ _ [] = ([], [])
blanchet@43085
   403
  | iter_type_class_pairs thy tycons classes =
blanchet@43263
   404
      let
blanchet@43263
   405
        fun maybe_insert_class s =
blanchet@43263
   406
          (s <> type_class andalso not (member (op =) classes s))
blanchet@43263
   407
          ? insert (op =) s
blanchet@43263
   408
        val cpairs = type_class_pairs thy tycons classes
blanchet@43263
   409
        val newclasses =
blanchet@43263
   410
          [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
blanchet@43263
   411
        val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
blanchet@43266
   412
      in (classes' @ classes, union (op =) cpairs' cpairs) end
blanchet@43085
   413
blanchet@43085
   414
fun make_arity_clauses thy tycons =
blanchet@43085
   415
  iter_type_class_pairs thy tycons ##> multi_arity_clause
blanchet@43085
   416
blanchet@43085
   417
blanchet@43085
   418
(** Isabelle class relations **)
blanchet@43085
   419
blanchet@43086
   420
type class_rel_clause =
blanchet@43496
   421
  {name : string,
blanchet@43496
   422
   subclass : name,
blanchet@43496
   423
   superclass : name}
blanchet@43085
   424
blanchet@43622
   425
(* Generate all pairs (sub, super) such that sub is a proper subclass of super
blanchet@43622
   426
   in theory "thy". *)
blanchet@43085
   427
fun class_pairs _ [] _ = []
blanchet@43085
   428
  | class_pairs thy subs supers =
blanchet@43085
   429
      let
blanchet@43085
   430
        val class_less = Sorts.class_less (Sign.classes_of thy)
blanchet@43085
   431
        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
blanchet@43085
   432
        fun add_supers sub = fold (add_super sub) supers
blanchet@43085
   433
      in fold add_supers subs [] end
blanchet@43085
   434
blanchet@43622
   435
fun make_class_rel_clause (sub, super) =
blanchet@43622
   436
  {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
blanchet@43086
   437
   superclass = `make_type_class super}
blanchet@43085
   438
blanchet@43085
   439
fun make_class_rel_clauses thy subs supers =
blanchet@43093
   440
  map make_class_rel_clause (class_pairs thy subs supers)
blanchet@43085
   441
blanchet@43859
   442
(* intermediate terms *)
blanchet@43859
   443
datatype iterm =
blanchet@43859
   444
  IConst of name * typ * typ list |
blanchet@43859
   445
  IVar of name * typ |
blanchet@43859
   446
  IApp of iterm * iterm |
blanchet@43859
   447
  IAbs of (name * typ) * iterm
blanchet@43085
   448
blanchet@43859
   449
fun ityp_of (IConst (_, T, _)) = T
blanchet@43859
   450
  | ityp_of (IVar (_, T)) = T
blanchet@43859
   451
  | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
blanchet@43859
   452
  | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
blanchet@43085
   453
blanchet@43085
   454
(*gets the head of a combinator application, along with the list of arguments*)
blanchet@43859
   455
fun strip_iterm_comb u =
blanchet@43496
   456
  let
blanchet@43859
   457
    fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
blanchet@43496
   458
      | stripc x = x
blanchet@43496
   459
  in stripc (u, []) end
blanchet@43085
   460
blanchet@43085
   461
fun atyps_of T = fold_atyps (insert (op =)) T []
blanchet@43085
   462
blanchet@43085
   463
fun new_skolem_const_name s num_T_args =
blanchet@43085
   464
  [new_skolem_const_prefix, s, string_of_int num_T_args]
blanchet@43085
   465
  |> space_implode Long_Name.separator
blanchet@43085
   466
blanchet@43859
   467
(* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
blanchet@43859
   468
   Also accumulates sort infomation. *)
blanchet@43859
   469
fun iterm_from_term thy bs (P $ Q) =
blanchet@43085
   470
    let
blanchet@43859
   471
      val (P', P_atomics_Ts) = iterm_from_term thy bs P
blanchet@43859
   472
      val (Q', Q_atomics_Ts) = iterm_from_term thy bs Q
blanchet@43859
   473
    in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
blanchet@43859
   474
  | iterm_from_term thy _ (Const (c, T)) =
blanchet@43907
   475
    (IConst (`make_fixed_const c, T,
blanchet@43907
   476
             if String.isPrefix old_skolem_const_prefix c then
blanchet@43907
   477
               [] |> Term.add_tvarsT T |> map TVar
blanchet@43907
   478
             else
blanchet@43907
   479
               (c, T) |> Sign.const_typargs thy),
blanchet@43907
   480
     atyps_of T)
blanchet@43907
   481
  | iterm_from_term _ _ (Free (s, T)) =
blanchet@43907
   482
    (IConst (`make_fixed_var s, T,
blanchet@43907
   483
             if String.isPrefix lambda_lifted_prefix s then [T] else []),
blanchet@43907
   484
     atyps_of T)
blanchet@43859
   485
  | iterm_from_term _ _ (Var (v as (s, _), T)) =
blanchet@43085
   486
    (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
blanchet@43085
   487
       let
blanchet@43085
   488
         val Ts = T |> strip_type |> swap |> op ::
blanchet@43085
   489
         val s' = new_skolem_const_name s (length Ts)
blanchet@43859
   490
       in IConst (`make_fixed_const s', T, Ts) end
blanchet@43085
   491
     else
blanchet@43859
   492
       IVar ((make_schematic_var v, s), T), atyps_of T)
blanchet@43859
   493
  | iterm_from_term _ bs (Bound j) =
blanchet@43859
   494
    nth bs j |> (fn (s, T) => (IConst (`make_bound_var s, T, []), atyps_of T))
blanchet@43859
   495
  | iterm_from_term thy bs (Abs (s, T, t)) =
nik@43678
   496
    let
nik@43678
   497
      fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
nik@43678
   498
      val s = vary s
blanchet@43859
   499
      val (tm, atomic_Ts) = iterm_from_term thy ((s, T) :: bs) t
nik@43678
   500
    in
blanchet@43859
   501
      (IAbs ((`make_bound_var s, T), tm),
nik@43677
   502
       union (op =) atomic_Ts (atyps_of T))
nik@43677
   503
    end
blanchet@43085
   504
blanchet@43421
   505
datatype locality =
blanchet@43421
   506
  General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
blanchet@43421
   507
  Chained
blanchet@43085
   508
blanchet@43085
   509
(* (quasi-)underapproximation of the truth *)
blanchet@43085
   510
fun is_locality_global Local = false
blanchet@43085
   511
  | is_locality_global Assum = false
blanchet@43085
   512
  | is_locality_global Chained = false
blanchet@43085
   513
  | is_locality_global _ = true
blanchet@43085
   514
blanchet@43624
   515
datatype order = First_Order | Higher_Order
blanchet@42613
   516
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
   517
datatype type_level =
blanchet@43362
   518
  All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
blanchet@43362
   519
  No_Types
blanchet@43128
   520
datatype type_heaviness = Heavyweight | Lightweight
blanchet@42613
   521
blanchet@43626
   522
datatype type_enc =
blanchet@43624
   523
  Simple_Types of order * type_level |
blanchet@42837
   524
  Preds of polymorphism * type_level * type_heaviness |
blanchet@42837
   525
  Tags of polymorphism * type_level * type_heaviness
blanchet@42613
   526
blanchet@42689
   527
fun try_unsuffixes ss s =
blanchet@42689
   528
  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
blanchet@42689
   529
blanchet@43626
   530
fun type_enc_from_string s =
blanchet@42722
   531
  (case try (unprefix "poly_") s of
blanchet@42722
   532
     SOME s => (SOME Polymorphic, s)
blanchet@42613
   533
   | NONE =>
blanchet@42613
   534
     case try (unprefix "mono_") s of
blanchet@42722
   535
       SOME s => (SOME Monomorphic, s)
blanchet@42722
   536
     | NONE =>
blanchet@42722
   537
       case try (unprefix "mangled_") s of
blanchet@42722
   538
         SOME s => (SOME Mangled_Monomorphic, s)
blanchet@42722
   539
       | NONE => (NONE, s))
blanchet@42613
   540
  ||> (fn s =>
blanchet@43624
   541
          (* "_query" and "_bang" are for the ASCII-challenged Metis and
blanchet@43624
   542
             Mirabelle. *)
blanchet@42689
   543
          case try_unsuffixes ["?", "_query"] s of
blanchet@43362
   544
            SOME s => (Noninf_Nonmono_Types, s)
blanchet@42613
   545
          | NONE =>
blanchet@42689
   546
            case try_unsuffixes ["!", "_bang"] s of
blanchet@43362
   547
              SOME s => (Fin_Nonmono_Types, s)
blanchet@42613
   548
            | NONE => (All_Types, s))
blanchet@42828
   549
  ||> apsnd (fn s =>
blanchet@42837
   550
                case try (unsuffix "_heavy") s of
blanchet@43128
   551
                  SOME s => (Heavyweight, s)
blanchet@43128
   552
                | NONE => (Lightweight, s))
blanchet@42837
   553
  |> (fn (poly, (level, (heaviness, core))) =>
blanchet@42837
   554
         case (core, (poly, level, heaviness)) of
blanchet@43624
   555
           ("simple", (NONE, _, Lightweight)) =>
blanchet@43624
   556
           Simple_Types (First_Order, level)
blanchet@43624
   557
         | ("simple_higher", (NONE, _, Lightweight)) =>
nik@43676
   558
           if level = Noninf_Nonmono_Types then raise Same.SAME
nik@43676
   559
           else Simple_Types (Higher_Order, level)
blanchet@42854
   560
         | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
blanchet@42886
   561
         | ("tags", (SOME Polymorphic, _, _)) =>
blanchet@43361
   562
           Tags (Polymorphic, level, heaviness)
blanchet@42854
   563
         | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
blanchet@43128
   564
         | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
blanchet@43128
   565
           Preds (poly, Const_Arg_Types, Lightweight)
blanchet@43128
   566
         | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
blanchet@43128
   567
           Preds (Polymorphic, No_Types, Lightweight)
blanchet@42753
   568
         | _ => raise Same.SAME)
blanchet@42753
   569
  handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
blanchet@42613
   570
blanchet@43626
   571
fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
blanchet@43626
   572
  | is_type_enc_higher_order _ = false
blanchet@43624
   573
blanchet@43626
   574
fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
blanchet@43626
   575
  | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
blanchet@43626
   576
  | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
blanchet@42613
   577
blanchet@43626
   578
fun level_of_type_enc (Simple_Types (_, level)) = level
blanchet@43626
   579
  | level_of_type_enc (Preds (_, level, _)) = level
blanchet@43626
   580
  | level_of_type_enc (Tags (_, level, _)) = level
blanchet@42828
   581
blanchet@43626
   582
fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
blanchet@43626
   583
  | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
blanchet@43626
   584
  | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
blanchet@42831
   585
blanchet@42687
   586
fun is_type_level_virtually_sound level =
blanchet@43362
   587
  level = All_Types orelse level = Noninf_Nonmono_Types
blanchet@43626
   588
val is_type_enc_virtually_sound =
blanchet@43626
   589
  is_type_level_virtually_sound o level_of_type_enc
blanchet@42613
   590
blanchet@42613
   591
fun is_type_level_fairly_sound level =
blanchet@43362
   592
  is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
blanchet@43626
   593
val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
blanchet@42613
   594
blanchet@43624
   595
fun choose_format formats (Simple_Types (order, level)) =
blanchet@43624
   596
    if member (op =) formats THF then
blanchet@43624
   597
      (THF, Simple_Types (order, level))
blanchet@43624
   598
    else if member (op =) formats TFF then
blanchet@43624
   599
      (TFF, Simple_Types (First_Order, level))
blanchet@43624
   600
    else
blanchet@43624
   601
      choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
blanchet@43626
   602
  | choose_format formats type_enc =
blanchet@43101
   603
    (case hd formats of
blanchet@43101
   604
       CNF_UEQ =>
blanchet@43626
   605
       (CNF_UEQ, case type_enc of
blanchet@43101
   606
                   Preds stuff =>
blanchet@43626
   607
                   (if is_type_enc_fairly_sound type_enc then Tags else Preds)
blanchet@43101
   608
                       stuff
blanchet@43626
   609
                 | _ => type_enc)
blanchet@43626
   610
     | format => (format, type_enc))
blanchet@43101
   611
blanchet@40114
   612
type translated_formula =
blanchet@43496
   613
  {name : string,
blanchet@43496
   614
   locality : locality,
blanchet@43496
   615
   kind : formula_kind,
blanchet@43859
   616
   iformula : (name, typ, iterm) formula,
blanchet@43496
   617
   atomic_types : typ list}
blanchet@38282
   618
blanchet@43859
   619
fun update_iformula f ({name, locality, kind, iformula, atomic_types}
blanchet@43859
   620
                       : translated_formula) =
blanchet@43859
   621
  {name = name, locality = locality, kind = kind, iformula = f iformula,
blanchet@42562
   622
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   623
blanchet@43859
   624
fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
blanchet@42558
   625
blanchet@43064
   626
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@43064
   627
blanchet@43064
   628
fun insert_type ctxt get_T x xs =
blanchet@43064
   629
  let val T = get_T x in
blanchet@43064
   630
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@43064
   631
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@43064
   632
  end
blanchet@42677
   633
blanchet@42753
   634
(* The Booleans indicate whether all type arguments should be kept. *)
blanchet@42753
   635
datatype type_arg_policy =
blanchet@42753
   636
  Explicit_Type_Args of bool |
blanchet@42753
   637
  Mangled_Type_Args of bool |
blanchet@42753
   638
  No_Type_Args
blanchet@41136
   639
blanchet@42836
   640
fun should_drop_arg_type_args (Simple_Types _) =
blanchet@42836
   641
    false (* since TFF doesn't support overloading *)
blanchet@43626
   642
  | should_drop_arg_type_args type_enc =
blanchet@43626
   643
    level_of_type_enc type_enc = All_Types andalso
blanchet@43626
   644
    heaviness_of_type_enc type_enc = Heavyweight
blanchet@42831
   645
blanchet@43626
   646
fun type_arg_policy type_enc s =
blanchet@43628
   647
  if s = type_tag_name then
blanchet@43626
   648
    (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
blanchet@43623
   649
       Mangled_Type_Args
blanchet@43623
   650
     else
blanchet@43623
   651
       Explicit_Type_Args) false
blanchet@43628
   652
  else case type_enc of
blanchet@43628
   653
    Tags (_, All_Types, Heavyweight) => No_Type_Args
blanchet@43628
   654
  | _ =>
blanchet@43628
   655
    if level_of_type_enc type_enc = No_Types orelse
blanchet@43628
   656
       s = @{const_name HOL.eq} orelse
blanchet@43628
   657
       (s = app_op_name andalso
blanchet@43628
   658
        level_of_type_enc type_enc = Const_Arg_Types) then
blanchet@43628
   659
      No_Type_Args
blanchet@43628
   660
    else
blanchet@43628
   661
      should_drop_arg_type_args type_enc
blanchet@43628
   662
      |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
blanchet@43628
   663
            Mangled_Type_Args
blanchet@43628
   664
          else
blanchet@43628
   665
            Explicit_Type_Args)
blanchet@42227
   666
blanchet@43628
   667
(* Make literals for sorted type variables. *)
blanchet@43263
   668
fun generic_add_sorts_on_type (_, []) = I
blanchet@43263
   669
  | generic_add_sorts_on_type ((x, i), s :: ss) =
blanchet@43263
   670
    generic_add_sorts_on_type ((x, i), ss)
blanchet@43263
   671
    #> (if s = the_single @{sort HOL.type} then
blanchet@43093
   672
          I
blanchet@43093
   673
        else if i = ~1 then
blanchet@43263
   674
          insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
blanchet@43093
   675
        else
blanchet@43263
   676
          insert (op =) (TyLitVar (`make_type_class s,
blanchet@43263
   677
                                   (make_schematic_type_var (x, i), x))))
blanchet@43263
   678
fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
blanchet@43263
   679
  | add_sorts_on_tfree _ = I
blanchet@43263
   680
fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
blanchet@43263
   681
  | add_sorts_on_tvar _ = I
blanchet@43085
   682
blanchet@43626
   683
fun type_literals_for_types type_enc add_sorts_on_typ Ts =
blanchet@43626
   684
  [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
blanchet@41137
   685
blanchet@42534
   686
fun mk_aconns c phis =
blanchet@42534
   687
  let val (phis', phi') = split_last phis in
blanchet@42534
   688
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   689
  end
blanchet@38282
   690
fun mk_ahorn [] phi = phi
blanchet@42534
   691
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   692
fun mk_aquant _ [] phi = phi
blanchet@42522
   693
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   694
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   695
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   696
blanchet@42522
   697
fun close_universally atom_vars phi =
blanchet@41145
   698
  let
blanchet@41145
   699
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   700
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   701
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   702
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   703
        union (op =) (atom_vars tm []
blanchet@42526
   704
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   705
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   706
blanchet@43859
   707
fun iterm_vars (IApp (tm1, tm2)) = fold iterm_vars [tm1, tm2]
blanchet@43859
   708
  | iterm_vars (IConst _) = I
blanchet@43859
   709
  | iterm_vars (IVar (name, T)) = insert (op =) (name, SOME T)
blanchet@43859
   710
  | iterm_vars (IAbs (_, tm)) = iterm_vars tm
blanchet@43859
   711
fun close_iformula_universally phi = close_universally iterm_vars phi
blanchet@42522
   712
nik@43676
   713
fun term_vars bounds (ATerm (name as (s, _), tms)) =
nik@43676
   714
    (is_tptp_variable s andalso not (member (op =) bounds name))
nik@43676
   715
    ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
nik@43676
   716
  | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
nik@43676
   717
fun close_formula_universally phi = close_universally (term_vars []) phi
blanchet@41145
   718
blanchet@42994
   719
val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
blanchet@42994
   720
val homo_infinite_type = Type (homo_infinite_type_name, [])
blanchet@42994
   721
nik@43676
   722
fun ho_term_from_typ format type_enc =
blanchet@42994
   723
  let
blanchet@42994
   724
    fun term (Type (s, Ts)) =
blanchet@43626
   725
      ATerm (case (is_type_enc_higher_order type_enc, s) of
blanchet@42994
   726
               (true, @{type_name bool}) => `I tptp_bool_type
blanchet@42994
   727
             | (true, @{type_name fun}) => `I tptp_fun_type
blanchet@43178
   728
             | _ => if s = homo_infinite_type_name andalso
blanchet@43178
   729
                       (format = TFF orelse format = THF) then
blanchet@43178
   730
                      `I tptp_individual_type
blanchet@43178
   731
                    else
blanchet@43178
   732
                      `make_fixed_type_const s,
blanchet@42994
   733
             map term Ts)
blanchet@42994
   734
    | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
blanchet@42994
   735
    | term (TVar ((x as (s, _)), _)) =
blanchet@42994
   736
      ATerm ((make_schematic_type_var x, s), [])
blanchet@42994
   737
  in term end
blanchet@42562
   738
nik@43676
   739
fun ho_term_for_type_arg format type_enc T =
nik@43676
   740
  if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
blanchet@43401
   741
blanchet@42562
   742
(* This shouldn't clash with anything else. *)
blanchet@42542
   743
val mangled_type_sep = "\000"
blanchet@42542
   744
blanchet@42562
   745
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   746
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42761
   747
    f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
blanchet@42761
   748
    ^ ")"
blanchet@43692
   749
  | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
blanchet@42542
   750
blanchet@42998
   751
val bool_atype = AType (`I tptp_bool_type)
blanchet@42998
   752
blanchet@43085
   753
fun make_simple_type s =
blanchet@43085
   754
  if s = tptp_bool_type orelse s = tptp_fun_type orelse
blanchet@43085
   755
     s = tptp_individual_type then
blanchet@43085
   756
    s
blanchet@43085
   757
  else
blanchet@43085
   758
    simple_type_prefix ^ ascii_of s
blanchet@43085
   759
nik@43676
   760
fun ho_type_from_ho_term type_enc pred_sym ary =
blanchet@42963
   761
  let
blanchet@42963
   762
    fun to_atype ty =
blanchet@42963
   763
      AType ((make_simple_type (generic_mangled_type_name fst ty),
blanchet@42963
   764
              generic_mangled_type_name snd ty))
blanchet@42963
   765
    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
blanchet@42998
   766
    fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
blanchet@42994
   767
      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
blanchet@43692
   768
      | to_fo _ _ = raise Fail "unexpected type abstraction"
blanchet@42994
   769
    fun to_ho (ty as ATerm ((s, _), tys)) =
nik@43676
   770
        if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
nik@43676
   771
      | to_ho _ = raise Fail "unexpected type abstraction"
blanchet@43626
   772
  in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
blanchet@42963
   773
nik@43677
   774
fun ho_type_from_typ format type_enc pred_sym ary =
nik@43676
   775
  ho_type_from_ho_term type_enc pred_sym ary
nik@43676
   776
  o ho_term_from_typ format type_enc
blanchet@42963
   777
blanchet@43626
   778
fun mangled_const_name format type_enc T_args (s, s') =
blanchet@42963
   779
  let
nik@43676
   780
    val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
blanchet@42963
   781
    fun type_suffix f g =
blanchet@42963
   782
      fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42963
   783
                o generic_mangled_type_name f) ty_args ""
blanchet@42963
   784
  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@42542
   785
blanchet@42542
   786
val parse_mangled_ident =
blanchet@42542
   787
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   788
blanchet@42542
   789
fun parse_mangled_type x =
blanchet@42542
   790
  (parse_mangled_ident
blanchet@42542
   791
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   792
                    [] >> ATerm) x
blanchet@42542
   793
and parse_mangled_types x =
blanchet@42542
   794
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   795
blanchet@42542
   796
fun unmangled_type s =
blanchet@42542
   797
  s |> suffix ")" |> raw_explode
blanchet@42542
   798
    |> Scan.finite Symbol.stopper
blanchet@42542
   799
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   800
                                                quote s)) parse_mangled_type))
blanchet@42542
   801
    |> fst
blanchet@42542
   802
blanchet@42561
   803
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   804
fun unmangled_const s =
blanchet@42542
   805
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   806
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   807
  end
blanchet@42542
   808
blanchet@43626
   809
fun introduce_proxies type_enc =
blanchet@42568
   810
  let
blanchet@43859
   811
    fun intro top_level (IApp (tm1, tm2)) =
blanchet@43859
   812
        IApp (intro top_level tm1, intro false tm2)
blanchet@43859
   813
      | intro top_level (IConst (name as (s, _), T, T_args)) =
blanchet@42570
   814
        (case proxify_const s of
blanchet@43159
   815
           SOME proxy_base =>
blanchet@43626
   816
           if top_level orelse is_type_enc_higher_order type_enc then
blanchet@43000
   817
             case (top_level, s) of
blanchet@43000
   818
               (_, "c_False") => (`I tptp_false, [])
blanchet@43000
   819
             | (_, "c_True") => (`I tptp_true, [])
blanchet@43000
   820
             | (false, "c_Not") => (`I tptp_not, [])
blanchet@43000
   821
             | (false, "c_conj") => (`I tptp_and, [])
blanchet@43000
   822
             | (false, "c_disj") => (`I tptp_or, [])
blanchet@43000
   823
             | (false, "c_implies") => (`I tptp_implies, [])
nik@43678
   824
             | (false, "c_All") => (`I tptp_ho_forall, [])
nik@43678
   825
             | (false, "c_Ex") => (`I tptp_ho_exists, [])
blanchet@43000
   826
             | (false, s) =>
blanchet@43017
   827
               if is_tptp_equal s then (`I tptp_equal, [])
blanchet@43017
   828
               else (proxy_base |>> prefix const_prefix, T_args)
blanchet@43000
   829
             | _ => (name, [])
blanchet@42569
   830
           else
blanchet@42574
   831
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   832
          | NONE => (name, T_args))
blanchet@43859
   833
        |> (fn (name, T_args) => IConst (name, T, T_args))
blanchet@43859
   834
      | intro _ (IAbs (bound, tm)) = IAbs (bound, intro false tm)
blanchet@43017
   835
      | intro _ tm = tm
blanchet@43017
   836
  in intro true end
blanchet@42568
   837
blanchet@43859
   838
fun iformula_from_prop thy type_enc eq_as_iff =
blanchet@38282
   839
  let
blanchet@42568
   840
    fun do_term bs t atomic_types =
blanchet@43859
   841
      iterm_from_term thy bs (Envir.eta_contract t)
blanchet@43626
   842
      |>> (introduce_proxies type_enc #> AAtom)
blanchet@42568
   843
      ||> union (op =) atomic_types
blanchet@38282
   844
    fun do_quant bs q s T t' =
wenzelm@43324
   845
      let val s = singleton (Name.variant_list (map fst bs)) s in
blanchet@38518
   846
        do_formula ((s, T) :: bs) t'
blanchet@42562
   847
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   848
      end
blanchet@38282
   849
    and do_conn bs c t1 t2 =
blanchet@43198
   850
      do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
blanchet@38282
   851
    and do_formula bs t =
blanchet@38282
   852
      case t of
blanchet@43096
   853
        @{const Trueprop} $ t1 => do_formula bs t1
blanchet@43096
   854
      | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   855
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   856
        do_quant bs AForall s T t'
blanchet@38282
   857
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   858
        do_quant bs AExists s T t'
haftmann@38795
   859
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   860
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   861
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   862
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   863
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   864
      | _ => do_term bs t
blanchet@38282
   865
  in do_formula [] end
blanchet@38282
   866
blanchet@43264
   867
fun presimplify_term _ [] t = t
blanchet@43264
   868
  | presimplify_term ctxt presimp_consts t =
blanchet@43264
   869
    t |> exists_Const (member (op =) presimp_consts o fst) t
blanchet@43264
   870
         ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@43264
   871
            #> Meson.presimplify ctxt
blanchet@43264
   872
            #> prop_of)
blanchet@38282
   873
blanchet@43863
   874
fun concealed_bound_name j = atp_weak_prefix ^ string_of_int j
blanchet@38282
   875
fun conceal_bounds Ts t =
blanchet@38282
   876
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   877
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   878
fun reveal_bounds Ts =
blanchet@38282
   879
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   880
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   881
blanchet@43265
   882
fun is_fun_equality (@{const_name HOL.eq},
blanchet@43265
   883
                     Type (_, [Type (@{type_name fun}, _), _])) = true
blanchet@43265
   884
  | is_fun_equality _ = false
blanchet@43265
   885
blanchet@42747
   886
fun extensionalize_term ctxt t =
blanchet@43265
   887
  if exists_Const is_fun_equality t then
blanchet@43265
   888
    let val thy = Proof_Context.theory_of ctxt in
blanchet@43265
   889
      t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@43265
   890
        |> prop_of |> Logic.dest_equals |> snd
blanchet@43265
   891
    end
blanchet@43265
   892
  else
blanchet@43265
   893
    t
blanchet@38608
   894
blanchet@43862
   895
fun simple_translate_lambdas do_lambdas ctxt t =
blanchet@43863
   896
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43863
   897
    if Meson.is_fol_term thy t then
blanchet@43863
   898
      t
blanchet@43863
   899
    else
blanchet@43863
   900
      let
blanchet@43863
   901
        fun aux Ts t =
blanchet@43863
   902
          case t of
blanchet@43863
   903
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@43863
   904
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@43863
   905
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@43863
   906
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@43863
   907
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@43863
   908
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@43863
   909
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@43863
   910
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@43863
   911
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@43863
   912
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
   913
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
   914
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
   915
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@43863
   916
              $ t1 $ t2 =>
blanchet@43863
   917
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
   918
          | _ =>
blanchet@43863
   919
            if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
blanchet@43863
   920
            else t |> Envir.eta_contract |> do_lambdas ctxt Ts
blanchet@43863
   921
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@43863
   922
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@43863
   923
  end
blanchet@43856
   924
blanchet@43856
   925
fun do_conceal_lambdas Ts (t1 $ t2) =
blanchet@43856
   926
    do_conceal_lambdas Ts t1 $ do_conceal_lambdas Ts t2
blanchet@43856
   927
  | do_conceal_lambdas Ts (Abs (_, T, t)) =
blanchet@43828
   928
    (* slightly unsound because of hash collisions *)
blanchet@43827
   929
    Free (concealed_lambda_prefix ^ string_of_int (hash_term t),
blanchet@43827
   930
          T --> fastype_of1 (Ts, t))
blanchet@43856
   931
  | do_conceal_lambdas _ t = t
blanchet@43862
   932
val conceal_lambdas = simple_translate_lambdas (K do_conceal_lambdas)
blanchet@43856
   933
blanchet@43862
   934
fun do_introduce_combinators ctxt Ts t =
wenzelm@42361
   935
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43905
   936
    t |> conceal_bounds Ts
blanchet@43905
   937
      |> cterm_of thy
blanchet@43905
   938
      |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@43905
   939
      |> prop_of |> Logic.dest_equals |> snd
blanchet@43905
   940
      |> reveal_bounds Ts
blanchet@38491
   941
  end
blanchet@43862
   942
  (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@43864
   943
  handle THM _ => t |> do_conceal_lambdas Ts
blanchet@43862
   944
val introduce_combinators = simple_translate_lambdas do_introduce_combinators
blanchet@43862
   945
blanchet@43864
   946
fun preprocess_abstractions_in_terms trans_lambdas facts =
blanchet@43862
   947
  let
blanchet@43863
   948
    val (facts, lambda_ts) =
blanchet@43863
   949
      facts |> map (snd o snd) |> trans_lambdas 
blanchet@43863
   950
            |>> map2 (fn (name, (kind, _)) => fn t => (name, (kind, t))) facts
blanchet@43863
   951
    val lambda_facts =
blanchet@43863
   952
      map2 (fn t => fn j =>
blanchet@43863
   953
               ((lambda_fact_prefix ^ Int.toString j, Helper), (Axiom, t)))
blanchet@43863
   954
           lambda_ts (1 upto length lambda_ts)
blanchet@43863
   955
  in (facts, lambda_facts) end
blanchet@38282
   956
blanchet@38282
   957
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   958
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   959
fun freeze_term t =
blanchet@38282
   960
  let
blanchet@38282
   961
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   962
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   963
      | aux (Var ((s, i), T)) =
blanchet@43863
   964
        Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   965
      | aux t = t
blanchet@38282
   966
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   967
blanchet@43863
   968
fun presimp_prop ctxt presimp_consts t =
blanchet@38282
   969
  let
wenzelm@42361
   970
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   971
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   972
              |> transform_elim_prop
blanchet@41211
   973
              |> Object_Logic.atomize_term thy
blanchet@42563
   974
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@43096
   975
  in
blanchet@43096
   976
    t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@43096
   977
      |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
blanchet@43096
   978
      |> extensionalize_term ctxt
blanchet@43264
   979
      |> presimplify_term ctxt presimp_consts
blanchet@43120
   980
      |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@43096
   981
  end
blanchet@43096
   982
blanchet@43096
   983
(* making fact and conjecture formulas *)
blanchet@43626
   984
fun make_formula thy type_enc eq_as_iff name loc kind t =
blanchet@43096
   985
  let
blanchet@43859
   986
    val (iformula, atomic_types) =
blanchet@43859
   987
      iformula_from_prop thy type_enc eq_as_iff t []
blanchet@38282
   988
  in
blanchet@43859
   989
    {name = name, locality = loc, kind = kind, iformula = iformula,
blanchet@42562
   990
     atomic_types = atomic_types}
blanchet@38282
   991
  end
blanchet@38282
   992
blanchet@43860
   993
fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) =
blanchet@43096
   994
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43860
   995
    case t |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
blanchet@43624
   996
                           loc Axiom of
blanchet@43859
   997
      formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
blanchet@43096
   998
      if s = tptp_true then NONE else SOME formula
blanchet@43295
   999
    | formula => SOME formula
blanchet@43096
  1000
  end
blanchet@42561
  1001
blanchet@43860
  1002
fun make_conjecture ctxt format type_enc ps =
blanchet@43096
  1003
  let
blanchet@43096
  1004
    val thy = Proof_Context.theory_of ctxt
blanchet@43860
  1005
    val last = length ps - 1
blanchet@43096
  1006
  in
blanchet@43863
  1007
    map2 (fn j => fn ((name, loc), (kind, t)) =>
blanchet@43863
  1008
             t |> make_formula thy type_enc (format <> CNF) name loc kind
blanchet@43860
  1009
               |> (j <> last) = (kind = Conjecture) ? update_iformula mk_anot)
blanchet@43860
  1010
         (0 upto last) ps
blanchet@38613
  1011
  end
blanchet@38282
  1012
blanchet@42682
  1013
(** Finite and infinite type inference **)
blanchet@42682
  1014
blanchet@42886
  1015
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
  1016
  | deep_freeze_atyp T = T
blanchet@42886
  1017
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
  1018
blanchet@42682
  1019
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
  1020
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
  1021
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
  1022
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
  1023
blanchet@42886
  1024
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
  1025
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
  1026
  | should_encode_type _ _ All_Types _ = true
blanchet@43572
  1027
  | should_encode_type ctxt _ Fin_Nonmono_Types T =
blanchet@43572
  1028
    is_type_surely_finite ctxt false T
blanchet@42682
  1029
  | should_encode_type _ _ _ _ = false
blanchet@42682
  1030
blanchet@42837
  1031
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
  1032
                             should_predicate_on_var T =
blanchet@43128
  1033
    (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
blanchet@42878
  1034
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
  1035
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
  1036
blanchet@43859
  1037
fun is_var_or_bound_var (IConst ((s, _), _, _)) =
blanchet@42836
  1038
    String.isPrefix bound_var_prefix s
blanchet@43859
  1039
  | is_var_or_bound_var (IVar _) = true
blanchet@42836
  1040
  | is_var_or_bound_var _ = false
blanchet@42836
  1041
blanchet@43361
  1042
datatype tag_site =
blanchet@43361
  1043
  Top_Level of bool option |
blanchet@43361
  1044
  Eq_Arg of bool option |
blanchet@43361
  1045
  Elsewhere
blanchet@42829
  1046
blanchet@43361
  1047
fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
blanchet@43361
  1048
  | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
blanchet@43361
  1049
                         u T =
blanchet@42837
  1050
    (case heaviness of
blanchet@43128
  1051
       Heavyweight => should_encode_type ctxt nonmono_Ts level T
blanchet@43128
  1052
     | Lightweight =>
blanchet@42836
  1053
       case (site, is_var_or_bound_var u) of
blanchet@43361
  1054
         (Eq_Arg pos, true) =>
blanchet@43361
  1055
         (* The first disjunct prevents a subtle soundness issue explained in
blanchet@43361
  1056
            Blanchette's Ph.D. thesis. See also
blanchet@43361
  1057
            "formula_lines_for_lightweight_tags_sym_decl". *)
blanchet@43361
  1058
         (pos <> SOME false andalso poly = Polymorphic andalso
blanchet@43361
  1059
          level <> All_Types andalso heaviness = Lightweight andalso
blanchet@43361
  1060
          exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
blanchet@43361
  1061
         should_encode_type ctxt nonmono_Ts level T
blanchet@42829
  1062
       | _ => false)
blanchet@42829
  1063
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
  1064
blanchet@42994
  1065
fun homogenized_type ctxt nonmono_Ts level =
blanchet@42994
  1066
  let
blanchet@42994
  1067
    val should_encode = should_encode_type ctxt nonmono_Ts level
blanchet@42994
  1068
    fun homo 0 T = if should_encode T then T else homo_infinite_type
blanchet@42994
  1069
      | homo ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@42994
  1070
        homo 0 T1 --> homo (ary - 1) T2
blanchet@42994
  1071
      | homo _ _ = raise Fail "expected function type"
blanchet@42994
  1072
  in homo end
blanchet@42682
  1073
blanchet@42573
  1074
(** "hBOOL" and "hAPP" **)
blanchet@41313
  1075
blanchet@42574
  1076
type sym_info =
blanchet@43064
  1077
  {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
blanchet@42563
  1078
blanchet@43859
  1079
fun add_iterm_syms_to_table ctxt explicit_apply =
blanchet@42558
  1080
  let
blanchet@43064
  1081
    fun consider_var_arity const_T var_T max_ary =
blanchet@43064
  1082
      let
blanchet@43064
  1083
        fun iter ary T =
blanchet@43210
  1084
          if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
blanchet@43210
  1085
             type_instance ctxt (T, var_T) then
blanchet@43210
  1086
            ary
blanchet@43210
  1087
          else
blanchet@43210
  1088
            iter (ary + 1) (range_type T)
blanchet@43064
  1089
      in iter 0 const_T end
blanchet@43201
  1090
    fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@43201
  1091
      if explicit_apply = NONE andalso
blanchet@43201
  1092
         (can dest_funT T orelse T = @{typ bool}) then
blanchet@43201
  1093
        let
blanchet@43201
  1094
          val bool_vars' = bool_vars orelse body_type T = @{typ bool}
blanchet@43201
  1095
          fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
blanchet@43201
  1096
            {pred_sym = pred_sym andalso not bool_vars',
blanchet@43213
  1097
             min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
blanchet@43201
  1098
             max_ary = max_ary, types = types}
blanchet@43201
  1099
          val fun_var_Ts' =
blanchet@43201
  1100
            fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
blanchet@43201
  1101
        in
blanchet@43201
  1102
          if bool_vars' = bool_vars andalso
blanchet@43201
  1103
             pointer_eq (fun_var_Ts', fun_var_Ts) then
blanchet@43201
  1104
            accum
blanchet@43167
  1105
          else
blanchet@43213
  1106
            ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
blanchet@43201
  1107
        end
blanchet@43201
  1108
      else
blanchet@43201
  1109
        accum
blanchet@43201
  1110
    fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@43859
  1111
      let val (head, args) = strip_iterm_comb tm in
blanchet@42558
  1112
        (case head of
blanchet@43859
  1113
           IConst ((s, _), T, _) =>
blanchet@42558
  1114
           if String.isPrefix bound_var_prefix s then
blanchet@43201
  1115
             add_var_or_bound_var T accum
blanchet@42558
  1116
           else
blanchet@43139
  1117
             let val ary = length args in
blanchet@43201
  1118
               ((bool_vars, fun_var_Ts),
blanchet@43064
  1119
                case Symtab.lookup sym_tab s of
blanchet@43064
  1120
                  SOME {pred_sym, min_ary, max_ary, types} =>
blanchet@43064
  1121
                  let
blanchet@43201
  1122
                    val pred_sym =
blanchet@43201
  1123
                      pred_sym andalso top_level andalso not bool_vars
blanchet@43064
  1124
                    val types' = types |> insert_type ctxt I T
blanchet@43064
  1125
                    val min_ary =
blanchet@43064
  1126
                      if is_some explicit_apply orelse
blanchet@43064
  1127
                         pointer_eq (types', types) then
blanchet@43064
  1128
                        min_ary
blanchet@43064
  1129
                      else
blanchet@43201
  1130
                        fold (consider_var_arity T) fun_var_Ts min_ary
blanchet@43064
  1131
                  in
blanchet@43201
  1132
                    Symtab.update (s, {pred_sym = pred_sym,
blanchet@43064
  1133
                                       min_ary = Int.min (ary, min_ary),
blanchet@43064
  1134
                                       max_ary = Int.max (ary, max_ary),
blanchet@43064
  1135
                                       types = types'})
blanchet@43064
  1136
                                  sym_tab
blanchet@43064
  1137
                  end
blanchet@43064
  1138
                | NONE =>
blanchet@43064
  1139
                  let
blanchet@43201
  1140
                    val pred_sym = top_level andalso not bool_vars
blanchet@43064
  1141
                    val min_ary =
blanchet@43064
  1142
                      case explicit_apply of
blanchet@43064
  1143
                        SOME true => 0
blanchet@43064
  1144
                      | SOME false => ary
blanchet@43201
  1145
                      | NONE => fold (consider_var_arity T) fun_var_Ts ary
blanchet@43064
  1146
                  in
blanchet@43201
  1147
                    Symtab.update_new (s, {pred_sym = pred_sym,
blanchet@43064
  1148
                                           min_ary = min_ary, max_ary = ary,
blanchet@43064
  1149
                                           types = [T]})
blanchet@43064
  1150
                                      sym_tab
blanchet@43064
  1151
                  end)
blanchet@43064
  1152
             end
blanchet@43859
  1153
         | IVar (_, T) => add_var_or_bound_var T accum
blanchet@43859
  1154
         | IAbs ((_, T), tm) => accum |> add_var_or_bound_var T |> add false tm
blanchet@43064
  1155
         | _ => accum)
blanchet@43064
  1156
        |> fold (add false) args
blanchet@42558
  1157
      end
blanchet@43064
  1158
  in add true end
blanchet@43064
  1159
fun add_fact_syms_to_table ctxt explicit_apply =
blanchet@43064
  1160
  fact_lift (formula_fold NONE
blanchet@43859
  1161
                          (K (add_iterm_syms_to_table ctxt explicit_apply)))
blanchet@38282
  1162
blanchet@43139
  1163
val default_sym_tab_entries : (string * sym_info) list =
blanchet@43174
  1164
  (prefixed_predicator_name,
blanchet@43139
  1165
   {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
blanchet@42568
  1166
  ([tptp_false, tptp_true]
blanchet@43139
  1167
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
blanchet@43139
  1168
  ([tptp_equal, tptp_old_equal]
blanchet@43139
  1169
   |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
blanchet@41140
  1170
blanchet@43064
  1171
fun sym_table_for_facts ctxt explicit_apply facts =
blanchet@43201
  1172
  ((false, []), Symtab.empty)
blanchet@43201
  1173
  |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
blanchet@43139
  1174
  |> fold Symtab.update default_sym_tab_entries
blanchet@38282
  1175
blanchet@42558
  1176
fun min_arity_of sym_tab s =
blanchet@42558
  1177
  case Symtab.lookup sym_tab s of
blanchet@42574
  1178
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
  1179
  | NONE =>
blanchet@42558
  1180
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
  1181
      SOME s =>
blanchet@42570
  1182
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
  1183
        if s = predicator_name then 1
blanchet@42966
  1184
        else if s = app_op_name then 2
blanchet@42966
  1185
        else if s = type_pred_name then 1
blanchet@42557
  1186
        else 0
blanchet@42547
  1187
      end
blanchet@42544
  1188
    | NONE => 0
blanchet@38282
  1189
blanchet@38282
  1190
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
  1191
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
  1192
   type instantiations). If false, the constant always receives all of its
blanchet@38282
  1193
   arguments and is used as a predicate. *)
blanchet@42558
  1194
fun is_pred_sym sym_tab s =
blanchet@42558
  1195
  case Symtab.lookup sym_tab s of
blanchet@42574
  1196
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
  1197
    pred_sym andalso min_ary = max_ary
blanchet@42558
  1198
  | NONE => false
blanchet@38282
  1199
blanchet@42568
  1200
val predicator_combconst =
blanchet@43859
  1201
  IConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
blanchet@43859
  1202
fun predicator tm = IApp (predicator_combconst, tm)
blanchet@42542
  1203
blanchet@43859
  1204
fun introduce_predicators_in_iterm sym_tab tm =
blanchet@43859
  1205
  case strip_iterm_comb tm of
blanchet@43859
  1206
    (IConst ((s, _), _, _), _) =>
blanchet@42568
  1207
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
  1208
  | _ => predicator tm
blanchet@42542
  1209
blanchet@43859
  1210
fun list_app head args = fold (curry (IApp o swap)) args head
blanchet@42544
  1211
blanchet@43130
  1212
val app_op = `make_fixed_const app_op_name
blanchet@43130
  1213
blanchet@42544
  1214
fun explicit_app arg head =
blanchet@42544
  1215
  let
blanchet@43859
  1216
    val head_T = ityp_of head
blanchet@42693
  1217
    val (arg_T, res_T) = dest_funT head_T
blanchet@43859
  1218
    val explicit_app = IConst (app_op, head_T --> head_T, [arg_T, res_T])
blanchet@42544
  1219
  in list_app explicit_app [head, arg] end
blanchet@42544
  1220
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
  1221
blanchet@43859
  1222
fun introduce_explicit_apps_in_iterm sym_tab =
blanchet@42544
  1223
  let
blanchet@42544
  1224
    fun aux tm =
blanchet@43859
  1225
      case strip_iterm_comb tm of
blanchet@43859
  1226
        (head as IConst ((s, _), _, _), args) =>
blanchet@42544
  1227
        args |> map aux
blanchet@42557
  1228
             |> chop (min_arity_of sym_tab s)
blanchet@42544
  1229
             |>> list_app head
blanchet@42544
  1230
             |-> list_explicit_app
blanchet@42544
  1231
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
  1232
  in aux end
blanchet@38282
  1233
blanchet@42753
  1234
fun chop_fun 0 T = ([], T)
blanchet@42753
  1235
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
  1236
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
  1237
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
  1238
blanchet@42780
  1239
fun filter_type_args _ _ _ [] = []
blanchet@42780
  1240
  | filter_type_args thy s arity T_args =
blanchet@42834
  1241
    let
blanchet@42834
  1242
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42966
  1243
      val U = if s = app_op_name then
blanchet@42834
  1244
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
  1245
              else
blanchet@42834
  1246
                s |> Sign.the_const_type thy
blanchet@42834
  1247
    in
blanchet@42781
  1248
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
  1249
        [] => []
blanchet@42781
  1250
      | res_U_vars =>
blanchet@42781
  1251
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
  1252
          U_args ~~ T_args
blanchet@43401
  1253
          |> map (fn (U, T) =>
blanchet@43401
  1254
                     if member (op =) res_U_vars (dest_TVar U) then T
blanchet@43401
  1255
                     else dummyT)
blanchet@42781
  1256
        end
blanchet@42780
  1257
    end
blanchet@42780
  1258
    handle TYPE _ => T_args
blanchet@42753
  1259
blanchet@43859
  1260
fun enforce_type_arg_policy_in_iterm ctxt format type_enc =
blanchet@42753
  1261
  let
blanchet@42753
  1262
    val thy = Proof_Context.theory_of ctxt
blanchet@43859
  1263
    fun aux arity (IApp (tm1, tm2)) = IApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@43859
  1264
      | aux arity (IConst (name as (s, _), T, T_args)) =
blanchet@43179
  1265
        (case strip_prefix_and_unascii const_prefix s of
blanchet@43179
  1266
           NONE => (name, T_args)
blanchet@43179
  1267
         | SOME s'' =>
blanchet@43179
  1268
           let
blanchet@43179
  1269
             val s'' = invert_const s''
blanchet@43179
  1270
             fun filtered_T_args false = T_args
blanchet@43179
  1271
               | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@43179
  1272
           in
blanchet@43626
  1273
             case type_arg_policy type_enc s'' of
blanchet@43179
  1274
               Explicit_Type_Args drop_args =>
blanchet@43179
  1275
               (name, filtered_T_args drop_args)
blanchet@43179
  1276
             | Mangled_Type_Args drop_args =>
blanchet@43626
  1277
               (mangled_const_name format type_enc (filtered_T_args drop_args)
blanchet@43179
  1278
                                   name, [])
blanchet@43179
  1279
             | No_Type_Args => (name, [])
blanchet@43179
  1280
           end)
blanchet@43859
  1281
        |> (fn (name, T_args) => IConst (name, T, T_args))
blanchet@43859
  1282
      | aux _ (IAbs (bound, tm)) = IAbs (bound, aux 0 tm)
blanchet@42753
  1283
      | aux _ tm = tm
blanchet@42753
  1284
  in aux 0 end
blanchet@42573
  1285
blanchet@43859
  1286
fun repair_iterm ctxt format type_enc sym_tab =
blanchet@43626
  1287
  not (is_type_enc_higher_order type_enc)
blanchet@43859
  1288
  ? (introduce_explicit_apps_in_iterm sym_tab
blanchet@43859
  1289
     #> introduce_predicators_in_iterm sym_tab)
blanchet@43859
  1290
  #> enforce_type_arg_policy_in_iterm ctxt format type_enc
blanchet@43626
  1291
fun repair_fact ctxt format type_enc sym_tab =
blanchet@43859
  1292
  update_iformula (formula_map (repair_iterm ctxt format type_enc sym_tab))
blanchet@42573
  1293
blanchet@42573
  1294
(** Helper facts **)
blanchet@42573
  1295
blanchet@43194
  1296
(* The Boolean indicates that a fairly sound type encoding is needed. *)
blanchet@43085
  1297
val helper_table =
blanchet@43194
  1298
  [(("COMBI", false), @{thms Meson.COMBI_def}),
blanchet@43194
  1299
   (("COMBK", false), @{thms Meson.COMBK_def}),
blanchet@43194
  1300
   (("COMBB", false), @{thms Meson.COMBB_def}),
blanchet@43194
  1301
   (("COMBC", false), @{thms Meson.COMBC_def}),
blanchet@43194
  1302
   (("COMBS", false), @{thms Meson.COMBS_def}),
blanchet@43194
  1303
   (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
blanchet@43194
  1304
   (("fFalse", true), @{thms True_or_False}),
blanchet@43194
  1305
   (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
blanchet@43194
  1306
   (("fTrue", true), @{thms True_or_False}),
blanchet@43194
  1307
   (("fNot", false),
blanchet@43194
  1308
    @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
blanchet@43194
  1309
           fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
blanchet@43194
  1310
   (("fconj", false),
blanchet@43194
  1311
    @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
blanchet@43194
  1312
        by (unfold fconj_def) fast+}),
blanchet@43194
  1313
   (("fdisj", false),
blanchet@43194
  1314
    @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
blanchet@43194
  1315
        by (unfold fdisj_def) fast+}),
blanchet@43194
  1316
   (("fimplies", false),
blanchet@43210
  1317
    @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
blanchet@43194
  1318
        by (unfold fimplies_def) fast+}),
nik@43678
  1319
   (("fequal", true),
nik@43678
  1320
    (* This is a lie: Higher-order equality doesn't need a sound type encoding.
nik@43678
  1321
       However, this is done so for backward compatibility: Including the
nik@43678
  1322
       equality helpers by default in Metis breaks a few existing proofs. *)
nik@43678
  1323
    @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
nik@43678
  1324
           fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
nik@43678
  1325
   (("fAll", false), []), (*TODO: add helpers*)
nik@43678
  1326
   (("fEx", false), []), (*TODO: add helpers*)
blanchet@43194
  1327
   (("If", true), @{thms if_True if_False True_or_False})]
blanchet@43194
  1328
  |> map (apsnd (map zero_var_indexes))
blanchet@43085
  1329
blanchet@43130
  1330
val type_tag = `make_fixed_const type_tag_name
blanchet@43130
  1331
blanchet@43159
  1332
fun type_tag_idempotence_fact () =
blanchet@42573
  1333
  let
blanchet@42573
  1334
    fun var s = ATerm (`I s, [])
blanchet@43159
  1335
    fun tag tm = ATerm (type_tag, [var "T", tm])
blanchet@43207
  1336
    val tagged_a = tag (var "A")
blanchet@42573
  1337
  in
blanchet@43159
  1338
    Formula (type_tag_idempotence_helper_name, Axiom,
blanchet@43207
  1339
             AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
blanchet@43693
  1340
             |> close_formula_universally, isabelle_info simpN, NONE)
blanchet@42573
  1341
  end
blanchet@42573
  1342
blanchet@43626
  1343
fun should_specialize_helper type_enc t =
blanchet@43628
  1344
  polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
blanchet@43628
  1345
  level_of_type_enc type_enc <> No_Types andalso
blanchet@43628
  1346
  not (null (Term.hidden_polymorphism t))
blanchet@43159
  1347
blanchet@43858
  1348
fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
blanchet@42573
  1349
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
  1350
    SOME mangled_s =>
blanchet@42573
  1351
    let
blanchet@42573
  1352
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
  1353
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@43628
  1354
      fun dub needs_fairly_sound j k =
blanchet@43628
  1355
        (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
blanchet@43628
  1356
         (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
blanchet@43628
  1357
         (if needs_fairly_sound then typed_helper_suffix
blanchet@43628
  1358
          else untyped_helper_suffix),
blanchet@43628
  1359
         Helper)
blanchet@43159
  1360
      fun dub_and_inst needs_fairly_sound (th, j) =
blanchet@43628
  1361
        let val t = prop_of th in
blanchet@43628
  1362
          if should_specialize_helper type_enc t then
blanchet@43628
  1363
            map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
blanchet@43628
  1364
                types
blanchet@43628
  1365
          else
blanchet@43628
  1366
            [t]
blanchet@43628
  1367
        end
blanchet@43628
  1368
        |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
blanchet@43860
  1369
      val make_facts = map_filter (make_fact ctxt format type_enc false)
blanchet@43626
  1370
      val fairly_sound = is_type_enc_fairly_sound type_enc
blanchet@42573
  1371
    in
blanchet@43085
  1372
      helper_table
blanchet@43194
  1373
      |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
blanchet@43159
  1374
                  if helper_s <> unmangled_s orelse
blanchet@42894
  1375
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
  1376
                    []
blanchet@42573
  1377
                  else
blanchet@42573
  1378
                    ths ~~ (1 upto length ths)
blanchet@43628
  1379
                    |> maps (dub_and_inst needs_fairly_sound)
blanchet@43159
  1380
                    |> make_facts)
blanchet@42573
  1381
    end
blanchet@42573
  1382
  | NONE => []
blanchet@43858
  1383
fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
blanchet@43858
  1384
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
blanchet@43858
  1385
                  []
blanchet@42573
  1386
blanchet@43085
  1387
(***************************************************************)
blanchet@43085
  1388
(* Type Classes Present in the Axiom or Conjecture Clauses     *)
blanchet@43085
  1389
(***************************************************************)
blanchet@43085
  1390
blanchet@43085
  1391
fun set_insert (x, s) = Symtab.update (x, ()) s
blanchet@43085
  1392
blanchet@43085
  1393
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
blanchet@43085
  1394
blanchet@43085
  1395
(* Remove this trivial type class (FIXME: similar code elsewhere) *)
blanchet@43085
  1396
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
blanchet@43085
  1397
blanchet@43093
  1398
fun classes_of_terms get_Ts =
blanchet@43121
  1399
  map (map snd o get_Ts)
blanchet@43093
  1400
  #> List.foldl add_classes Symtab.empty
blanchet@43093
  1401
  #> delete_type #> Symtab.keys
blanchet@43085
  1402
blanchet@43093
  1403
val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
blanchet@43093
  1404
val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
blanchet@43085
  1405
blanchet@43622
  1406
fun fold_type_constrs f (Type (s, Ts)) x =
blanchet@43622
  1407
    fold (fold_type_constrs f) Ts (f (s, x))
blanchet@43189
  1408
  | fold_type_constrs _ _ x = x
blanchet@43085
  1409
blanchet@43907
  1410
(* Type constructors used to instantiate overloaded constants are the only ones
blanchet@43907
  1411
   needed. *)
blanchet@43189
  1412
fun add_type_constrs_in_term thy =
blanchet@43085
  1413
  let
blanchet@43188
  1414
    fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
blanchet@43181
  1415
      | add (t $ u) = add t #> add u
blanchet@43188
  1416
      | add (Const (x as (s, _))) =
blanchet@43188
  1417
        if String.isPrefix skolem_const_prefix s then I
blanchet@43189
  1418
        else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
blanchet@43907
  1419
      | add (Free (s, T)) =
blanchet@43907
  1420
        if String.isPrefix lambda_lifted_prefix s then
blanchet@43907
  1421
          T |> fold_type_constrs set_insert
blanchet@43907
  1422
        else
blanchet@43907
  1423
          I
blanchet@43181
  1424
      | add (Abs (_, _, u)) = add u
blanchet@43181
  1425
      | add _ = I
blanchet@43181
  1426
  in add end
blanchet@43085
  1427
blanchet@43189
  1428
fun type_constrs_of_terms thy ts =
blanchet@43189
  1429
  Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
blanchet@43085
  1430
blanchet@43856
  1431
fun translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
blanchet@43828
  1432
                       hyp_ts concl_t facts =
blanchet@42573
  1433
  let
blanchet@42573
  1434
    val thy = Proof_Context.theory_of ctxt
blanchet@43264
  1435
    val presimp_consts = Meson.presimplified_consts ctxt
blanchet@43861
  1436
    val fact_ts = facts |> map snd
blanchet@42573
  1437
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
  1438
       boost an ATP's performance (for some reason). *)
blanchet@43192
  1439
    val hyp_ts =
blanchet@43192
  1440
      hyp_ts
blanchet@43192
  1441
      |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
blanchet@43864
  1442
    val facts = facts |> map (apsnd (pair Axiom))
blanchet@43864
  1443
    val conjs =
blanchet@43861
  1444
      map (pair prem_kind) hyp_ts @ [(Conjecture, concl_t)]
blanchet@43863
  1445
      |> map2 (pair o rpair Local o string_of_int) (0 upto length hyp_ts)
blanchet@43864
  1446
    val ((conjs, facts), lambdas) =
blanchet@43864
  1447
      if preproc then
blanchet@43864
  1448
        conjs @ facts
blanchet@43864
  1449
        |> map (apsnd (apsnd (presimp_prop ctxt presimp_consts)))
blanchet@43864
  1450
        |> preprocess_abstractions_in_terms trans_lambdas
blanchet@43864
  1451
        |>> chop (length conjs)
blanchet@43864
  1452
        |>> apfst (map (apsnd (apsnd freeze_term)))
blanchet@43864
  1453
      else
blanchet@43864
  1454
        ((conjs, facts), [])
blanchet@43864
  1455
    val conjs = conjs |> make_conjecture ctxt format type_enc
blanchet@43863
  1456
    val (fact_names, facts) =
blanchet@43864
  1457
      facts
blanchet@43863
  1458
      |> map_filter (fn (name, (_, t)) =>
blanchet@43863
  1459
                        make_fact ctxt format type_enc true (name, t)
blanchet@43863
  1460
                        |> Option.map (pair name))
blanchet@43861
  1461
      |> ListPair.unzip
blanchet@43863
  1462
    val lambdas =
blanchet@43864
  1463
      lambdas |> map_filter (make_fact ctxt format type_enc true o apsnd snd)
blanchet@43861
  1464
    val all_ts = concl_t :: hyp_ts @ fact_ts
blanchet@42573
  1465
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
  1466
    val supers = tvar_classes_of_terms all_ts
blanchet@43189
  1467
    val tycons = type_constrs_of_terms thy all_ts
blanchet@43861
  1468
    val (supers, arity_clauses) =
blanchet@43626
  1469
      if level_of_type_enc type_enc = No_Types then ([], [])
blanchet@42573
  1470
      else make_arity_clauses thy tycons supers
blanchet@43861
  1471
    val class_rel_clauses = make_class_rel_clauses thy subs supers
blanchet@42573
  1472
  in
blanchet@43863
  1473
    (fact_names |> map single,
blanchet@43863
  1474
     (conjs, facts @ lambdas, class_rel_clauses, arity_clauses))
blanchet@42573
  1475
  end
blanchet@42573
  1476
blanchet@42573
  1477
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
  1478
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
  1479
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
  1480
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
  1481
blanchet@42573
  1482
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
  1483
blanchet@43130
  1484
val type_pred = `make_fixed_const type_pred_name
blanchet@43130
  1485
blanchet@43859
  1486
fun type_pred_iterm ctxt format type_enc T tm =
blanchet@43859
  1487
  IApp (IConst (type_pred, T --> @{typ bool}, [T])
blanchet@43859
  1488
        |> enforce_type_arg_policy_in_iterm ctxt format type_enc, tm)
blanchet@42573
  1489
blanchet@43421
  1490
fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@43421
  1491
  | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@43000
  1492
    accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
blanchet@43692
  1493
  | is_var_positively_naked_in_term _ _ _ _ = true
blanchet@43493
  1494
fun should_predicate_on_var_in_formula pos phi (SOME true) name =
blanchet@43421
  1495
    formula_fold pos (is_var_positively_naked_in_term name) phi false
blanchet@43493
  1496
  | should_predicate_on_var_in_formula _ _ _ _ = true
blanchet@42834
  1497
nik@43677
  1498
fun mk_aterm format type_enc name T_args args =
nik@43677
  1499
  ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
blanchet@42994
  1500
blanchet@43626
  1501
fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
blanchet@43859
  1502
  IConst (type_tag, T --> T, [T])
blanchet@43859
  1503
  |> enforce_type_arg_policy_in_iterm ctxt format type_enc
blanchet@43859
  1504
  |> ho_term_from_iterm ctxt format nonmono_Ts type_enc (Top_Level pos)
blanchet@43692
  1505
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
blanchet@43692
  1506
       | _ => raise Fail "unexpected lambda-abstraction")
blanchet@43859
  1507
and ho_term_from_iterm ctxt format nonmono_Ts type_enc =
blanchet@42573
  1508
  let
blanchet@42962
  1509
    fun aux site u =
blanchet@42962
  1510
      let
blanchet@43859
  1511
        val (head, args) = strip_iterm_comb u
nik@43677
  1512
        val pos =
blanchet@43361
  1513
          case site of
nik@43677
  1514
            Top_Level pos => pos
nik@43677
  1515
          | Eq_Arg pos => pos
nik@43677
  1516
          | Elsewhere => NONE
nik@43677
  1517
        val t =
nik@43677
  1518
          case head of
blanchet@43859
  1519
            IConst (name as (s, _), _, T_args) =>
nik@43677
  1520
            let
nik@43677
  1521
              val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
nik@43677
  1522
            in
nik@43677
  1523
              mk_aterm format type_enc name T_args (map (aux arg_site) args)
nik@43677
  1524
            end
blanchet@43859
  1525
          | IVar (name, _) =>
blanchet@43859
  1526
            mk_aterm format type_enc name [] (map (aux Elsewhere) args)
blanchet@43859
  1527
          | IAbs ((name, T), tm) =>
blanchet@43859
  1528
            AAbs ((name, ho_type_from_typ format type_enc true 0 T),
blanchet@43859
  1529
                  aux Elsewhere tm)
blanchet@43859
  1530
          | IApp _ => raise Fail "impossible \"IApp\""
blanchet@43859
  1531
        val T = ityp_of u
blanchet@42962
  1532
      in
blanchet@43626
  1533
        t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
blanchet@43626
  1534
                tag_with_type ctxt format nonmono_Ts type_enc pos T
blanchet@42962
  1535
              else
blanchet@42962
  1536
                I)
blanchet@42962
  1537
      end
blanchet@42962
  1538
  in aux end
blanchet@43859
  1539
and formula_from_iformula ctxt format nonmono_Ts type_enc
blanchet@43859
  1540
                          should_predicate_on_var =
blanchet@42829
  1541
  let
blanchet@43860
  1542
    val do_term = ho_term_from_iterm ctxt format nonmono_Ts type_enc o Top_Level
blanchet@42573
  1543
    val do_bound_type =
blanchet@43626
  1544
      case type_enc of
blanchet@43624
  1545
        Simple_Types (_, level) =>
blanchet@42994
  1546
        homogenized_type ctxt nonmono_Ts level 0
nik@43677
  1547
        #> ho_type_from_typ format type_enc false 0 #> SOME
blanchet@42682
  1548
      | _ => K NONE
blanchet@42878
  1549
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@43626
  1550
      if should_predicate_on_type ctxt nonmono_Ts type_enc
blanchet@42878
  1551
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@43859
  1552
        IVar (name, T)
blanchet@43859
  1553
        |> type_pred_iterm ctxt format type_enc T
blanchet@43361
  1554
        |> do_term pos |> AAtom |> SOME
blanchet@42573
  1555
      else
blanchet@42573
  1556
        NONE
blanchet@42878
  1557
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
  1558
        let
blanchet@42878
  1559
          val phi = phi |> do_formula pos
blanchet@42878
  1560
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
  1561
        in
blanchet@42834
  1562
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
  1563
                                        | SOME T => do_bound_type T)),
blanchet@42834
  1564
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
  1565
                      (map_filter
blanchet@42834
  1566
                           (fn (_, NONE) => NONE
blanchet@42834
  1567
                             | (s, SOME T) =>
blanchet@42878
  1568
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
  1569
                           xs)
blanchet@42834
  1570
                      phi)
blanchet@42834
  1571
        end
blanchet@42878
  1572
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@43361
  1573
      | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
blanchet@43493
  1574
  in do_formula end
blanchet@42573
  1575
blanchet@43626
  1576
fun bound_tvars type_enc Ts =
blanchet@42727
  1577
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@43626
  1578
                (type_literals_for_types type_enc add_sorts_on_tvar Ts))
blanchet@42727
  1579
blanchet@42573
  1580
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
  1581
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
  1582
   the remote provers might care. *)
blanchet@43501
  1583
fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
blanchet@43859
  1584
        type_enc (j, {name, locality, kind, iformula, atomic_types}) =
blanchet@43864
  1585
  (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name, kind,
blanchet@43859
  1586
   iformula
blanchet@43859
  1587
   |> close_iformula_universally
blanchet@43859
  1588
   |> formula_from_iformula ctxt format nonmono_Ts type_enc
blanchet@43859
  1589
                            should_predicate_on_var_in_formula
blanchet@43859
  1590
                            (if pos then SOME true else NONE)
blanchet@43626
  1591
   |> bound_tvars type_enc atomic_types
blanchet@43493
  1592
   |> close_formula_universally,
blanchet@43493
  1593
   NONE,
blanchet@43493
  1594
   case locality of
blanchet@43693
  1595
     Intro => isabelle_info introN
blanchet@43693
  1596
   | Elim => isabelle_info elimN
blanchet@43693
  1597
   | Simp => isabelle_info simpN
blanchet@43493
  1598
   | _ => NONE)
blanchet@43493
  1599
  |> Formula
blanchet@42573
  1600
blanchet@43086
  1601
fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
blanchet@43086
  1602
                                       : class_rel_clause) =
blanchet@42573
  1603
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
  1604
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
  1605
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
  1606
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@43693
  1607
             |> close_formula_universally, isabelle_info introN, NONE)
blanchet@42573
  1608
  end
blanchet@42573
  1609
blanchet@42573
  1610
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
  1611
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
  1612
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
  1613
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
  1614
blanchet@43086
  1615
fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
blanchet@43086
  1616
                                   : arity_clause) =
blanchet@43495
  1617
  Formula (arity_clause_prefix ^ name, Axiom,
blanchet@42573
  1618
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
  1619
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
  1620
                    (formula_from_fo_literal
blanchet@42895
  1621
                         (fo_literal_from_arity_literal concl_lits))
blanchet@43693
  1622
           |> close_formula_universally, isabelle_info introN, NONE)
blanchet@42573
  1623
blanchet@43626
  1624
fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
blanchet@43859
  1625
        ({name, kind, iformula, atomic_types, ...} : translated_formula) =
blanchet@42577
  1626
  Formula (conjecture_prefix ^ name, kind,
blanchet@43859
  1627
           formula_from_iformula ctxt format nonmono_Ts type_enc
blanchet@43493
  1628
               should_predicate_on_var_in_formula (SOME false)
blanchet@43859
  1629
               (close_iformula_universally iformula)
blanchet@43626
  1630
           |> bound_tvars type_enc atomic_types
blanchet@42573
  1631
           |> close_formula_universally, NONE, NONE)
blanchet@42573
  1632
blanchet@43626
  1633
fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
blanchet@43626
  1634
  atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
blanchet@42573
  1635
               |> map fo_literal_from_type_literal
blanchet@42573
  1636
blanchet@42573
  1637
fun formula_line_for_free_type j lit =
blanchet@43085
  1638
  Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
  1639
           formula_from_fo_literal lit, NONE, NONE)
blanchet@43626
  1640
fun formula_lines_for_free_types type_enc facts =
blanchet@42573
  1641
  let
blanchet@43626
  1642
    val litss = map (free_type_literals type_enc) facts
blanchet@42573
  1643
    val lits = fold (union (op =)) litss []
blanchet@42573
  1644
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
  1645
blanchet@42573
  1646
(** Symbol declarations **)
blanchet@42544
  1647
blanchet@43626
  1648
fun should_declare_sym type_enc pred_sym s =
blanchet@42998
  1649
  is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
blanchet@43626
  1650
  (case type_enc of
blanchet@42894
  1651
     Simple_Types _ => true
blanchet@43128
  1652
   | Tags (_, _, Lightweight) => true
blanchet@42894
  1653
   | _ => not pred_sym)
blanchet@38282
  1654
blanchet@43626
  1655
fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
blanchet@42574
  1656
  let
blanchet@43859
  1657
    fun add_iterm in_conj tm =
blanchet@43859
  1658
      let val (head, args) = strip_iterm_comb tm in
blanchet@42574
  1659
        (case head of
blanchet@43859
  1660
           IConst ((s, s'), T, T_args) =>
blanchet@42574
  1661
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@43626
  1662
             if should_declare_sym type_enc pred_sym s then
blanchet@42576
  1663
               Symtab.map_default (s, [])
blanchet@42886
  1664
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1665
                                         in_conj))
blanchet@42574
  1666
             else
blanchet@42574
  1667
               I
blanchet@42574
  1668
           end
blanchet@43859
  1669
         | IAbs (_, tm) => add_iterm in_conj tm
blanchet@42574
  1670
         | _ => I)
blanchet@43859
  1671
        #> fold (add_iterm in_conj) args
blanchet@42574
  1672
      end
blanchet@43859
  1673
    fun add_fact in_conj = fact_lift (formula_fold NONE (K (add_iterm in_conj)))
blanchet@42698
  1674
  in
blanchet@42698
  1675
    Symtab.empty
blanchet@43626
  1676
    |> is_type_enc_fairly_sound type_enc
blanchet@42698
  1677
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
  1678
  end
blanchet@42533
  1679
blanchet@42685
  1680
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1681
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@43859
  1682
fun add_iterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
blanchet@43859
  1683
  | add_iterm_nonmonotonic_types ctxt level sound locality _
blanchet@43859
  1684
        (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
blanchet@43000
  1685
    (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1686
     (case level of
blanchet@43362
  1687
        Noninf_Nonmono_Types =>
blanchet@43293
  1688
        not (is_locality_global locality) orelse
blanchet@43572
  1689
        not (is_type_surely_infinite ctxt sound T)
blanchet@43572
  1690
      | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
blanchet@42886
  1691
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@43859
  1692
  | add_iterm_nonmonotonic_types _ _ _ _ _ _ = I
blanchet@43572
  1693
fun add_fact_nonmonotonic_types ctxt level sound
blanchet@43859
  1694
        ({kind, locality, iformula, ...} : translated_formula) =
blanchet@42834
  1695
  formula_fold (SOME (kind <> Conjecture))
blanchet@43859
  1696
               (add_iterm_nonmonotonic_types ctxt level sound locality)
blanchet@43859
  1697
               iformula
blanchet@43626
  1698
fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
blanchet@43626
  1699
  let val level = level_of_type_enc type_enc in
blanchet@43362
  1700
    if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
blanchet@43572
  1701
      [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
blanchet@42886
  1702
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1703
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1704
            nonmonotonic types not being empty. *)
blanchet@42886
  1705
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1706
    else
blanchet@42886
  1707
      []
blanchet@42829
  1708
  end
blanchet@42677
  1709
blanchet@43626
  1710
fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
blanchet@42994
  1711
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  1712
  let
blanchet@43178
  1713
    val (T_arg_Ts, level) =
blanchet@43626
  1714
      case type_enc of
blanchet@43624
  1715
        Simple_Types (_, level) => ([], level)
blanchet@43178
  1716
      | _ => (replicate (length T_args) homo_infinite_type, No_Types)
blanchet@42994
  1717
  in
blanchet@42998
  1718
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@42994
  1719
          (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
nik@43677
  1720
          |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
blanchet@42994
  1721
  end
blanchet@42579
  1722
blanchet@43125
  1723
fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
blanchet@43626
  1724
        poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1725
  let
blanchet@42709
  1726
    val (kind, maybe_negate) =
blanchet@42709
  1727
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1728
      else (Axiom, I)
blanchet@42753
  1729
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@43399
  1730
    val num_args = length arg_Ts
blanchet@42579
  1731
    val bound_names =
blanchet@43399
  1732
      1 upto num_args |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1733
    val bounds =
blanchet@43859
  1734
      bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
blanchet@43907
  1735
    val sym_needs_arg_types = exists (curry (op =) dummyT) T_args
blanchet@43401
  1736
    fun should_keep_arg_type T =
blanchet@43401
  1737
      sym_needs_arg_types orelse
blanchet@43626
  1738
      not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
blanchet@42579
  1739
    val bound_Ts =
blanchet@43401
  1740
      arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
blanchet@42579
  1741
  in
blanchet@43125
  1742
    Formula (preds_sym_formula_prefix ^ s ^
blanchet@42709
  1743
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@43859
  1744
             IConst ((s, s'), T, T_args)
blanchet@43859
  1745
             |> fold (curry (IApp o swap)) bounds
blanchet@43859
  1746
             |> type_pred_iterm ctxt format type_enc res_T
blanchet@42963
  1747
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@43859
  1748
             |> formula_from_iformula ctxt format poly_nonmono_Ts type_enc
blanchet@43859
  1749
                                      (K (K (K (K true)))) (SOME true)
blanchet@43626
  1750
             |> n > 1 ? bound_tvars type_enc (atyps_of T)
blanchet@42709
  1751
             |> close_formula_universally
blanchet@42709
  1752
             |> maybe_negate,
blanchet@43693
  1753
             isabelle_info introN, NONE)
blanchet@42579
  1754
  end
blanchet@42579
  1755
blanchet@43129
  1756
fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
blanchet@43626
  1757
        poly_nonmono_Ts type_enc n s
blanchet@43401
  1758
        (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1759
  let
blanchet@42829
  1760
    val ident_base =
blanchet@43129
  1761
      lightweight_tags_sym_formula_prefix ^ s ^
blanchet@43125
  1762
      (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1763
    val (kind, maybe_negate) =
blanchet@42852
  1764
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1765
      else (Axiom, I)
blanchet@42829
  1766
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1767
    val bound_names =
blanchet@42829
  1768
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1769
    val bounds = bound_names |> map (fn name => ATerm (name, []))
nik@43677
  1770
    val cst = mk_aterm format type_enc (s, s') T_args
blanchet@42830
  1771
    val atomic_Ts = atyps_of T
blanchet@42834
  1772
    fun eq tms =
blanchet@42834
  1773
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@43000
  1774
       else AAtom (ATerm (`I tptp_equal, tms)))
blanchet@43626
  1775
      |> bound_tvars type_enc atomic_Ts
blanchet@42830
  1776
      |> close_formula_universally
blanchet@42852
  1777
      |> maybe_negate
blanchet@43361
  1778
    (* See also "should_tag_with_type". *)
blanchet@43361
  1779
    fun should_encode T =
blanchet@43401
  1780
      should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
blanchet@43626
  1781
      (case type_enc of
blanchet@43361
  1782
         Tags (Polymorphic, level, Lightweight) =>
blanchet@43361
  1783
         level <> All_Types andalso Monomorph.typ_has_tvars T
blanchet@43361
  1784
       | _ => false)
blanchet@43626
  1785
    val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
blanchet@42829
  1786
    val add_formula_for_res =
blanchet@42829
  1787
      if should_encode res_T then
blanchet@42852
  1788
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42994
  1789
                       eq [tag_with res_T (cst bounds), cst bounds],
blanchet@43693
  1790
                       isabelle_info simpN, NONE))
blanchet@42829
  1791
      else
blanchet@42829
  1792
        I
blanchet@42829
  1793
    fun add_formula_for_arg k =
blanchet@42829
  1794
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1795
        if should_encode arg_T then
blanchet@42829
  1796
          case chop k bounds of
blanchet@42829
  1797
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1798
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42994
  1799
                           eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
blanchet@42994
  1800
                               cst bounds],
blanchet@43693
  1801
                           isabelle_info simpN, NONE))
blanchet@42829
  1802
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1803
        else
blanchet@42829
  1804
          I
blanchet@42829
  1805
      end
blanchet@42829
  1806
  in
blanchet@42834
  1807
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1808
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1809
  end
blanchet@42829
  1810
blanchet@42836
  1811
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1812
blanchet@43401
  1813
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
blanchet@43626
  1814
                                poly_nonmono_Ts type_enc (s, decls) =
blanchet@43626
  1815
  case type_enc of
blanchet@42998
  1816
    Simple_Types _ =>
blanchet@43626
  1817
    decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
blanchet@42998
  1818
  | Preds _ =>
blanchet@42998
  1819
    let
blanchet@42998
  1820
      val decls =
blanchet@42998
  1821
        case decls of
blanchet@42998
  1822
          decl :: (decls' as _ :: _) =>
blanchet@42998
  1823
          let val T = result_type_of_decl decl in
blanchet@42998
  1824
            if forall (curry (type_instance ctxt o swap) T
blanchet@42998
  1825
                       o result_type_of_decl) decls' then
blanchet@42998
  1826
              [decl]
blanchet@42998
  1827
            else
blanchet@42998
  1828
              decls
blanchet@42998
  1829
          end
blanchet@42998
  1830
        | _ => decls
blanchet@42998
  1831
      val n = length decls
blanchet@42998
  1832
      val decls =
blanchet@43626
  1833
        decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
blanchet@43401
  1834
                                                  (K true)
blanchet@43401
  1835
                         o result_type_of_decl)
blanchet@42998
  1836
    in
blanchet@42998
  1837
      (0 upto length decls - 1, decls)
blanchet@43125
  1838
      |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
blanchet@43626
  1839
                   nonmono_Ts poly_nonmono_Ts type_enc n s)
blanchet@42998
  1840
    end
blanchet@42998
  1841
  | Tags (_, _, heaviness) =>
blanchet@42998
  1842
    (case heaviness of
blanchet@43128
  1843
       Heavyweight => []
blanchet@43128
  1844
     | Lightweight =>
blanchet@42998
  1845
       let val n = length decls in
blanchet@42998
  1846
         (0 upto n - 1 ~~ decls)
blanchet@43129
  1847
         |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
blanchet@43626
  1848
                      conj_sym_kind poly_nonmono_Ts type_enc n s)
blanchet@42998
  1849
       end)
blanchet@42579
  1850
blanchet@42956
  1851
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@43626
  1852
                                     poly_nonmono_Ts type_enc sym_decl_tab =
blanchet@42998
  1853
  sym_decl_tab
blanchet@42998
  1854
  |> Symtab.dest
blanchet@42998
  1855
  |> sort_wrt fst
blanchet@42998
  1856
  |> rpair []
blanchet@42998
  1857
  |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
blanchet@43626
  1858
                             nonmono_Ts poly_nonmono_Ts type_enc)
blanchet@42543
  1859
blanchet@43185
  1860
fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
blanchet@43185
  1861
    poly <> Mangled_Monomorphic andalso
blanchet@43185
  1862
    ((level = All_Types andalso heaviness = Lightweight) orelse
blanchet@43362
  1863
     level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
blanchet@43159
  1864
  | needs_type_tag_idempotence _ = false
blanchet@42831
  1865
blanchet@42939
  1866
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1867
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1868
    if heading = needle then j
blanchet@42939
  1869
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1870
blanchet@42998
  1871
val implicit_declsN = "Should-be-implicit typings"
blanchet@42998
  1872
val explicit_declsN = "Explicit typings"
blanchet@41157
  1873
val factsN = "Relevant facts"
blanchet@41157
  1874
val class_relsN = "Class relationships"
blanchet@42543
  1875
val aritiesN = "Arities"
blanchet@41157
  1876
val helpersN = "Helper facts"
blanchet@41157
  1877
val conjsN = "Conjectures"
blanchet@41313
  1878
val free_typesN = "Type variables"
blanchet@41157
  1879
blanchet@43828
  1880
val explicit_apply = NONE (* for experiments *)
blanchet@43259
  1881
blanchet@43626
  1882
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
blanchet@43856
  1883
        exporter trans_lambdas readable_names preproc hyp_ts concl_t facts =
blanchet@38282
  1884
  let
blanchet@43626
  1885
    val (format, type_enc) = choose_format [format] type_enc
blanchet@41313
  1886
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@43856
  1887
      translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
blanchet@43828
  1888
                         hyp_ts concl_t facts
blanchet@43064
  1889
    val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
blanchet@43572
  1890
    val nonmono_Ts =
blanchet@43626
  1891
      conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
blanchet@43626
  1892
    val repair = repair_fact ctxt format type_enc sym_tab
blanchet@42682
  1893
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@43064
  1894
    val repaired_sym_tab =
blanchet@43064
  1895
      conjs @ facts |> sym_table_for_facts ctxt (SOME false)
blanchet@42573
  1896
    val helpers =
blanchet@43858
  1897
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
blanchet@43858
  1898
                       |> map repair
blanchet@43401
  1899
    val poly_nonmono_Ts =
blanchet@43213
  1900
      if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
blanchet@43626
  1901
         polymorphism_of_type_enc type_enc <> Polymorphic then
blanchet@42894
  1902
        nonmono_Ts
blanchet@42894
  1903
      else
blanchet@42894
  1904
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1905
    val sym_decl_lines =
blanchet@42731
  1906
      (conjs, helpers @ facts)
blanchet@43626
  1907
      |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
blanchet@43401
  1908
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@43626
  1909
                                               poly_nonmono_Ts type_enc
blanchet@42881
  1910
    val helper_lines =
blanchet@42956
  1911
      0 upto length helpers - 1 ~~ helpers
blanchet@43501
  1912
      |> map (formula_line_for_fact ctxt format helper_prefix I false true
blanchet@43626
  1913
                                    poly_nonmono_Ts type_enc)
blanchet@43626
  1914
      |> (if needs_type_tag_idempotence type_enc then
blanchet@43159
  1915
            cons (type_tag_idempotence_fact ())
blanchet@43159
  1916
          else
blanchet@43159
  1917
            I)
blanchet@42522
  1918
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@43039
  1919
       FLOTTER hack. *)
blanchet@38282
  1920
    val problem =
blanchet@42998
  1921
      [(explicit_declsN, sym_decl_lines),
blanchet@42956
  1922
       (factsN,
blanchet@43501
  1923
        map (formula_line_for_fact ctxt format fact_prefix ascii_of
blanchet@43501
  1924
                                   (not exporter) (not exporter) nonmono_Ts
blanchet@43626
  1925
                                   type_enc)
blanchet@42956
  1926
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1927
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1928
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1929
       (helpersN, helper_lines),
blanchet@42962
  1930
       (conjsN,
blanchet@43626
  1931
        map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
blanchet@42962
  1932
            conjs),
blanchet@43626
  1933
       (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
blanchet@42543
  1934
    val problem =
blanchet@42561
  1935
      problem
blanchet@43092
  1936
      |> (case format of
blanchet@43092
  1937
            CNF => ensure_cnf_problem
blanchet@43092
  1938
          | CNF_UEQ => filter_cnf_ueq_problem
blanchet@43092
  1939
          | _ => I)
blanchet@42998
  1940
      |> (if is_format_typed format then
blanchet@42998
  1941
            declare_undeclared_syms_in_atp_problem type_decl_prefix
blanchet@42998
  1942
                                                   implicit_declsN
blanchet@42998
  1943
          else
blanchet@42998
  1944
            I)
blanchet@43092
  1945
    val (problem, pool) = problem |> nice_atp_problem readable_names
blanchet@42881
  1946
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1947
    val typed_helpers =
blanchet@42881
  1948
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1949
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1950
                     else NONE)
blanchet@42881
  1951
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1952
                  ~~ helpers)
blanchet@42778
  1953
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1954
      if min_ary > 0 then
blanchet@42755
  1955
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1956
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1957
        | NONE => I
blanchet@42755
  1958
      else
blanchet@42755
  1959
        I
blanchet@38282
  1960
  in
blanchet@38282
  1961
    (problem,
blanchet@38282
  1962
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1963
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1964
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1965
     fact_names |> Vector.fromList,
blanchet@42881
  1966
     typed_helpers,
blanchet@42755
  1967
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1968
  end
blanchet@38282
  1969
blanchet@41313
  1970
(* FUDGE *)
blanchet@41313
  1971
val conj_weight = 0.0
blanchet@41770
  1972
val hyp_weight = 0.1
blanchet@41770
  1973
val fact_min_weight = 0.2
blanchet@41313
  1974
val fact_max_weight = 1.0
blanchet@42608
  1975
val type_info_default_weight = 0.8
blanchet@41313
  1976
blanchet@41313
  1977
fun add_term_weights weight (ATerm (s, tms)) =
nik@43676
  1978
    is_tptp_user_symbol s ? Symtab.default (s, weight)
nik@43676
  1979
    #> fold (add_term_weights weight) tms
nik@43676
  1980
  | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
blanchet@42577
  1981
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1982
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1983
  | add_problem_line_weights _ _ = I
blanchet@41313
  1984
blanchet@41313
  1985
fun add_conjectures_weights [] = I
blanchet@41313
  1986
  | add_conjectures_weights conjs =
blanchet@41313
  1987
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1988
      add_problem_line_weights conj_weight conj
blanchet@41313
  1989
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1990
    end
blanchet@41313
  1991
blanchet@41313
  1992
fun add_facts_weights facts =
blanchet@41313
  1993
  let
blanchet@41313
  1994
    val num_facts = length facts
blanchet@41313
  1995
    fun weight_of j =
blanchet@41313
  1996
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1997
                        / Real.fromInt num_facts
blanchet@41313
  1998
  in
blanchet@41313
  1999
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  2000
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  2001
  end
blanchet@41313
  2002
blanchet@41313
  2003
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  2004
fun atp_problem_weights problem =
blanchet@42608
  2005
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  2006
    Symtab.empty
blanchet@42608
  2007
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  2008
    |> add_facts_weights (get factsN)
blanchet@42608
  2009
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42998
  2010
            [explicit_declsN, class_relsN, aritiesN]
blanchet@42608
  2011
    |> Symtab.dest
blanchet@42608
  2012
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  2013
  end
blanchet@41313
  2014
blanchet@38282
  2015
end;