src/HOL/Tools/ATP/atp_translate.ML
author blanchet
Wed Aug 31 11:12:27 2011 +0200 (2011-08-31)
changeset 44622 779f79ed0ddc
parent 44595 444d111bde7d
child 44623 1e2d5cdef3d0
permissions -rw-r--r--
avoid relying on dubious TFF1 feature
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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 | Induction | Extensionality | Intro | Elim | Simp |
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    Local | Assum | Chained
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  datatype order = First_Order | Higher_Order
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  datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
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  datatype soundness = Unsound | Sound_Modulo_Infiniteness | Sound
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  datatype type_level =
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    All_Types |
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    Noninf_Nonmono_Types of soundness |
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    Fin_Nonmono_Types |
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    Const_Arg_Types |
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    No_Types
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  datatype type_uniformity = Uniform | Nonuniform
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  datatype type_enc =
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    Simple_Types of order * polymorphism * type_level |
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    Guards of polymorphism * type_level * type_uniformity |
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    Tags of polymorphism * type_level * type_uniformity
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  val type_tag_idempotence : bool Config.T
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  val type_tag_arguments : bool Config.T
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  val no_lambdasN : string
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  val concealedN : string
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  val liftingN : string
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  val combinatorsN : string
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  val hybridN : string
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  val lambdasN : string
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  val smartN : 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 polymorphic_free_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 guards_sym_formula_prefix : string
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  val 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_guard_name : string
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  val type_tag_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 type_enc_from_string : soundness -> 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_quasi_sound : type_enc -> bool
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  val is_type_enc_fairly_sound : type_enc -> bool
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  val adjust_type_enc : format -> type_enc -> 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 prepare_atp_problem :
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    Proof.context -> format -> formula_kind -> formula_kind -> type_enc
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    -> bool -> string -> bool -> bool -> term list -> term
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    -> ((string * locality) * term) list
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    -> string problem * string Symtab.table * int * int
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       * (string * locality) list vector * int list * int Symtab.table
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  val atp_problem_weights : string problem -> (string * real) list
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end;
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structure ATP_Translate : ATP_TRANSLATE =
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struct
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open ATP_Util
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open ATP_Problem
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type name = string * string
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val type_tag_idempotence =
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  Attrib.setup_config_bool @{binding atp_type_tag_idempotence} (K false)
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val type_tag_arguments =
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  Attrib.setup_config_bool @{binding atp_type_tag_arguments} (K false)
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val no_lambdasN = "no_lambdas"
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val concealedN = "concealed"
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val liftingN = "lifting"
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val combinatorsN = "combinators"
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val hybridN = "hybrid"
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val lambdasN = "lambdas"
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val smartN = "smart"
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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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(* TFF1 is still in development, and it is still unclear whether symbols will be
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   allowed to have types like "$tType > $o" (i.e., "![A : $tType] : $o"), with
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   "dummy" type variables. *)
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val exploit_tff1_dummy_type_vars = false
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val bound_var_prefix = "B_"
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val all_bound_var_prefix = "BA_"
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val exist_bound_var_prefix = "BE_"
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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 simple_type_prefix = "s_"
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val class_prefix = "cl_"
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val polymorphic_free_prefix = "poly_free"
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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 guards_sym_formula_prefix = "gsy_"
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val 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 = "pp"
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val app_op_name = "aa"
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val type_guard_name = "gg"
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val type_tag_name = "tt"
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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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(*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_all_bound_var x = all_bound_var_prefix ^ ascii_of x
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fun make_exist_bound_var x = exist_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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nik@44587
   322
(* "HOL.eq" and Choice are mapped to the ATP's equivalents *)
nik@44587
   323
local
nik@44587
   324
  val choice_const = (fst o dest_Const o HOLogic.choice_const) Term.dummyT
nik@44587
   325
  fun default c = const_prefix ^ lookup_const c
nik@44587
   326
in
nik@44587
   327
  fun make_fixed_const _ @{const_name HOL.eq} = tptp_old_equal
blanchet@44589
   328
    | make_fixed_const (SOME (THF0 THF_With_Choice)) c =
nik@44587
   329
        if c = choice_const then tptp_choice else default c
nik@44587
   330
    | make_fixed_const _ c = default c
nik@44587
   331
end
blanchet@43085
   332
blanchet@43085
   333
fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
blanchet@43085
   334
blanchet@43085
   335
fun make_type_class clas = class_prefix ^ ascii_of clas
blanchet@43085
   336
blanchet@43093
   337
fun new_skolem_var_name_from_const s =
blanchet@43093
   338
  let val ss = s |> space_explode Long_Name.separator in
blanchet@43093
   339
    nth ss (length ss - 2)
blanchet@43093
   340
  end
blanchet@43093
   341
blanchet@43248
   342
(* These are either simplified away by "Meson.presimplify" (most of the time) or
blanchet@43248
   343
   handled specially via "fFalse", "fTrue", ..., "fequal". *)
blanchet@43248
   344
val atp_irrelevant_consts =
blanchet@43248
   345
  [@{const_name False}, @{const_name True}, @{const_name Not},
blanchet@43248
   346
   @{const_name conj}, @{const_name disj}, @{const_name implies},
blanchet@43248
   347
   @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
blanchet@43248
   348
blanchet@43248
   349
val atp_monomorph_bad_consts =
blanchet@43248
   350
  atp_irrelevant_consts @
blanchet@43248
   351
  (* These are ignored anyway by the relevance filter (unless they appear in
blanchet@43248
   352
     higher-order places) but not by the monomorphizer. *)
blanchet@43248
   353
  [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
blanchet@43248
   354
   @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
blanchet@43248
   355
   @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
blanchet@43248
   356
blanchet@43258
   357
fun add_schematic_const (x as (_, T)) =
blanchet@43258
   358
  Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
blanchet@43258
   359
val add_schematic_consts_of =
blanchet@43258
   360
  Term.fold_aterms (fn Const (x as (s, _)) =>
blanchet@43258
   361
                       not (member (op =) atp_monomorph_bad_consts s)
blanchet@43258
   362
                       ? add_schematic_const x
blanchet@43258
   363
                      | _ => I)
blanchet@43258
   364
fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
blanchet@43248
   365
blanchet@43085
   366
(** Definitions and functions for FOL clauses and formulas for TPTP **)
blanchet@43085
   367
blanchet@43085
   368
(* The first component is the type class; the second is a "TVar" or "TFree". *)
blanchet@43085
   369
datatype type_literal =
blanchet@43085
   370
  TyLitVar of name * name |
blanchet@43085
   371
  TyLitFree of name * name
blanchet@43085
   372
blanchet@43085
   373
blanchet@43085
   374
(** Isabelle arities **)
blanchet@43085
   375
blanchet@43085
   376
datatype arity_literal =
blanchet@44622
   377
  AryLitConst of name * name * name list |
blanchet@44622
   378
  AryLitVar of name * name
blanchet@43085
   379
blanchet@43263
   380
val type_class = the_single @{sort type}
blanchet@43263
   381
blanchet@43263
   382
fun add_packed_sort tvar =
blanchet@43263
   383
  fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
blanchet@43085
   384
blanchet@43086
   385
type arity_clause =
blanchet@43496
   386
  {name : string,
blanchet@43496
   387
   prem_lits : arity_literal list,
blanchet@43496
   388
   concl_lits : arity_literal}
blanchet@43085
   389
blanchet@43085
   390
(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
blanchet@43085
   391
fun make_axiom_arity_clause (tcons, name, (cls, args)) =
blanchet@43085
   392
  let
blanchet@44595
   393
    val tvars = map (prefix tvar_prefix o string_of_int) (1 upto length args)
blanchet@43085
   394
    val tvars_srts = ListPair.zip (tvars, args)
blanchet@43085
   395
  in
blanchet@43086
   396
    {name = name,
blanchet@44622
   397
     prem_lits =
blanchet@44622
   398
       [] |> fold (uncurry add_packed_sort) tvars_srts |> map AryLitVar,
blanchet@44622
   399
     concl_lits =
blanchet@44622
   400
       AryLitConst (`make_type_class cls, `make_fixed_type_const tcons,
blanchet@44622
   401
                    tvars ~~ tvars)}
blanchet@43085
   402
  end
blanchet@43085
   403
blanchet@43085
   404
fun arity_clause _ _ (_, []) = []
blanchet@43495
   405
  | arity_clause seen n (tcons, ("HOL.type", _) :: ars) =  (* ignore *)
blanchet@43495
   406
    arity_clause seen n (tcons, ars)
blanchet@43495
   407
  | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
blanchet@43495
   408
    if member (op =) seen class then
blanchet@43495
   409
      (* multiple arities for the same (tycon, class) pair *)
blanchet@43495
   410
      make_axiom_arity_clause (tcons,
blanchet@43495
   411
          lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
blanchet@43495
   412
          ar) ::
blanchet@43495
   413
      arity_clause seen (n + 1) (tcons, ars)
blanchet@43495
   414
    else
blanchet@43495
   415
      make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
blanchet@43495
   416
                               ascii_of class, ar) ::
blanchet@43495
   417
      arity_clause (class :: seen) n (tcons, ars)
blanchet@43085
   418
blanchet@43085
   419
fun multi_arity_clause [] = []
blanchet@43085
   420
  | multi_arity_clause ((tcons, ars) :: tc_arlists) =
blanchet@43085
   421
      arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
blanchet@43085
   422
blanchet@43622
   423
(* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
blanchet@43622
   424
   theory thy provided its arguments have the corresponding sorts. *)
blanchet@43085
   425
fun type_class_pairs thy tycons classes =
blanchet@43093
   426
  let
blanchet@43093
   427
    val alg = Sign.classes_of thy
blanchet@43093
   428
    fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
blanchet@43093
   429
    fun add_class tycon class =
blanchet@43093
   430
      cons (class, domain_sorts tycon class)
blanchet@43093
   431
      handle Sorts.CLASS_ERROR _ => I
blanchet@43093
   432
    fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
blanchet@43093
   433
  in map try_classes tycons end
blanchet@43085
   434
blanchet@43085
   435
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
blanchet@43085
   436
fun iter_type_class_pairs _ _ [] = ([], [])
blanchet@43085
   437
  | iter_type_class_pairs thy tycons classes =
blanchet@43263
   438
      let
blanchet@43263
   439
        fun maybe_insert_class s =
blanchet@43263
   440
          (s <> type_class andalso not (member (op =) classes s))
blanchet@43263
   441
          ? insert (op =) s
blanchet@43263
   442
        val cpairs = type_class_pairs thy tycons classes
blanchet@43263
   443
        val newclasses =
blanchet@43263
   444
          [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
blanchet@43263
   445
        val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
blanchet@43266
   446
      in (classes' @ classes, union (op =) cpairs' cpairs) end
blanchet@43085
   447
blanchet@43085
   448
fun make_arity_clauses thy tycons =
blanchet@43085
   449
  iter_type_class_pairs thy tycons ##> multi_arity_clause
blanchet@43085
   450
blanchet@43085
   451
blanchet@43085
   452
(** Isabelle class relations **)
blanchet@43085
   453
blanchet@43086
   454
type class_rel_clause =
blanchet@43496
   455
  {name : string,
blanchet@43496
   456
   subclass : name,
blanchet@43496
   457
   superclass : name}
blanchet@43085
   458
blanchet@43622
   459
(* Generate all pairs (sub, super) such that sub is a proper subclass of super
blanchet@43622
   460
   in theory "thy". *)
blanchet@43085
   461
fun class_pairs _ [] _ = []
blanchet@43085
   462
  | class_pairs thy subs supers =
blanchet@43085
   463
      let
blanchet@43085
   464
        val class_less = Sorts.class_less (Sign.classes_of thy)
blanchet@43085
   465
        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
blanchet@43085
   466
        fun add_supers sub = fold (add_super sub) supers
blanchet@43085
   467
      in fold add_supers subs [] end
blanchet@43085
   468
blanchet@43622
   469
fun make_class_rel_clause (sub, super) =
blanchet@43622
   470
  {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
blanchet@43086
   471
   superclass = `make_type_class super}
blanchet@43085
   472
blanchet@43085
   473
fun make_class_rel_clauses thy subs supers =
blanchet@43093
   474
  map make_class_rel_clause (class_pairs thy subs supers)
blanchet@43085
   475
blanchet@43859
   476
(* intermediate terms *)
blanchet@43859
   477
datatype iterm =
blanchet@43859
   478
  IConst of name * typ * typ list |
blanchet@43859
   479
  IVar of name * typ |
blanchet@43859
   480
  IApp of iterm * iterm |
blanchet@43859
   481
  IAbs of (name * typ) * iterm
blanchet@43085
   482
blanchet@43859
   483
fun ityp_of (IConst (_, T, _)) = T
blanchet@43859
   484
  | ityp_of (IVar (_, T)) = T
blanchet@43859
   485
  | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
blanchet@43859
   486
  | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
blanchet@43085
   487
blanchet@43085
   488
(*gets the head of a combinator application, along with the list of arguments*)
blanchet@43859
   489
fun strip_iterm_comb u =
blanchet@43496
   490
  let
blanchet@43859
   491
    fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
blanchet@43496
   492
      | stripc x = x
blanchet@43496
   493
  in stripc (u, []) end
blanchet@43085
   494
blanchet@43085
   495
fun atyps_of T = fold_atyps (insert (op =)) T []
blanchet@43085
   496
blanchet@43085
   497
fun new_skolem_const_name s num_T_args =
blanchet@43085
   498
  [new_skolem_const_prefix, s, string_of_int num_T_args]
blanchet@43085
   499
  |> space_implode Long_Name.separator
blanchet@43085
   500
blanchet@44594
   501
fun robust_const_type thy s =
blanchet@44594
   502
  if s = app_op_name then Logic.varifyT_global @{typ "('a => 'b) => 'a => 'b"}
blanchet@44594
   503
  else s |> Sign.the_const_type thy
blanchet@44594
   504
blanchet@44594
   505
(* This function only makes sense if "T" is as general as possible. *)
blanchet@44594
   506
fun robust_const_typargs thy (s, T) =
blanchet@44594
   507
  (s, T) |> Sign.const_typargs thy
blanchet@44594
   508
  handle TYPE _ => [] |> Term.add_tvarsT T |> rev |> map TVar
blanchet@44594
   509
blanchet@43859
   510
(* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
blanchet@43859
   511
   Also accumulates sort infomation. *)
nik@44495
   512
fun iterm_from_term thy format bs (P $ Q) =
blanchet@43085
   513
    let
nik@44495
   514
      val (P', P_atomics_Ts) = iterm_from_term thy format bs P
nik@44495
   515
      val (Q', Q_atomics_Ts) = iterm_from_term thy format bs Q
blanchet@43859
   516
    in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
nik@44495
   517
  | iterm_from_term thy format _ (Const (c, T)) =
nik@44495
   518
    (IConst (`(make_fixed_const (SOME format)) c, T,
blanchet@44594
   519
             robust_const_typargs thy (c, T)),
blanchet@43907
   520
     atyps_of T)
nik@44495
   521
  | iterm_from_term _ _ _ (Free (s, T)) =
blanchet@43907
   522
    (IConst (`make_fixed_var s, T,
blanchet@43936
   523
             if String.isPrefix polymorphic_free_prefix s then [T] else []),
blanchet@43907
   524
     atyps_of T)
nik@44495
   525
  | iterm_from_term _ format _ (Var (v as (s, _), T)) =
blanchet@43085
   526
    (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
blanchet@43085
   527
       let
blanchet@43085
   528
         val Ts = T |> strip_type |> swap |> op ::
blanchet@43085
   529
         val s' = new_skolem_const_name s (length Ts)
nik@44495
   530
       in IConst (`(make_fixed_const (SOME format)) s', T, Ts) end
blanchet@43085
   531
     else
blanchet@43859
   532
       IVar ((make_schematic_var v, s), T), atyps_of T)
nik@44495
   533
  | iterm_from_term _ _ bs (Bound j) =
blanchet@44403
   534
    nth bs j |> (fn (_, (name, T)) => (IConst (name, T, []), atyps_of T))
nik@44495
   535
  | iterm_from_term thy format bs (Abs (s, T, t)) =
nik@43678
   536
    let
nik@43678
   537
      fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
nik@43678
   538
      val s = vary s
blanchet@44403
   539
      val name = `make_bound_var s
nik@44495
   540
      val (tm, atomic_Ts) = iterm_from_term thy format ((s, (name, T)) :: bs) t
blanchet@44403
   541
    in (IAbs ((name, T), tm), union (op =) atomic_Ts (atyps_of T)) end
blanchet@43085
   542
blanchet@43421
   543
datatype locality =
nik@44585
   544
  General | Helper | Induction | Extensionality | Intro | Elim | Simp |
nik@44585
   545
  Local | Assum | Chained
blanchet@43085
   546
blanchet@43624
   547
datatype order = First_Order | Higher_Order
blanchet@44494
   548
datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
blanchet@44397
   549
datatype soundness = Unsound | Sound_Modulo_Infiniteness | Sound
blanchet@42613
   550
datatype type_level =
blanchet@44397
   551
  All_Types |
blanchet@44397
   552
  Noninf_Nonmono_Types of soundness |
blanchet@44397
   553
  Fin_Nonmono_Types |
blanchet@44397
   554
  Const_Arg_Types |
blanchet@43362
   555
  No_Types
blanchet@44402
   556
datatype type_uniformity = Uniform | Nonuniform
blanchet@42613
   557
blanchet@43626
   558
datatype type_enc =
blanchet@44591
   559
  Simple_Types of order * polymorphism * type_level |
blanchet@44402
   560
  Guards of polymorphism * type_level * type_uniformity |
blanchet@44402
   561
  Tags of polymorphism * type_level * type_uniformity
blanchet@42613
   562
blanchet@42689
   563
fun try_unsuffixes ss s =
blanchet@42689
   564
  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
blanchet@42689
   565
blanchet@44397
   566
fun type_enc_from_string soundness s =
blanchet@42722
   567
  (case try (unprefix "poly_") s of
blanchet@42722
   568
     SOME s => (SOME Polymorphic, s)
blanchet@42613
   569
   | NONE =>
blanchet@44494
   570
     case try (unprefix "raw_mono_") s of
blanchet@44494
   571
       SOME s => (SOME Raw_Monomorphic, s)
blanchet@42722
   572
     | NONE =>
blanchet@44494
   573
       case try (unprefix "mono_") s of
blanchet@42722
   574
         SOME s => (SOME Mangled_Monomorphic, s)
blanchet@42722
   575
       | NONE => (NONE, s))
blanchet@42613
   576
  ||> (fn s =>
blanchet@43624
   577
          (* "_query" and "_bang" are for the ASCII-challenged Metis and
blanchet@43624
   578
             Mirabelle. *)
blanchet@42689
   579
          case try_unsuffixes ["?", "_query"] s of
blanchet@44397
   580
            SOME s => (Noninf_Nonmono_Types soundness, s)
blanchet@42613
   581
          | NONE =>
blanchet@42689
   582
            case try_unsuffixes ["!", "_bang"] s of
blanchet@43362
   583
              SOME s => (Fin_Nonmono_Types, s)
blanchet@42613
   584
            | NONE => (All_Types, s))
blanchet@42828
   585
  ||> apsnd (fn s =>
blanchet@44402
   586
                case try (unsuffix "_uniform") s of
blanchet@44402
   587
                  SOME s => (Uniform, s)
blanchet@44402
   588
                | NONE => (Nonuniform, s))
blanchet@44402
   589
  |> (fn (poly, (level, (uniformity, core))) =>
blanchet@44402
   590
         case (core, (poly, level, uniformity)) of
blanchet@44591
   591
           ("simple", (SOME poly, _, Nonuniform)) =>
blanchet@44591
   592
           (case poly of
blanchet@44591
   593
              Raw_Monomorphic => raise Same.SAME
blanchet@44591
   594
            | _ => Simple_Types (First_Order, poly, level))
blanchet@44591
   595
         | ("simple_higher", (SOME poly, _, Nonuniform)) =>
blanchet@44591
   596
           (case (poly, level) of
blanchet@44591
   597
              (Raw_Monomorphic, _) => raise Same.SAME
blanchet@44591
   598
            | (_, Noninf_Nonmono_Types _) => raise Same.SAME
blanchet@44591
   599
            | _ => Simple_Types (Higher_Order, poly, level))
blanchet@44402
   600
         | ("guards", (SOME poly, _, _)) => Guards (poly, level, uniformity)
blanchet@42886
   601
         | ("tags", (SOME Polymorphic, _, _)) =>
blanchet@44402
   602
           Tags (Polymorphic, level, uniformity)
blanchet@44402
   603
         | ("tags", (SOME poly, _, _)) => Tags (poly, level, uniformity)
blanchet@44402
   604
         | ("args", (SOME poly, All_Types (* naja *), Nonuniform)) =>
blanchet@44402
   605
           Guards (poly, Const_Arg_Types, Nonuniform)
blanchet@44402
   606
         | ("erased", (NONE, All_Types (* naja *), Nonuniform)) =>
blanchet@44402
   607
           Guards (Polymorphic, No_Types, Nonuniform)
blanchet@42753
   608
         | _ => raise Same.SAME)
blanchet@42753
   609
  handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
blanchet@42613
   610
blanchet@44591
   611
fun is_type_enc_higher_order (Simple_Types (Higher_Order, _, _)) = true
blanchet@43626
   612
  | is_type_enc_higher_order _ = false
blanchet@43624
   613
blanchet@44591
   614
fun polymorphism_of_type_enc (Simple_Types (_, poly, _)) = poly
blanchet@43989
   615
  | polymorphism_of_type_enc (Guards (poly, _, _)) = poly
blanchet@43626
   616
  | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
blanchet@42613
   617
blanchet@44591
   618
fun level_of_type_enc (Simple_Types (_, _, level)) = level
blanchet@43989
   619
  | level_of_type_enc (Guards (_, level, _)) = level
blanchet@43626
   620
  | level_of_type_enc (Tags (_, level, _)) = level
blanchet@42828
   621
blanchet@44402
   622
fun uniformity_of_type_enc (Simple_Types _) = Uniform
blanchet@44402
   623
  | uniformity_of_type_enc (Guards (_, _, uniformity)) = uniformity
blanchet@44402
   624
  | uniformity_of_type_enc (Tags (_, _, uniformity)) = uniformity
blanchet@42831
   625
blanchet@44397
   626
fun is_type_level_quasi_sound All_Types = true
blanchet@44397
   627
  | is_type_level_quasi_sound (Noninf_Nonmono_Types _) = true
blanchet@44397
   628
  | is_type_level_quasi_sound _ = false
blanchet@44397
   629
val is_type_enc_quasi_sound =
blanchet@44397
   630
  is_type_level_quasi_sound o level_of_type_enc
blanchet@42613
   631
blanchet@42613
   632
fun is_type_level_fairly_sound level =
blanchet@44397
   633
  is_type_level_quasi_sound level orelse level = Fin_Nonmono_Types
blanchet@43626
   634
val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
blanchet@42613
   635
blanchet@44397
   636
fun is_type_level_monotonicity_based (Noninf_Nonmono_Types _) = true
blanchet@44397
   637
  | is_type_level_monotonicity_based Fin_Nonmono_Types = true
blanchet@44397
   638
  | is_type_level_monotonicity_based _ = false
blanchet@44397
   639
blanchet@44591
   640
fun adjust_type_enc (THF0 _) (Simple_Types (order, Polymorphic, level)) =
blanchet@44591
   641
    Simple_Types (order, Mangled_Monomorphic, level)
blanchet@44591
   642
  | adjust_type_enc (THF0 _) type_enc = type_enc
blanchet@44591
   643
  | adjust_type_enc (TFF (TFF_Monomorphic, _)) (Simple_Types (_, _, level)) =
blanchet@44591
   644
    Simple_Types (First_Order, Mangled_Monomorphic, level)
blanchet@44591
   645
  | adjust_type_enc (TFF (_, _)) (Simple_Types (_, poly, level)) =
blanchet@44591
   646
    Simple_Types (First_Order, poly, level)
blanchet@44591
   647
  | adjust_type_enc format (Simple_Types (_, poly, level)) =
blanchet@44591
   648
    adjust_type_enc format (Guards (poly, level, Uniform))
blanchet@44416
   649
  | adjust_type_enc CNF_UEQ (type_enc as Guards stuff) =
blanchet@44416
   650
    (if is_type_enc_fairly_sound type_enc then Tags else Guards) stuff
blanchet@44416
   651
  | adjust_type_enc _ type_enc = type_enc
blanchet@43101
   652
blanchet@44088
   653
fun lift_lambdas ctxt type_enc =
blanchet@44088
   654
  map (close_form o Envir.eta_contract) #> rpair ctxt
blanchet@44088
   655
  #-> Lambda_Lifting.lift_lambdas
blanchet@44088
   656
          (if polymorphism_of_type_enc type_enc = Polymorphic then
blanchet@44088
   657
             SOME polymorphic_free_prefix
blanchet@44088
   658
           else
blanchet@44088
   659
             NONE)
blanchet@44088
   660
          Lambda_Lifting.is_quantifier
blanchet@44088
   661
  #> fst
blanchet@44088
   662
blanchet@44088
   663
fun intentionalize_def (Const (@{const_name All}, _) $ Abs (_, _, t)) =
blanchet@44088
   664
    intentionalize_def t
blanchet@44088
   665
  | intentionalize_def (Const (@{const_name HOL.eq}, _) $ t $ u) =
blanchet@44088
   666
    let
blanchet@44088
   667
      fun lam T t = Abs (Name.uu, T, t)
blanchet@44088
   668
      val (head, args) = strip_comb t ||> rev
blanchet@44088
   669
      val head_T = fastype_of head
blanchet@44088
   670
      val n = length args
blanchet@44088
   671
      val arg_Ts = head_T |> binder_types |> take n |> rev
blanchet@44088
   672
      val u = u |> subst_atomic (args ~~ map Bound (0 upto n - 1))
blanchet@44088
   673
    in HOLogic.eq_const head_T $ head $ fold lam arg_Ts u end
blanchet@44088
   674
  | intentionalize_def t = t
blanchet@44088
   675
blanchet@40114
   676
type translated_formula =
blanchet@43496
   677
  {name : string,
blanchet@43496
   678
   locality : locality,
blanchet@43496
   679
   kind : formula_kind,
blanchet@43859
   680
   iformula : (name, typ, iterm) formula,
blanchet@43496
   681
   atomic_types : typ list}
blanchet@38282
   682
blanchet@43859
   683
fun update_iformula f ({name, locality, kind, iformula, atomic_types}
blanchet@43859
   684
                       : translated_formula) =
blanchet@43859
   685
  {name = name, locality = locality, kind = kind, iformula = f iformula,
blanchet@42562
   686
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   687
blanchet@43859
   688
fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
blanchet@42558
   689
blanchet@43064
   690
fun insert_type ctxt get_T x xs =
blanchet@43064
   691
  let val T = get_T x in
blanchet@44399
   692
    if exists (type_instance ctxt T o get_T) xs then xs
blanchet@44399
   693
    else x :: filter_out (type_generalization ctxt T o get_T) xs
blanchet@43064
   694
  end
blanchet@42677
   695
blanchet@42753
   696
(* The Booleans indicate whether all type arguments should be kept. *)
blanchet@42753
   697
datatype type_arg_policy =
blanchet@42753
   698
  Explicit_Type_Args of bool |
blanchet@42753
   699
  Mangled_Type_Args of bool |
blanchet@42753
   700
  No_Type_Args
blanchet@41136
   701
blanchet@44594
   702
fun should_drop_arg_type_args (Simple_Types _) = false
blanchet@43626
   703
  | should_drop_arg_type_args type_enc =
blanchet@43626
   704
    level_of_type_enc type_enc = All_Types andalso
blanchet@44402
   705
    uniformity_of_type_enc type_enc = Uniform
blanchet@42831
   706
blanchet@43626
   707
fun type_arg_policy type_enc s =
blanchet@43628
   708
  if s = type_tag_name then
blanchet@43626
   709
    (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
blanchet@43623
   710
       Mangled_Type_Args
blanchet@43623
   711
     else
blanchet@43623
   712
       Explicit_Type_Args) false
blanchet@43628
   713
  else case type_enc of
blanchet@44402
   714
    Tags (_, All_Types, Uniform) => No_Type_Args
blanchet@43628
   715
  | _ =>
blanchet@44398
   716
    let val level = level_of_type_enc type_enc in
blanchet@44398
   717
      if level = No_Types orelse s = @{const_name HOL.eq} orelse
blanchet@44398
   718
         (s = app_op_name andalso level = Const_Arg_Types) then
blanchet@44398
   719
        No_Type_Args
blanchet@44398
   720
      else
blanchet@44398
   721
        should_drop_arg_type_args type_enc
blanchet@44398
   722
        |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
blanchet@44398
   723
              Mangled_Type_Args
blanchet@44398
   724
            else
blanchet@44398
   725
              Explicit_Type_Args)
blanchet@44398
   726
    end
blanchet@42227
   727
blanchet@43628
   728
(* Make literals for sorted type variables. *)
blanchet@43263
   729
fun generic_add_sorts_on_type (_, []) = I
blanchet@43263
   730
  | generic_add_sorts_on_type ((x, i), s :: ss) =
blanchet@43263
   731
    generic_add_sorts_on_type ((x, i), ss)
blanchet@43263
   732
    #> (if s = the_single @{sort HOL.type} then
blanchet@43093
   733
          I
blanchet@43093
   734
        else if i = ~1 then
blanchet@43263
   735
          insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
blanchet@43093
   736
        else
blanchet@43263
   737
          insert (op =) (TyLitVar (`make_type_class s,
blanchet@43263
   738
                                   (make_schematic_type_var (x, i), x))))
blanchet@43263
   739
fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
blanchet@43263
   740
  | add_sorts_on_tfree _ = I
blanchet@43263
   741
fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
blanchet@43263
   742
  | add_sorts_on_tvar _ = I
blanchet@43085
   743
blanchet@43626
   744
fun type_literals_for_types type_enc add_sorts_on_typ Ts =
blanchet@43626
   745
  [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
blanchet@41137
   746
blanchet@42534
   747
fun mk_aconns c phis =
blanchet@42534
   748
  let val (phis', phi') = split_last phis in
blanchet@42534
   749
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   750
  end
blanchet@38282
   751
fun mk_ahorn [] phi = phi
blanchet@42534
   752
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   753
fun mk_aquant _ [] phi = phi
blanchet@42522
   754
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   755
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   756
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   757
blanchet@42522
   758
fun close_universally atom_vars phi =
blanchet@41145
   759
  let
blanchet@41145
   760
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   761
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   762
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   763
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   764
        union (op =) (atom_vars tm []
blanchet@42526
   765
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   766
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   767
blanchet@43859
   768
fun iterm_vars (IApp (tm1, tm2)) = fold iterm_vars [tm1, tm2]
blanchet@43859
   769
  | iterm_vars (IConst _) = I
blanchet@43859
   770
  | iterm_vars (IVar (name, T)) = insert (op =) (name, SOME T)
blanchet@43859
   771
  | iterm_vars (IAbs (_, tm)) = iterm_vars tm
blanchet@43859
   772
fun close_iformula_universally phi = close_universally iterm_vars phi
blanchet@42522
   773
blanchet@44593
   774
fun term_vars type_enc =
blanchet@44593
   775
  let
blanchet@44593
   776
    fun vars bounds (ATerm (name as (s, _), tms)) =
blanchet@44593
   777
        (if is_tptp_variable s andalso not (member (op =) bounds name) then
blanchet@44593
   778
           (case type_enc of
blanchet@44593
   779
              Simple_Types (_, Polymorphic, _) =>
blanchet@44595
   780
              if String.isPrefix tvar_prefix s then SOME atype_of_types
blanchet@44595
   781
              else NONE
blanchet@44593
   782
            | _ => NONE)
blanchet@44593
   783
           |> pair name |> insert (op =)
blanchet@44593
   784
         else
blanchet@44593
   785
           I)
blanchet@44593
   786
        #> fold (vars bounds) tms
blanchet@44593
   787
      | vars bounds (AAbs ((name, _), tm)) = vars (name :: bounds) tm
blanchet@44593
   788
  in vars end
blanchet@44593
   789
fun close_formula_universally type_enc =
blanchet@44593
   790
  close_universally (term_vars type_enc [])
blanchet@41145
   791
blanchet@44594
   792
val fused_infinite_type_name = @{type_name ind} (* any infinite type *)
blanchet@44594
   793
val fused_infinite_type = Type (fused_infinite_type_name, [])
blanchet@44594
   794
blanchet@44594
   795
fun tvar_name (x as (s, _)) = (make_schematic_type_var x, s)
blanchet@42994
   796
nik@43676
   797
fun ho_term_from_typ format type_enc =
blanchet@42994
   798
  let
blanchet@42994
   799
    fun term (Type (s, Ts)) =
blanchet@43626
   800
      ATerm (case (is_type_enc_higher_order type_enc, s) of
blanchet@42994
   801
               (true, @{type_name bool}) => `I tptp_bool_type
blanchet@42994
   802
             | (true, @{type_name fun}) => `I tptp_fun_type
blanchet@44594
   803
             | _ => if s = fused_infinite_type_name andalso
blanchet@44235
   804
                       is_format_typed format then
blanchet@43178
   805
                      `I tptp_individual_type
blanchet@43178
   806
                    else
blanchet@43178
   807
                      `make_fixed_type_const s,
blanchet@42994
   808
             map term Ts)
blanchet@42994
   809
    | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
blanchet@44594
   810
    | term (TVar (x, _)) = ATerm (tvar_name x, [])
blanchet@42994
   811
  in term end
blanchet@42562
   812
nik@43676
   813
fun ho_term_for_type_arg format type_enc T =
nik@43676
   814
  if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
blanchet@43401
   815
blanchet@42562
   816
(* This shouldn't clash with anything else. *)
blanchet@42542
   817
val mangled_type_sep = "\000"
blanchet@42542
   818
blanchet@42562
   819
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   820
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42761
   821
    f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
blanchet@42761
   822
    ^ ")"
blanchet@43692
   823
  | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
blanchet@42542
   824
blanchet@44396
   825
fun mangled_type format type_enc =
blanchet@44396
   826
  generic_mangled_type_name fst o ho_term_from_typ format type_enc
blanchet@44396
   827
blanchet@43085
   828
fun make_simple_type s =
blanchet@43085
   829
  if s = tptp_bool_type orelse s = tptp_fun_type orelse
blanchet@43085
   830
     s = tptp_individual_type then
blanchet@43085
   831
    s
blanchet@43085
   832
  else
blanchet@43085
   833
    simple_type_prefix ^ ascii_of s
blanchet@43085
   834
nik@43676
   835
fun ho_type_from_ho_term type_enc pred_sym ary =
blanchet@42963
   836
  let
blanchet@44593
   837
    fun to_mangled_atype ty =
blanchet@42963
   838
      AType ((make_simple_type (generic_mangled_type_name fst ty),
blanchet@44593
   839
              generic_mangled_type_name snd ty), [])
blanchet@44593
   840
    fun to_poly_atype (ATerm (name, tys)) = AType (name, map to_poly_atype tys)
blanchet@44593
   841
      | to_poly_atype _ = raise Fail "unexpected type abstraction"
blanchet@44593
   842
    val to_atype =
blanchet@44593
   843
      if polymorphism_of_type_enc type_enc = Polymorphic then to_poly_atype
blanchet@44593
   844
      else to_mangled_atype
blanchet@42963
   845
    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
blanchet@42998
   846
    fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
blanchet@42994
   847
      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
blanchet@43692
   848
      | to_fo _ _ = raise Fail "unexpected type abstraction"
blanchet@42994
   849
    fun to_ho (ty as ATerm ((s, _), tys)) =
nik@43676
   850
        if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
nik@43676
   851
      | to_ho _ = raise Fail "unexpected type abstraction"
blanchet@43626
   852
  in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
blanchet@42963
   853
nik@43677
   854
fun ho_type_from_typ format type_enc pred_sym ary =
nik@43676
   855
  ho_type_from_ho_term type_enc pred_sym ary
nik@43676
   856
  o ho_term_from_typ format type_enc
blanchet@42963
   857
blanchet@43626
   858
fun mangled_const_name format type_enc T_args (s, s') =
blanchet@42963
   859
  let
nik@43676
   860
    val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
blanchet@42963
   861
    fun type_suffix f g =
blanchet@42963
   862
      fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42963
   863
                o generic_mangled_type_name f) ty_args ""
blanchet@42963
   864
  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@42542
   865
blanchet@42542
   866
val parse_mangled_ident =
blanchet@42542
   867
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   868
blanchet@42542
   869
fun parse_mangled_type x =
blanchet@42542
   870
  (parse_mangled_ident
blanchet@42542
   871
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   872
                    [] >> ATerm) x
blanchet@42542
   873
and parse_mangled_types x =
blanchet@42542
   874
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   875
blanchet@42542
   876
fun unmangled_type s =
blanchet@42542
   877
  s |> suffix ")" |> raw_explode
blanchet@42542
   878
    |> Scan.finite Symbol.stopper
blanchet@42542
   879
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   880
                                                quote s)) parse_mangled_type))
blanchet@42542
   881
    |> fst
blanchet@42542
   882
blanchet@42561
   883
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   884
fun unmangled_const s =
blanchet@42542
   885
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   886
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   887
  end
blanchet@42542
   888
blanchet@43626
   889
fun introduce_proxies type_enc =
blanchet@42568
   890
  let
blanchet@43987
   891
    fun tweak_ho_quant ho_quant T [IAbs _] = IConst (`I ho_quant, T, [])
blanchet@43987
   892
      | tweak_ho_quant ho_quant (T as Type (_, [p_T as Type (_, [x_T, _]), _]))
blanchet@43987
   893
                       _ =
blanchet@43987
   894
        (* Eta-expand "!!" and "??", to work around LEO-II 1.2.8 parser
blanchet@43987
   895
           limitation. This works in conjuction with special code in
blanchet@43987
   896
           "ATP_Problem" that uses the syntactic sugar "!" and "?" whenever
blanchet@43987
   897
           possible. *)
blanchet@43987
   898
        IAbs ((`I "P", p_T),
blanchet@43987
   899
              IApp (IConst (`I ho_quant, T, []),
blanchet@43987
   900
                    IAbs ((`I "X", x_T),
blanchet@43987
   901
                          IApp (IConst (`I "P", p_T, []),
blanchet@43987
   902
                                IConst (`I "X", x_T, [])))))
blanchet@43987
   903
      | tweak_ho_quant _ _ _ = raise Fail "unexpected type for quantifier"
blanchet@43987
   904
    fun intro top_level args (IApp (tm1, tm2)) =
blanchet@43987
   905
        IApp (intro top_level (tm2 :: args) tm1, intro false [] tm2)
blanchet@43987
   906
      | intro top_level args (IConst (name as (s, _), T, T_args)) =
blanchet@42570
   907
        (case proxify_const s of
blanchet@43159
   908
           SOME proxy_base =>
blanchet@43626
   909
           if top_level orelse is_type_enc_higher_order type_enc then
blanchet@43000
   910
             case (top_level, s) of
blanchet@43987
   911
               (_, "c_False") => IConst (`I tptp_false, T, [])
blanchet@43987
   912
             | (_, "c_True") => IConst (`I tptp_true, T, [])
blanchet@43987
   913
             | (false, "c_Not") => IConst (`I tptp_not, T, [])
blanchet@43987
   914
             | (false, "c_conj") => IConst (`I tptp_and, T, [])
blanchet@43987
   915
             | (false, "c_disj") => IConst (`I tptp_or, T, [])
blanchet@43987
   916
             | (false, "c_implies") => IConst (`I tptp_implies, T, [])
blanchet@43987
   917
             | (false, "c_All") => tweak_ho_quant tptp_ho_forall T args
blanchet@43987
   918
             | (false, "c_Ex") => tweak_ho_quant tptp_ho_exists T args
blanchet@43000
   919
             | (false, s) =>
blanchet@44097
   920
               if is_tptp_equal s andalso length args = 2 then
blanchet@44097
   921
                 IConst (`I tptp_equal, T, [])
blanchet@44097
   922
               else
blanchet@44589
   923
                 (* Use a proxy even for partially applied THF0 equality,
blanchet@44589
   924
                    because the LEO-II and Satallax parsers complain about not
blanchet@44589
   925
                    being able to infer the type of "=". *)
blanchet@44097
   926
                 IConst (proxy_base |>> prefix const_prefix, T, T_args)
blanchet@43987
   927
             | _ => IConst (name, T, [])
blanchet@42569
   928
           else
blanchet@43987
   929
             IConst (proxy_base |>> prefix const_prefix, T, T_args)
nik@44495
   930
          | NONE => if s = tptp_choice then
nik@44495
   931
                      tweak_ho_quant tptp_choice T args
blanchet@44589
   932
                    else
blanchet@44589
   933
                      IConst (name, T, T_args))
blanchet@43987
   934
      | intro _ _ (IAbs (bound, tm)) = IAbs (bound, intro false [] tm)
blanchet@43987
   935
      | intro _ _ tm = tm
blanchet@43987
   936
  in intro true [] end
blanchet@42568
   937
nik@44495
   938
fun iformula_from_prop thy format type_enc eq_as_iff =
blanchet@38282
   939
  let
blanchet@42568
   940
    fun do_term bs t atomic_types =
nik@44495
   941
      iterm_from_term thy format bs (Envir.eta_contract t)
blanchet@43626
   942
      |>> (introduce_proxies type_enc #> AAtom)
blanchet@42568
   943
      ||> union (op =) atomic_types
blanchet@44403
   944
    fun do_quant bs q pos s T t' =
blanchet@44403
   945
      let
blanchet@44403
   946
        val s = singleton (Name.variant_list (map fst bs)) s
blanchet@44403
   947
        val universal = Option.map (q = AExists ? not) pos
blanchet@44403
   948
        val name =
blanchet@44403
   949
          s |> `(case universal of
blanchet@44403
   950
                   SOME true => make_all_bound_var
blanchet@44403
   951
                 | SOME false => make_exist_bound_var
blanchet@44403
   952
                 | NONE => make_bound_var)
blanchet@44403
   953
      in
blanchet@44403
   954
        do_formula ((s, (name, T)) :: bs) pos t'
blanchet@44403
   955
        #>> mk_aquant q [(name, SOME T)]
blanchet@38518
   956
      end
blanchet@44403
   957
    and do_conn bs c pos1 t1 pos2 t2 =
blanchet@44403
   958
      do_formula bs pos1 t1 ##>> do_formula bs pos2 t2 #>> uncurry (mk_aconn c)
blanchet@44403
   959
    and do_formula bs pos t =
blanchet@38282
   960
      case t of
blanchet@44403
   961
        @{const Trueprop} $ t1 => do_formula bs pos t1
blanchet@44403
   962
      | @{const Not} $ t1 => do_formula bs (Option.map not pos) t1 #>> mk_anot
blanchet@38282
   963
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@44403
   964
        do_quant bs AForall pos s T t'
blanchet@38282
   965
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@44403
   966
        do_quant bs AExists pos s T t'
blanchet@44403
   967
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd pos t1 pos t2
blanchet@44403
   968
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr pos t1 pos t2
blanchet@44403
   969
      | @{const HOL.implies} $ t1 $ t2 =>
blanchet@44403
   970
        do_conn bs AImplies (Option.map not pos) t1 pos t2
haftmann@38864
   971
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@44403
   972
        if eq_as_iff then do_conn bs AIff NONE t1 NONE t2 else do_term bs t
blanchet@41140
   973
      | _ => do_term bs t
blanchet@38282
   974
  in do_formula [] end
blanchet@38282
   975
blanchet@43264
   976
fun presimplify_term _ [] t = t
blanchet@43264
   977
  | presimplify_term ctxt presimp_consts t =
blanchet@43264
   978
    t |> exists_Const (member (op =) presimp_consts o fst) t
blanchet@43264
   979
         ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@43264
   980
            #> Meson.presimplify ctxt
blanchet@43264
   981
            #> prop_of)
blanchet@38282
   982
blanchet@43863
   983
fun concealed_bound_name j = atp_weak_prefix ^ string_of_int j
blanchet@38282
   984
fun conceal_bounds Ts t =
blanchet@38282
   985
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   986
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   987
fun reveal_bounds Ts =
blanchet@38282
   988
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   989
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   990
blanchet@43265
   991
fun is_fun_equality (@{const_name HOL.eq},
blanchet@43265
   992
                     Type (_, [Type (@{type_name fun}, _), _])) = true
blanchet@43265
   993
  | is_fun_equality _ = false
blanchet@43265
   994
blanchet@42747
   995
fun extensionalize_term ctxt t =
blanchet@43265
   996
  if exists_Const is_fun_equality t then
blanchet@43265
   997
    let val thy = Proof_Context.theory_of ctxt in
blanchet@43265
   998
      t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@43265
   999
        |> prop_of |> Logic.dest_equals |> snd
blanchet@43265
  1000
    end
blanchet@43265
  1001
  else
blanchet@43265
  1002
    t
blanchet@38608
  1003
blanchet@43862
  1004
fun simple_translate_lambdas do_lambdas ctxt t =
blanchet@43863
  1005
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43863
  1006
    if Meson.is_fol_term thy t then
blanchet@43863
  1007
      t
blanchet@43863
  1008
    else
blanchet@43863
  1009
      let
blanchet@43863
  1010
        fun aux Ts t =
blanchet@43863
  1011
          case t of
blanchet@43863
  1012
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@43863
  1013
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@43863
  1014
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@43863
  1015
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@43863
  1016
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@43863
  1017
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@43863
  1018
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@43863
  1019
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@43863
  1020
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@43863
  1021
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
  1022
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
  1023
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
  1024
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@43863
  1025
              $ t1 $ t2 =>
blanchet@43863
  1026
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@43863
  1027
          | _ =>
blanchet@43863
  1028
            if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
blanchet@43863
  1029
            else t |> Envir.eta_contract |> do_lambdas ctxt Ts
blanchet@43863
  1030
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@43863
  1031
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@43863
  1032
  end
blanchet@43856
  1033
blanchet@43997
  1034
fun do_cheaply_conceal_lambdas Ts (t1 $ t2) =
blanchet@43997
  1035
    do_cheaply_conceal_lambdas Ts t1
blanchet@43997
  1036
    $ do_cheaply_conceal_lambdas Ts t2
blanchet@43997
  1037
  | do_cheaply_conceal_lambdas Ts (Abs (_, T, t)) =
blanchet@43997
  1038
    Free (polymorphic_free_prefix ^ serial_string (),
blanchet@43997
  1039
          T --> fastype_of1 (T :: Ts, t))
blanchet@43997
  1040
  | do_cheaply_conceal_lambdas _ t = t
blanchet@43856
  1041
blanchet@43862
  1042
fun do_introduce_combinators ctxt Ts t =
wenzelm@42361
  1043
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43905
  1044
    t |> conceal_bounds Ts
blanchet@43905
  1045
      |> cterm_of thy
blanchet@43905
  1046
      |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@43905
  1047
      |> prop_of |> Logic.dest_equals |> snd
blanchet@43905
  1048
      |> reveal_bounds Ts
blanchet@38491
  1049
  end
blanchet@43862
  1050
  (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@43997
  1051
  handle THM _ => t |> do_cheaply_conceal_lambdas Ts
blanchet@43862
  1052
val introduce_combinators = simple_translate_lambdas do_introduce_combinators
blanchet@43862
  1053
blanchet@43864
  1054
fun preprocess_abstractions_in_terms trans_lambdas facts =
blanchet@43862
  1055
  let
blanchet@43863
  1056
    val (facts, lambda_ts) =
blanchet@44501
  1057
      facts |> map (snd o snd) |> trans_lambdas
blanchet@43863
  1058
            |>> map2 (fn (name, (kind, _)) => fn t => (name, (kind, t))) facts
blanchet@43863
  1059
    val lambda_facts =
blanchet@43863
  1060
      map2 (fn t => fn j =>
blanchet@43863
  1061
               ((lambda_fact_prefix ^ Int.toString j, Helper), (Axiom, t)))
blanchet@43863
  1062
           lambda_ts (1 upto length lambda_ts)
blanchet@43863
  1063
  in (facts, lambda_facts) end
blanchet@38282
  1064
blanchet@38282
  1065
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
  1066
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
  1067
fun freeze_term t =
blanchet@38282
  1068
  let
blanchet@38282
  1069
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
  1070
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
  1071
      | aux (Var ((s, i), T)) =
blanchet@43863
  1072
        Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
  1073
      | aux t = t
blanchet@38282
  1074
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
  1075
blanchet@43863
  1076
fun presimp_prop ctxt presimp_consts t =
blanchet@38282
  1077
  let
wenzelm@42361
  1078
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
  1079
    val t = t |> Envir.beta_eta_contract
blanchet@42944
  1080
              |> transform_elim_prop
blanchet@41211
  1081
              |> Object_Logic.atomize_term thy
blanchet@42563
  1082
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@43096
  1083
  in
blanchet@43096
  1084
    t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@43096
  1085
      |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
blanchet@43096
  1086
      |> extensionalize_term ctxt
blanchet@43264
  1087
      |> presimplify_term ctxt presimp_consts
blanchet@43120
  1088
      |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@43096
  1089
  end
blanchet@43096
  1090
blanchet@43096
  1091
(* making fact and conjecture formulas *)
nik@44495
  1092
fun make_formula thy format type_enc eq_as_iff name loc kind t =
blanchet@43096
  1093
  let
blanchet@43859
  1094
    val (iformula, atomic_types) =
nik@44495
  1095
      iformula_from_prop thy format type_enc eq_as_iff (SOME (kind <> Conjecture)) t []
blanchet@38282
  1096
  in
blanchet@43859
  1097
    {name = name, locality = loc, kind = kind, iformula = iformula,
blanchet@42562
  1098
     atomic_types = atomic_types}
blanchet@38282
  1099
  end
blanchet@38282
  1100
blanchet@43860
  1101
fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) =
blanchet@43096
  1102
  let val thy = Proof_Context.theory_of ctxt in
nik@44495
  1103
    case t |> make_formula thy format type_enc (eq_as_iff andalso format <> CNF)
nik@44495
  1104
                           name loc Axiom of
blanchet@43859
  1105
      formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
blanchet@43096
  1106
      if s = tptp_true then NONE else SOME formula
blanchet@43295
  1107
    | formula => SOME formula
blanchet@43096
  1108
  end
blanchet@42561
  1109
blanchet@44460
  1110
fun s_not_trueprop (@{const Trueprop} $ t) = @{const Trueprop} $ s_not t
blanchet@44460
  1111
  | s_not_trueprop t = s_not t
blanchet@44460
  1112
blanchet@44463
  1113
fun make_conjecture thy format type_enc =
blanchet@44463
  1114
  map (fn ((name, loc), (kind, t)) =>
blanchet@44463
  1115
          t |> kind = Conjecture ? s_not_trueprop
nik@44495
  1116
            |> make_formula thy format type_enc (format <> CNF) name loc kind)
blanchet@38282
  1117
blanchet@42682
  1118
(** Finite and infinite type inference **)
blanchet@42682
  1119
blanchet@44399
  1120
type monotonicity_info =
blanchet@44399
  1121
  {maybe_finite_Ts : typ list,
blanchet@44399
  1122
   surely_finite_Ts : typ list,
blanchet@44399
  1123
   maybe_infinite_Ts : typ list,
blanchet@44399
  1124
   surely_infinite_Ts : typ list,
blanchet@44399
  1125
   maybe_nonmono_Ts : typ list}
blanchet@44399
  1126
blanchet@44397
  1127
(* These types witness that the type classes they belong to allow infinite
blanchet@44397
  1128
   models and hence that any types with these type classes is monotonic. *)
blanchet@44397
  1129
val known_infinite_types =
blanchet@44397
  1130
  [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
blanchet@44397
  1131
blanchet@44500
  1132
fun is_type_kind_of_surely_infinite ctxt soundness cached_Ts T =
blanchet@44397
  1133
  soundness <> Sound andalso
blanchet@44500
  1134
  is_type_surely_infinite ctxt (soundness <> Unsound) cached_Ts T
blanchet@42886
  1135
blanchet@42682
  1136
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
  1137
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
  1138
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
  1139
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
  1140
blanchet@44399
  1141
fun should_encode_type _ (_ : monotonicity_info) All_Types _ = true
blanchet@44399
  1142
  | should_encode_type ctxt {maybe_finite_Ts, surely_infinite_Ts,
blanchet@44399
  1143
                             maybe_nonmono_Ts, ...}
blanchet@44399
  1144
                       (Noninf_Nonmono_Types soundness) T =
blanchet@44491
  1145
    exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
blanchet@44399
  1146
    not (exists (type_instance ctxt T) surely_infinite_Ts orelse
blanchet@44399
  1147
         (not (member (type_aconv ctxt) maybe_finite_Ts T) andalso
blanchet@44500
  1148
          is_type_kind_of_surely_infinite ctxt soundness surely_infinite_Ts T))
blanchet@44399
  1149
  | should_encode_type ctxt {surely_finite_Ts, maybe_infinite_Ts,
blanchet@44399
  1150
                             maybe_nonmono_Ts, ...}
blanchet@44399
  1151
                       Fin_Nonmono_Types T =
blanchet@44491
  1152
    exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
blanchet@44491
  1153
    (exists (type_generalization ctxt T) surely_finite_Ts orelse
blanchet@44399
  1154
     (not (member (type_aconv ctxt) maybe_infinite_Ts T) andalso
blanchet@44399
  1155
      is_type_surely_finite ctxt T))
blanchet@42682
  1156
  | should_encode_type _ _ _ _ = false
blanchet@42682
  1157
blanchet@44402
  1158
fun should_guard_type ctxt mono (Guards (_, level, uniformity)) should_guard_var
blanchet@44399
  1159
                      T =
blanchet@44402
  1160
    (uniformity = Uniform orelse should_guard_var ()) andalso
blanchet@44399
  1161
    should_encode_type ctxt mono level T
blanchet@44399
  1162
  | should_guard_type _ _ _ _ _ = false
blanchet@42682
  1163
blanchet@44403
  1164
fun is_maybe_universal_var (IConst ((s, _), _, _)) =
blanchet@44403
  1165
    String.isPrefix bound_var_prefix s orelse
blanchet@44403
  1166
    String.isPrefix all_bound_var_prefix s
blanchet@44403
  1167
  | is_maybe_universal_var (IVar _) = true
blanchet@44403
  1168
  | is_maybe_universal_var _ = false
blanchet@42836
  1169
blanchet@43361
  1170
datatype tag_site =
blanchet@43361
  1171
  Top_Level of bool option |
blanchet@43361
  1172
  Eq_Arg of bool option |
blanchet@43361
  1173
  Elsewhere
blanchet@42829
  1174
blanchet@43361
  1175
fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
blanchet@44402
  1176
  | should_tag_with_type ctxt mono (Tags (_, level, uniformity)) site u T =
blanchet@44402
  1177
    (case uniformity of
blanchet@44402
  1178
       Uniform => should_encode_type ctxt mono level T
blanchet@44402
  1179
     | Nonuniform =>
blanchet@44403
  1180
       case (site, is_maybe_universal_var u) of
blanchet@44399
  1181
         (Eq_Arg _, true) => should_encode_type ctxt mono level T
blanchet@42829
  1182
       | _ => false)
blanchet@42829
  1183
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
  1184
blanchet@44594
  1185
fun fused_type ctxt mono level =
blanchet@42994
  1186
  let
blanchet@44399
  1187
    val should_encode = should_encode_type ctxt mono level
blanchet@44594
  1188
    fun fuse 0 T = if should_encode T then T else fused_infinite_type
blanchet@44594
  1189
      | fuse ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@44594
  1190
        fuse 0 T1 --> fuse (ary - 1) T2
blanchet@44594
  1191
      | fuse _ _ = raise Fail "expected function type"
blanchet@44594
  1192
  in fuse end
blanchet@42682
  1193
blanchet@44450
  1194
(** predicators and application operators **)
blanchet@41313
  1195
blanchet@42574
  1196
type sym_info =
blanchet@43064
  1197
  {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
blanchet@42563
  1198
blanchet@43859
  1199
fun add_iterm_syms_to_table ctxt explicit_apply =
blanchet@42558
  1200
  let
blanchet@43064
  1201
    fun consider_var_arity const_T var_T max_ary =
blanchet@43064
  1202
      let
blanchet@43064
  1203
        fun iter ary T =
blanchet@44399
  1204
          if ary = max_ary orelse type_instance ctxt var_T T orelse
blanchet@44399
  1205
             type_instance ctxt T var_T then
blanchet@43210
  1206
            ary
blanchet@43210
  1207
          else
blanchet@43210
  1208
            iter (ary + 1) (range_type T)
blanchet@43064
  1209
      in iter 0 const_T end
blanchet@44403
  1210
    fun add_universal_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@43201
  1211
      if explicit_apply = NONE andalso
blanchet@43201
  1212
         (can dest_funT T orelse T = @{typ bool}) then
blanchet@43201
  1213
        let
blanchet@43201
  1214
          val bool_vars' = bool_vars orelse body_type T = @{typ bool}
blanchet@43201
  1215
          fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
blanchet@43201
  1216
            {pred_sym = pred_sym andalso not bool_vars',
blanchet@43213
  1217
             min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
blanchet@43201
  1218
             max_ary = max_ary, types = types}
blanchet@43201
  1219
          val fun_var_Ts' =
blanchet@43201
  1220
            fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
blanchet@43201
  1221
        in
blanchet@43201
  1222
          if bool_vars' = bool_vars andalso
blanchet@43201
  1223
             pointer_eq (fun_var_Ts', fun_var_Ts) then
blanchet@43201
  1224
            accum
blanchet@43167
  1225
          else
blanchet@43213
  1226
            ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
blanchet@43201
  1227
        end
blanchet@43201
  1228
      else
blanchet@43201
  1229
        accum
blanchet@43201
  1230
    fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@43859
  1231
      let val (head, args) = strip_iterm_comb tm in
blanchet@42558
  1232
        (case head of
blanchet@43859
  1233
           IConst ((s, _), T, _) =>
blanchet@44403
  1234
           if String.isPrefix bound_var_prefix s orelse
blanchet@44403
  1235
              String.isPrefix all_bound_var_prefix s then
blanchet@44403
  1236
             add_universal_var T accum
blanchet@44450
  1237
           else if String.isPrefix exist_bound_var_prefix s then
blanchet@44450
  1238
             accum
blanchet@42558
  1239
           else
blanchet@43139
  1240
             let val ary = length args in
blanchet@43201
  1241
               ((bool_vars, fun_var_Ts),
blanchet@43064
  1242
                case Symtab.lookup sym_tab s of
blanchet@43064
  1243
                  SOME {pred_sym, min_ary, max_ary, types} =>
blanchet@43064
  1244
                  let
blanchet@43201
  1245
                    val pred_sym =
blanchet@43201
  1246
                      pred_sym andalso top_level andalso not bool_vars
blanchet@43064
  1247
                    val types' = types |> insert_type ctxt I T
blanchet@43064
  1248
                    val min_ary =
blanchet@43064
  1249
                      if is_some explicit_apply orelse
blanchet@43064
  1250
                         pointer_eq (types', types) then
blanchet@43064
  1251
                        min_ary
blanchet@43064
  1252
                      else
blanchet@43201
  1253
                        fold (consider_var_arity T) fun_var_Ts min_ary
blanchet@43064
  1254
                  in
blanchet@43201
  1255
                    Symtab.update (s, {pred_sym = pred_sym,
blanchet@43064
  1256
                                       min_ary = Int.min (ary, min_ary),
blanchet@43064
  1257
                                       max_ary = Int.max (ary, max_ary),
blanchet@43064
  1258
                                       types = types'})
blanchet@43064
  1259
                                  sym_tab
blanchet@43064
  1260
                  end
blanchet@43064
  1261
                | NONE =>
blanchet@43064
  1262
                  let
blanchet@43201
  1263
                    val pred_sym = top_level andalso not bool_vars
blanchet@43064
  1264
                    val min_ary =
blanchet@43064
  1265
                      case explicit_apply of
blanchet@43064
  1266
                        SOME true => 0
blanchet@43064
  1267
                      | SOME false => ary
blanchet@43201
  1268
                      | NONE => fold (consider_var_arity T) fun_var_Ts ary
blanchet@43064
  1269
                  in
blanchet@43201
  1270
                    Symtab.update_new (s, {pred_sym = pred_sym,
blanchet@43064
  1271
                                           min_ary = min_ary, max_ary = ary,
blanchet@43064
  1272
                                           types = [T]})
blanchet@43064
  1273
                                      sym_tab
blanchet@43064
  1274
                  end)
blanchet@43064
  1275
             end
blanchet@44403
  1276
         | IVar (_, T) => add_universal_var T accum
blanchet@44403
  1277
         | IAbs ((_, T), tm) => accum |> add_universal_var T |> add false tm
blanchet@43064
  1278
         | _ => accum)
blanchet@43064
  1279
        |> fold (add false) args
blanchet@42558
  1280
      end
blanchet@43064
  1281
  in add true end
blanchet@43064
  1282
fun add_fact_syms_to_table ctxt explicit_apply =
blanchet@44501
  1283
  K (add_iterm_syms_to_table ctxt explicit_apply)
blanchet@44501
  1284
  |> formula_fold NONE |> fact_lift
blanchet@38282
  1285
blanchet@44622
  1286
val tvar_a_str = "'a"
blanchet@44622
  1287
val tvar_a = TVar ((tvar_a_str, 0), HOLogic.typeS)
blanchet@44622
  1288
val tvar_a_name = (make_schematic_type_var (tvar_a_str, 0), tvar_a_str)
blanchet@44622
  1289
val itself_name = `make_fixed_type_const @{type_name itself}
blanchet@44622
  1290
val TYPE_name = `(make_fixed_const NONE) @{const_name TYPE}
blanchet@44622
  1291
val tvar_a_atype = AType (tvar_a_name, [])
blanchet@44622
  1292
val a_itself_atype = AType (itself_name, [tvar_a_atype])
blanchet@43966
  1293
blanchet@43139
  1294
val default_sym_tab_entries : (string * sym_info) list =
blanchet@43174
  1295
  (prefixed_predicator_name,
blanchet@44508
  1296
   {pred_sym = true, min_ary = 1, max_ary = 1, types = []})
blanchet@44508
  1297
       (* FIXME: needed? *) ::
nik@44495
  1298
  (make_fixed_const NONE @{const_name undefined},
blanchet@43966
  1299
   {pred_sym = false, min_ary = 0, max_ary = 0, types = []}) ::
blanchet@42568
  1300
  ([tptp_false, tptp_true]
blanchet@43139
  1301
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
blanchet@43139
  1302
  ([tptp_equal, tptp_old_equal]
blanchet@43139
  1303
   |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
blanchet@41140
  1304
blanchet@44496
  1305
fun sym_table_for_facts ctxt explicit_apply facts =
blanchet@43201
  1306
  ((false, []), Symtab.empty)
blanchet@43201
  1307
  |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
blanchet@43139
  1308
  |> fold Symtab.update default_sym_tab_entries
blanchet@38282
  1309
blanchet@42558
  1310
fun min_arity_of sym_tab s =
blanchet@42558
  1311
  case Symtab.lookup sym_tab s of
blanchet@42574
  1312
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
  1313
  | NONE =>
blanchet@42558
  1314
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
  1315
      SOME s =>
blanchet@42570
  1316
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
  1317
        if s = predicator_name then 1
blanchet@42966
  1318
        else if s = app_op_name then 2
blanchet@44396
  1319
        else if s = type_guard_name then 1
blanchet@42557
  1320
        else 0
blanchet@42547
  1321
      end
blanchet@42544
  1322
    | NONE => 0
blanchet@38282
  1323
blanchet@38282
  1324
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
  1325
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
  1326
   type instantiations). If false, the constant always receives all of its
blanchet@38282
  1327
   arguments and is used as a predicate. *)
blanchet@42558
  1328
fun is_pred_sym sym_tab s =
blanchet@42558
  1329
  case Symtab.lookup sym_tab s of
blanchet@42574
  1330
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
  1331
    pred_sym andalso min_ary = max_ary
blanchet@42558
  1332
  | NONE => false
blanchet@38282
  1333
blanchet@42568
  1334
val predicator_combconst =
nik@44495
  1335
  IConst (`(make_fixed_const NONE) predicator_name, @{typ "bool => bool"}, [])
blanchet@43859
  1336
fun predicator tm = IApp (predicator_combconst, tm)
blanchet@42542
  1337
blanchet@43859
  1338
fun introduce_predicators_in_iterm sym_tab tm =
blanchet@43859
  1339
  case strip_iterm_comb tm of
blanchet@43859
  1340
    (IConst ((s, _), _, _), _) =>
blanchet@42568
  1341
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
  1342
  | _ => predicator tm
blanchet@42542
  1343
blanchet@43859
  1344
fun list_app head args = fold (curry (IApp o swap)) args head
blanchet@42544
  1345
nik@44495
  1346
val app_op = `(make_fixed_const NONE) app_op_name
blanchet@43130
  1347
blanchet@42544
  1348
fun explicit_app arg head =
blanchet@42544
  1349
  let
blanchet@43859
  1350
    val head_T = ityp_of head
blanchet@42693
  1351
    val (arg_T, res_T) = dest_funT head_T
blanchet@43859
  1352
    val explicit_app = IConst (app_op, head_T --> head_T, [arg_T, res_T])
blanchet@42544
  1353
  in list_app explicit_app [head, arg] end
blanchet@42544
  1354
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
  1355
blanchet@43859
  1356
fun introduce_explicit_apps_in_iterm sym_tab =
blanchet@42544
  1357
  let
blanchet@42544
  1358
    fun aux tm =
blanchet@43859
  1359
      case strip_iterm_comb tm of
blanchet@43859
  1360
        (head as IConst ((s, _), _, _), args) =>
blanchet@42544
  1361
        args |> map aux
blanchet@42557
  1362
             |> chop (min_arity_of sym_tab s)
blanchet@42544
  1363
             |>> list_app head
blanchet@42544
  1364
             |-> list_explicit_app
blanchet@42544
  1365
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
  1366
  in aux end
blanchet@38282
  1367
blanchet@42753
  1368
fun chop_fun 0 T = ([], T)
blanchet@42753
  1369
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
  1370
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
  1371
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
  1372
blanchet@42780
  1373
fun filter_type_args _ _ _ [] = []
blanchet@42780
  1374
  | filter_type_args thy s arity T_args =
blanchet@44594
  1375
    let val U = robust_const_type thy s in
blanchet@42781
  1376
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
  1377
        [] => []
blanchet@42781
  1378
      | res_U_vars =>
blanchet@42781
  1379
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
  1380
          U_args ~~ T_args
blanchet@43401
  1381
          |> map (fn (U, T) =>
blanchet@43401
  1382
                     if member (op =) res_U_vars (dest_TVar U) then T
blanchet@43401
  1383
                     else dummyT)
blanchet@42781
  1384
        end
blanchet@42780
  1385
    end
blanchet@42780
  1386
    handle TYPE _ => T_args
blanchet@42753
  1387
blanchet@43859
  1388
fun enforce_type_arg_policy_in_iterm ctxt format type_enc =
blanchet@42753
  1389
  let
blanchet@42753
  1390
    val thy = Proof_Context.theory_of ctxt
blanchet@43859
  1391
    fun aux arity (IApp (tm1, tm2)) = IApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@43859
  1392
      | aux arity (IConst (name as (s, _), T, T_args)) =
blanchet@43179
  1393
        (case strip_prefix_and_unascii const_prefix s of
blanchet@43961
  1394
           NONE =>
nik@44495
  1395
           (name, if level_of_type_enc type_enc = No_Types orelse s = tptp_choice
nik@44495
  1396
                  then [] else T_args)
blanchet@43179
  1397
         | SOME s'' =>
blanchet@43179
  1398
           let
blanchet@43179
  1399
             val s'' = invert_const s''
blanchet@43179
  1400
             fun filtered_T_args false = T_args
blanchet@43179
  1401
               | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@43179
  1402
           in
blanchet@43626
  1403
             case type_arg_policy type_enc s'' of
blanchet@43179
  1404
               Explicit_Type_Args drop_args =>
blanchet@43179
  1405
               (name, filtered_T_args drop_args)
blanchet@43179
  1406
             | Mangled_Type_Args drop_args =>
blanchet@43626
  1407
               (mangled_const_name format type_enc (filtered_T_args drop_args)
blanchet@43179
  1408
                                   name, [])
blanchet@43179
  1409
             | No_Type_Args => (name, [])
blanchet@43179
  1410
           end)
blanchet@43859
  1411
        |> (fn (name, T_args) => IConst (name, T, T_args))
blanchet@43859
  1412
      | aux _ (IAbs (bound, tm)) = IAbs (bound, aux 0 tm)
blanchet@42753
  1413
      | aux _ tm = tm
blanchet@42753
  1414
  in aux 0 end
blanchet@42573
  1415
blanchet@43859
  1416
fun repair_iterm ctxt format type_enc sym_tab =
blanchet@43626
  1417
  not (is_type_enc_higher_order type_enc)
blanchet@43859
  1418
  ? (introduce_explicit_apps_in_iterm sym_tab
blanchet@43859
  1419
     #> introduce_predicators_in_iterm sym_tab)
blanchet@43859
  1420
  #> enforce_type_arg_policy_in_iterm ctxt format type_enc
blanchet@43626
  1421
fun repair_fact ctxt format type_enc sym_tab =
blanchet@43859
  1422
  update_iformula (formula_map (repair_iterm ctxt format type_enc sym_tab))
blanchet@42573
  1423
blanchet@42573
  1424
(** Helper facts **)
blanchet@42573
  1425
blanchet@44450
  1426
val not_ffalse = @{lemma "~ fFalse" by (unfold fFalse_def) fast}
blanchet@44450
  1427
val ftrue = @{lemma "fTrue" by (unfold fTrue_def) fast}
blanchet@44450
  1428
blanchet@43194
  1429
(* The Boolean indicates that a fairly sound type encoding is needed. *)
blanchet@43085
  1430
val helper_table =
blanchet@43194
  1431
  [(("COMBI", false), @{thms Meson.COMBI_def}),
blanchet@43194
  1432
   (("COMBK", false), @{thms Meson.COMBK_def}),
blanchet@43194
  1433
   (("COMBB", false), @{thms Meson.COMBB_def}),
blanchet@43194
  1434
   (("COMBC", false), @{thms Meson.COMBC_def}),
blanchet@43194
  1435
   (("COMBS", false), @{thms Meson.COMBS_def}),
blanchet@44450
  1436
   ((predicator_name, false), [not_ffalse, ftrue]),
blanchet@44450
  1437
   (("fFalse", false), [not_ffalse]),
blanchet@43194
  1438
   (("fFalse", true), @{thms True_or_False}),
blanchet@44450
  1439
   (("fTrue", false), [ftrue]),
blanchet@43194
  1440
   (("fTrue", true), @{thms True_or_False}),
blanchet@43194
  1441
   (("fNot", false),
blanchet@43194
  1442
    @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
blanchet@43194
  1443
           fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
blanchet@43194
  1444
   (("fconj", false),
blanchet@43194
  1445
    @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
blanchet@43194
  1446
        by (unfold fconj_def) fast+}),
blanchet@43194
  1447
   (("fdisj", false),
blanchet@43194
  1448
    @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
blanchet@43194
  1449
        by (unfold fdisj_def) fast+}),
blanchet@43194
  1450
   (("fimplies", false),
blanchet@43210
  1451
    @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
blanchet@43194
  1452
        by (unfold fimplies_def) fast+}),
nik@43678
  1453
   (("fequal", true),
nik@43678
  1454
    (* This is a lie: Higher-order equality doesn't need a sound type encoding.
nik@43678
  1455
       However, this is done so for backward compatibility: Including the
nik@43678
  1456
       equality helpers by default in Metis breaks a few existing proofs. *)
nik@43678
  1457
    @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
nik@43678
  1458
           fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
blanchet@44003
  1459
   (* Partial characterization of "fAll" and "fEx". A complete characterization
blanchet@44003
  1460
      would require the axiom of choice for replay with Metis. *)
blanchet@44003
  1461
   (("fAll", false), [@{lemma "~ fAll P | P x" by (auto simp: fAll_def)}]),
blanchet@44003
  1462
   (("fEx", false), [@{lemma "~ P x | fEx P" by (auto simp: fEx_def)}]),
blanchet@43194
  1463
   (("If", true), @{thms if_True if_False True_or_False})]
blanchet@43194
  1464
  |> map (apsnd (map zero_var_indexes))
blanchet@43085
  1465
blanchet@44622
  1466
fun type_class_aterm type_enc class arg =
blanchet@44622
  1467
  case type_enc of
blanchet@44622
  1468
    Simple_Types (_, Polymorphic, _) =>
blanchet@44622
  1469
    if exploit_tff1_dummy_type_vars then ATerm (class, [arg])
blanchet@44622
  1470
    else ATerm (class, [arg, ATerm (TYPE_name, [arg])])
blanchet@44622
  1471
  | _ => ATerm (class, [arg])
blanchet@44622
  1472
blanchet@44622
  1473
fun fo_literal_from_type_literal type_enc (TyLitVar (class, name)) =
blanchet@44622
  1474
    (true, type_class_aterm type_enc class (ATerm (name, [])))
blanchet@44622
  1475
  | fo_literal_from_type_literal type_enc (TyLitFree (class, name)) =
blanchet@44622
  1476
    (true, type_class_aterm type_enc class (ATerm (name, [])))
blanchet@44622
  1477
(* FIXME: Really "true" in both cases? If so, merge "TyLitVar" and
blanchet@44622
  1478
   "TyLitFree". *)
blanchet@44404
  1479
blanchet@44404
  1480
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@44404
  1481
blanchet@44404
  1482
fun bound_tvars type_enc Ts =
blanchet@44622
  1483
  mk_ahorn (map (formula_from_fo_literal
blanchet@44622
  1484
                 o fo_literal_from_type_literal type_enc)
blanchet@44404
  1485
                (type_literals_for_types type_enc add_sorts_on_tvar Ts))
blanchet@44404
  1486
blanchet@44404
  1487
fun eq_formula type_enc atomic_Ts pred_sym tm1 tm2 =
blanchet@44404
  1488
  (if pred_sym then AConn (AIff, [AAtom tm1, AAtom tm2])
blanchet@44404
  1489
   else AAtom (ATerm (`I tptp_equal, [tm1, tm2])))
blanchet@44404
  1490
  |> bound_tvars type_enc atomic_Ts
blanchet@44593
  1491
  |> close_formula_universally type_enc
blanchet@44404
  1492
nik@44495
  1493
val type_tag = `(make_fixed_const NONE) type_tag_name
blanchet@43130
  1494
blanchet@44404
  1495
fun type_tag_idempotence_fact type_enc =
blanchet@42573
  1496
  let
blanchet@42573
  1497
    fun var s = ATerm (`I s, [])
blanchet@44408
  1498
    fun tag tm = ATerm (type_tag, [var "A", tm])
blanchet@44408
  1499
    val tagged_var = tag (var "X")
blanchet@42573
  1500
  in
blanchet@43159
  1501
    Formula (type_tag_idempotence_helper_name, Axiom,
blanchet@44405
  1502
             eq_formula type_enc [] false (tag tagged_var) tagged_var,
blanchet@44404
  1503
             isabelle_info simpN, NONE)
blanchet@42573
  1504
  end
blanchet@42573
  1505
blanchet@43626
  1506
fun should_specialize_helper type_enc t =
blanchet@44493
  1507
  polymorphism_of_type_enc type_enc <> Polymorphic andalso
blanchet@43628
  1508
  level_of_type_enc type_enc <> No_Types andalso
blanchet@43628
  1509
  not (null (Term.hidden_polymorphism t))
blanchet@43159
  1510
blanchet@43858
  1511
fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
blanchet@42573
  1512
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
  1513
    SOME mangled_s =>
blanchet@42573
  1514
    let
blanchet@42573
  1515
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
  1516
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@43628
  1517
      fun dub needs_fairly_sound j k =
blanchet@43628
  1518
        (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
blanchet@43628
  1519
         (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
blanchet@43628
  1520
         (if needs_fairly_sound then typed_helper_suffix
blanchet@43628
  1521
          else untyped_helper_suffix),
blanchet@43628
  1522
         Helper)
blanchet@43159
  1523
      fun dub_and_inst needs_fairly_sound (th, j) =
blanchet@43628
  1524
        let val t = prop_of th in
blanchet@43628
  1525
          if should_specialize_helper type_enc t then
blanchet@43628
  1526
            map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
blanchet@43628
  1527
                types
blanchet@43628
  1528
          else
blanchet@43628
  1529
            [t]
blanchet@43628
  1530
        end
blanchet@43628
  1531
        |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
blanchet@43860
  1532
      val make_facts = map_filter (make_fact ctxt format type_enc false)
blanchet@43626
  1533
      val fairly_sound = is_type_enc_fairly_sound type_enc
blanchet@42573
  1534
    in
blanchet@43085
  1535
      helper_table
blanchet@43194
  1536
      |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
blanchet@43159
  1537
                  if helper_s <> unmangled_s orelse
blanchet@42894
  1538
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
  1539
                    []
blanchet@42573
  1540
                  else
blanchet@42573
  1541
                    ths ~~ (1 upto length ths)
blanchet@43628
  1542
                    |> maps (dub_and_inst needs_fairly_sound)
blanchet@43159
  1543
                    |> make_facts)
blanchet@42573
  1544
    end
blanchet@42573
  1545
  | NONE => []
blanchet@43858
  1546
fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
blanchet@43858
  1547
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
blanchet@43858
  1548
                  []
blanchet@42573
  1549
blanchet@43085
  1550
(***************************************************************)
blanchet@43085
  1551
(* Type Classes Present in the Axiom or Conjecture Clauses     *)
blanchet@43085
  1552
(***************************************************************)
blanchet@43085
  1553
blanchet@43085
  1554
fun set_insert (x, s) = Symtab.update (x, ()) s
blanchet@43085
  1555
blanchet@43085
  1556
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
blanchet@43085
  1557
blanchet@43085
  1558
(* Remove this trivial type class (FIXME: similar code elsewhere) *)
blanchet@43085
  1559
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
blanchet@43085
  1560
blanchet@43093
  1561
fun classes_of_terms get_Ts =
blanchet@43121
  1562
  map (map snd o get_Ts)
blanchet@43093
  1563
  #> List.foldl add_classes Symtab.empty
blanchet@43093
  1564
  #> delete_type #> Symtab.keys
blanchet@43085
  1565
wenzelm@44121
  1566
val tfree_classes_of_terms = classes_of_terms Misc_Legacy.term_tfrees
wenzelm@44121
  1567
val tvar_classes_of_terms = classes_of_terms Misc_Legacy.term_tvars
blanchet@43085
  1568
blanchet@43622
  1569
fun fold_type_constrs f (Type (s, Ts)) x =
blanchet@43622
  1570
    fold (fold_type_constrs f) Ts (f (s, x))
blanchet@43189
  1571
  | fold_type_constrs _ _ x = x
blanchet@43085
  1572
blanchet@43907
  1573
(* Type constructors used to instantiate overloaded constants are the only ones
blanchet@43907
  1574
   needed. *)
blanchet@43189
  1575
fun add_type_constrs_in_term thy =
blanchet@43085
  1576
  let
blanchet@43188
  1577
    fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
blanchet@43181
  1578
      | add (t $ u) = add t #> add u
blanchet@43188
  1579
      | add (Const (x as (s, _))) =
blanchet@43188
  1580
        if String.isPrefix skolem_const_prefix s then I
blanchet@43189
  1581
        else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
blanchet@43907
  1582
      | add (Free (s, T)) =
blanchet@43936
  1583
        if String.isPrefix polymorphic_free_prefix s then
blanchet@43907
  1584
          T |> fold_type_constrs set_insert
blanchet@43907
  1585
        else
blanchet@43907
  1586
          I
blanchet@43181
  1587
      | add (Abs (_, _, u)) = add u
blanchet@43181
  1588
      | add _ = I
blanchet@43181
  1589
  in add end
blanchet@43085
  1590
blanchet@43189
  1591
fun type_constrs_of_terms thy ts =
blanchet@43189
  1592
  Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
blanchet@43085
  1593
blanchet@43856
  1594
fun translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
blanchet@43828
  1595
                       hyp_ts concl_t facts =
blanchet@42573
  1596
  let
blanchet@42573
  1597
    val thy = Proof_Context.theory_of ctxt
blanchet@43264
  1598
    val presimp_consts = Meson.presimplified_consts ctxt
blanchet@43861
  1599
    val fact_ts = facts |> map snd
blanchet@42573
  1600
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
  1601
       boost an ATP's performance (for some reason). *)
blanchet@43192
  1602
    val hyp_ts =
blanchet@43192
  1603
      hyp_ts
blanchet@43192
  1604
      |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
blanchet@43864
  1605
    val facts = facts |> map (apsnd (pair Axiom))
blanchet@43864
  1606
    val conjs =
blanchet@44460
  1607
      map (pair prem_kind) hyp_ts @ [(Conjecture, s_not_trueprop concl_t)]
blanchet@43863
  1608
      |> map2 (pair o rpair Local o string_of_int) (0 upto length hyp_ts)
blanchet@43864
  1609
    val ((conjs, facts), lambdas) =
blanchet@43864
  1610
      if preproc then
blanchet@43864
  1611
        conjs @ facts
blanchet@43864
  1612
        |> map (apsnd (apsnd (presimp_prop ctxt presimp_consts)))
blanchet@43864
  1613
        |> preprocess_abstractions_in_terms trans_lambdas
blanchet@43864
  1614
        |>> chop (length conjs)
blanchet@43864
  1615
        |>> apfst (map (apsnd (apsnd freeze_term)))
blanchet@43864
  1616
      else
blanchet@43864
  1617
        ((conjs, facts), [])
blanchet@44460
  1618
    val conjs = conjs |> make_conjecture thy format type_enc
blanchet@43863
  1619
    val (fact_names, facts) =
blanchet@43864
  1620
      facts
blanchet@43863
  1621
      |> map_filter (fn (name, (_, t)) =>
blanchet@43863
  1622
                        make_fact ctxt format type_enc true (name, t)
blanchet@43863
  1623
                        |> Option.map (pair name))
blanchet@43861
  1624
      |> ListPair.unzip
blanchet@43863
  1625
    val lambdas =
blanchet@43864
  1626
      lambdas |> map_filter (make_fact ctxt format type_enc true o apsnd snd)
blanchet@43861
  1627
    val all_ts = concl_t :: hyp_ts @ fact_ts
blanchet@42573
  1628
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
  1629
    val supers = tvar_classes_of_terms all_ts
blanchet@43189
  1630
    val tycons = type_constrs_of_terms thy all_ts
blanchet@43861
  1631
    val (supers, arity_clauses) =
blanchet@43626
  1632
      if level_of_type_enc type_enc = No_Types then ([], [])
blanchet@42573
  1633
      else make_arity_clauses thy tycons supers
blanchet@43861
  1634
    val class_rel_clauses = make_class_rel_clauses thy subs supers
blanchet@42573
  1635
  in
blanchet@44595
  1636
    (fact_names |> map single, union (op =) subs supers, conjs, facts @ lambdas,
blanchet@44595
  1637
     class_rel_clauses, arity_clauses)
blanchet@42573
  1638
  end
blanchet@42573
  1639
nik@44495
  1640
val type_guard = `(make_fixed_const NONE) type_guard_name
blanchet@43130
  1641
blanchet@44396
  1642
fun type_guard_iterm ctxt format type_enc T tm =
blanchet@44396
  1643
  IApp (IConst (type_guard, T --> @{typ bool}, [T])
blanchet@43859
  1644
        |> enforce_type_arg_policy_in_iterm ctxt format type_enc, tm)
blanchet@42573
  1645
blanchet@43421
  1646
fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@43421
  1647
  | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@43000
  1648
    accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
blanchet@43692
  1649
  | is_var_positively_naked_in_term _ _ _ _ = true
blanchet@44403
  1650
blanchet@44406
  1651
fun should_guard_var_in_formula pos phi (SOME true) name =
blanchet@43421
  1652
    formula_fold pos (is_var_positively_naked_in_term name) phi false
blanchet@44406
  1653
  | should_guard_var_in_formula _ _ _ _ = true
blanchet@42834
  1654
blanchet@44405
  1655
fun should_generate_tag_bound_decl _ _ _ (SOME true) _ = false
blanchet@44405
  1656
  | should_generate_tag_bound_decl ctxt mono (Tags (_, level, Nonuniform)) _ T =
blanchet@44404
  1657
    should_encode_type ctxt mono level T
blanchet@44405
  1658
  | should_generate_tag_bound_decl _ _ _ _ _ = false
blanchet@44404
  1659
nik@43677
  1660
fun mk_aterm format type_enc name T_args args =
nik@43677
  1661
  ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
blanchet@42994
  1662
blanchet@44399
  1663
fun tag_with_type ctxt format mono type_enc pos T tm =
blanchet@43859
  1664
  IConst (type_tag, T --> T, [T])
blanchet@43859
  1665
  |> enforce_type_arg_policy_in_iterm ctxt format type_enc
blanchet@44399
  1666
  |> ho_term_from_iterm ctxt format mono type_enc (Top_Level pos)
blanchet@43692
  1667
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
blanchet@43692
  1668
       | _ => raise Fail "unexpected lambda-abstraction")
blanchet@44399
  1669
and ho_term_from_iterm ctxt format mono type_enc =
blanchet@42573
  1670
  let
blanchet@42962
  1671
    fun aux site u =
blanchet@42962
  1672
      let
blanchet@43859
  1673
        val (head, args) = strip_iterm_comb u
nik@43677
  1674
        val pos =
blanchet@43361
  1675
          case site of
nik@43677
  1676
            Top_Level pos => pos
nik@43677
  1677
          | Eq_Arg pos => pos
nik@43677
  1678
          | Elsewhere => NONE
nik@43677
  1679
        val t =
nik@43677
  1680
          case head of
blanchet@43859
  1681
            IConst (name as (s, _), _, T_args) =>
nik@43677
  1682
            let
nik@43677
  1683
              val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
nik@43677
  1684
            in
nik@43677
  1685
              mk_aterm format type_enc name T_args (map (aux arg_site) args)
nik@43677
  1686
            end
blanchet@43859
  1687
          | IVar (name, _) =>
blanchet@43859
  1688
            mk_aterm format type_enc name [] (map (aux Elsewhere) args)
blanchet@43859
  1689
          | IAbs ((name, T), tm) =>
blanchet@43859
  1690
            AAbs ((name, ho_type_from_typ format type_enc true 0 T),
blanchet@43859
  1691
                  aux Elsewhere tm)
blanchet@43859
  1692
          | IApp _ => raise Fail "impossible \"IApp\""
blanchet@43859
  1693
        val T = ityp_of u
blanchet@42962
  1694
      in
blanchet@44399
  1695
        t |> (if should_tag_with_type ctxt mono type_enc site u T then
blanchet@44399
  1696
                tag_with_type ctxt format mono type_enc pos T
blanchet@42962
  1697
              else
blanchet@42962
  1698
                I)
blanchet@42962
  1699
      end
blanchet@42962
  1700
  in aux end
blanchet@44399
  1701
and formula_from_iformula ctxt format mono type_enc should_guard_var =
blanchet@42829
  1702
  let
blanchet@44399
  1703
    val do_term = ho_term_from_iterm ctxt format mono type_enc o Top_Level
blanchet@42573
  1704
    val do_bound_type =
blanchet@43626
  1705
      case type_enc of
blanchet@44594
  1706
        Simple_Types (_, _, level) => fused_type ctxt mono level 0
nik@43677
  1707
        #> ho_type_from_typ format type_enc false 0 #> SOME
blanchet@42682
  1708
      | _ => K NONE
blanchet@42878
  1709
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@44399
  1710
      if should_guard_type ctxt mono type_enc
blanchet@44399
  1711
             (fn () => should_guard_var pos phi universal name) T then
blanchet@43859
  1712
        IVar (name, T)
blanchet@44396
  1713
        |> type_guard_iterm ctxt format type_enc T
blanchet@43361
  1714
        |> do_term pos |> AAtom |> SOME
blanchet@44405
  1715
      else if should_generate_tag_bound_decl ctxt mono type_enc universal T then
blanchet@44405
  1716
        let
blanchet@44405
  1717
          val var = ATerm (name, [])
blanchet@44505
  1718
          val tagged_var = var |> tag_with_type ctxt format mono type_enc pos T
blanchet@44405
  1719
        in SOME (AAtom (ATerm (`I tptp_equal, [tagged_var, var]))) end
blanchet@42573
  1720
      else
blanchet@42573
  1721
        NONE
blanchet@42878
  1722
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
  1723
        let
blanchet@42878
  1724
          val phi = phi |> do_formula pos
blanchet@42878
  1725
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
  1726
        in
blanchet@42834
  1727
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
  1728
                                        | SOME T => do_bound_type T)),
blanchet@42834
  1729
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
  1730
                      (map_filter
blanchet@42834
  1731
                           (fn (_, NONE) => NONE
blanchet@42834
  1732
                             | (s, SOME T) =>
blanchet@42878
  1733
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
  1734
                           xs)
blanchet@42834
  1735
                      phi)
blanchet@42834
  1736
        end
blanchet@42878
  1737
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@43361
  1738
      | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
blanchet@43493
  1739
  in do_formula end
blanchet@42573
  1740
blanchet@42573
  1741
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
  1742
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
  1743
   the remote provers might care. *)
blanchet@44399
  1744
fun formula_line_for_fact ctxt format prefix encode freshen pos mono type_enc
blanchet@44399
  1745
                          (j, {name, locality, kind, iformula, atomic_types}) =
blanchet@43864
  1746
  (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name, kind,
blanchet@43859
  1747
   iformula
blanchet@43859
  1748
   |> close_iformula_universally
blanchet@44399
  1749
   |> formula_from_iformula ctxt format mono type_enc
blanchet@44399
  1750
                            should_guard_var_in_formula
blanchet@43859
  1751
                            (if pos then SOME true else NONE)
blanchet@43626
  1752
   |> bound_tvars type_enc atomic_types
blanchet@44593
  1753
   |> close_formula_universally type_enc,
blanchet@43493
  1754
   NONE,
blanchet@43493
  1755
   case locality of
blanchet@43693
  1756
     Intro => isabelle_info introN
blanchet@43693
  1757
   | Elim => isabelle_info elimN
blanchet@43693
  1758
   | Simp => isabelle_info simpN
blanchet@43493
  1759
   | _ => NONE)
blanchet@43493
  1760
  |> Formula
blanchet@42573
  1761
blanchet@44593
  1762
fun formula_line_for_class_rel_clause type_enc
blanchet@44593
  1763
        ({name, subclass, superclass, ...} : class_rel_clause) =
blanchet@44622
  1764
  let val ty_arg = ATerm (tvar_a_name, []) in
blanchet@42577
  1765
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@44622
  1766
             AConn (AImplies,
blanchet@44622
  1767
                    [AAtom (type_class_aterm type_enc subclass ty_arg),
blanchet@44622
  1768
                     AAtom (type_class_aterm type_enc superclass ty_arg)])
blanchet@44593
  1769
             |> close_formula_universally type_enc, isabelle_info introN, NONE)
blanchet@42573
  1770
  end
blanchet@42573
  1771
blanchet@44622
  1772
fun fo_literal_from_arity_literal type_enc (AryLitConst (class, t, args)) =
blanchet@44622
  1773
    (true, type_class_aterm type_enc class
blanchet@44622
  1774
                            (ATerm (t, map (fn arg => ATerm (arg, [])) args)))
blanchet@44622
  1775
  | fo_literal_from_arity_literal type_enc (AryLitVar (class, var)) =
blanchet@44622
  1776
    (false, type_class_aterm type_enc class (ATerm (var, [])))
blanchet@42573
  1777
blanchet@44593
  1778
fun formula_line_for_arity_clause type_enc
blanchet@44593
  1779
        ({name, prem_lits, concl_lits, ...} : arity_clause) =
blanchet@43495
  1780
  Formula (arity_clause_prefix ^ name, Axiom,
blanchet@42573
  1781
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@44622
  1782
                          o fo_literal_from_arity_literal type_enc) prem_lits)
blanchet@42573
  1783
                    (formula_from_fo_literal
blanchet@44622
  1784
                         (fo_literal_from_arity_literal type_enc concl_lits))
blanchet@44593
  1785
           |> close_formula_universally type_enc, isabelle_info introN, NONE)
blanchet@42573
  1786
blanchet@44399
  1787
fun formula_line_for_conjecture ctxt format mono type_enc
blanchet@43859
  1788
        ({name, kind, iformula, atomic_types, ...} : translated_formula) =
blanchet@42577
  1789
  Formula (conjecture_prefix ^ name, kind,
blanchet@44399
  1790
           formula_from_iformula ctxt format mono type_enc
blanchet@44399
  1791
               should_guard_var_in_formula (SOME false)
blanchet@43859
  1792
               (close_iformula_universally iformula)
blanchet@43626
  1793
           |> bound_tvars type_enc atomic_types
blanchet@44593
  1794
           |> close_formula_universally type_enc, NONE, NONE)
blanchet@42573
  1795
blanchet@43626
  1796
fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
blanchet@43626
  1797
  atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
blanchet@44622
  1798
               |> map (fo_literal_from_type_literal type_enc)
blanchet@42573
  1799
blanchet@42573
  1800
fun formula_line_for_free_type j lit =
blanchet@43085
  1801
  Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
  1802
           formula_from_fo_literal lit, NONE, NONE)
blanchet@43626
  1803
fun formula_lines_for_free_types type_enc facts =
blanchet@42573
  1804
  let
blanchet@43626
  1805
    val litss = map (free_type_literals type_enc) facts
blanchet@42573
  1806
    val lits = fold (union (op =)) litss []
blanchet@42573
  1807
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
  1808
blanchet@42573
  1809
(** Symbol declarations **)
blanchet@42544
  1810
blanchet@44595
  1811
fun decl_line_for_class s =
blanchet@44595
  1812
  let val name as (s, _) = `make_type_class s in
blanchet@44622
  1813
    Decl (sym_decl_prefix ^ s, name,
blanchet@44622
  1814
          if exploit_tff1_dummy_type_vars then
blanchet@44622
  1815
            AFun (atype_of_types, bool_atype)
blanchet@44622
  1816
          else
blanchet@44622
  1817
            ATyAbs ([tvar_a_name], AFun (a_itself_atype, bool_atype)))
blanchet@44595
  1818
  end
blanchet@44595
  1819
blanchet@44595
  1820
fun decl_lines_for_classes type_enc classes =
blanchet@44595
  1821
  case type_enc of
blanchet@44595
  1822
    Simple_Types (_, Polymorphic, _) => map decl_line_for_class classes
blanchet@44595
  1823
  | _ => []
blanchet@44595
  1824
blanchet@43984
  1825
fun sym_decl_table_for_facts ctxt format type_enc repaired_sym_tab
blanchet@43984
  1826
                             (conjs, facts) =
blanchet@42574
  1827
  let
blanchet@43966
  1828
    fun add_iterm_syms in_conj tm =
blanchet@43859
  1829
      let val (head, args) = strip_iterm_comb tm in
blanchet@42574
  1830
        (case head of
blanchet@43859
  1831
           IConst ((s, s'), T, T_args) =>
blanchet@44594
  1832
           let
blanchet@44594
  1833
             val pred_sym = is_pred_sym repaired_sym_tab s
blanchet@44594
  1834
             val decl_sym =
blanchet@44594
  1835
               (case type_enc of
blanchet@44594
  1836
                  Guards _ => not pred_sym
blanchet@44594
  1837
                | _ => true) andalso
blanchet@44594
  1838
               is_tptp_user_symbol s
blanchet@44594
  1839
           in
blanchet@44594
  1840
             if decl_sym then
blanchet@42576
  1841
               Symtab.map_default (s, [])
blanchet@42886
  1842
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1843
                                         in_conj))
blanchet@42574
  1844
             else
blanchet@42574
  1845
               I
blanchet@42574
  1846
           end
blanchet@43966
  1847
         | IAbs (_, tm) => add_iterm_syms in_conj tm
blanchet@42574
  1848
         | _ => I)
blanchet@43966
  1849
        #> fold (add_iterm_syms in_conj) args
blanchet@42574
  1850
      end
blanchet@43966
  1851
    fun add_fact_syms in_conj =
blanchet@44501
  1852
      K (add_iterm_syms in_conj) |> formula_fold NONE |> fact_lift
blanchet@43966
  1853
    fun add_formula_var_types (AQuant (_, xs, phi)) =
blanchet@43966
  1854
        fold (fn (_, SOME T) => insert_type ctxt I T | _ => I) xs
blanchet@43966
  1855
        #> add_formula_var_types phi
blanchet@43966
  1856
      | add_formula_var_types (AConn (_, phis)) =
blanchet@43966
  1857
        fold add_formula_var_types phis
blanchet@43966
  1858
      | add_formula_var_types _ = I
blanchet@43966
  1859
    fun var_types () =
blanchet@43966
  1860
      if polymorphism_of_type_enc type_enc = Polymorphic then [tvar_a]
blanchet@43966
  1861
      else fold (fact_lift add_formula_var_types) (conjs @ facts) []
blanchet@43966
  1862
    fun add_undefined_const T =
blanchet@43984
  1863
      let
blanchet@43984
  1864
        val (s, s') =
blanchet@44622
  1865
          `(make_fixed_const NONE) @{const_name undefined}
blanchet@44001
  1866
          |> (case type_arg_policy type_enc @{const_name undefined} of
blanchet@44001
  1867
                Mangled_Type_Args _ => mangled_const_name format type_enc [T]
blanchet@44001
  1868
              | _ => I)
blanchet@43984
  1869
      in
blanchet@43984
  1870
        Symtab.map_default (s, [])
blanchet@43984
  1871
                           (insert_type ctxt #3 (s', [T], T, false, 0, false))
blanchet@43984
  1872
      end
blanchet@44622
  1873
    fun add_TYPE_const () =
blanchet@44622
  1874
      let val (s, s') = TYPE_name in
blanchet@44622
  1875
        Symtab.map_default (s, [])
blanchet@44622
  1876
            (insert_type ctxt #3
blanchet@44622
  1877
                         (s', [tvar_a], @{typ "'a itself"}, false, 0, false))
blanchet@44622
  1878
      end
blanchet@42698
  1879
  in
blanchet@42698
  1880
    Symtab.empty
blanchet@43626
  1881
    |> is_type_enc_fairly_sound type_enc
blanchet@43966
  1882
       ? (fold (add_fact_syms true) conjs
blanchet@43966
  1883
          #> fold (add_fact_syms false) facts
blanchet@43985
  1884
          #> (case type_enc of
blanchet@44622
  1885
                Simple_Types (_, poly, _) =>
blanchet@44622
  1886
                if poly = Polymorphic then add_TYPE_const () else I
blanchet@43985
  1887
              | _ => fold add_undefined_const (var_types ())))
blanchet@42698
  1888
  end
blanchet@42533
  1889
blanchet@44399
  1890
(* We add "bool" in case the helper "True_or_False" is included later. *)
blanchet@44399
  1891
val default_mono =
blanchet@44399
  1892
  {maybe_finite_Ts = [@{typ bool}],
blanchet@44399
  1893
   surely_finite_Ts = [@{typ bool}],
blanchet@44399
  1894
   maybe_infinite_Ts = known_infinite_types,
blanchet@44399
  1895
   surely_infinite_Ts = known_infinite_types,
blanchet@44399
  1896
   maybe_nonmono_Ts = [@{typ bool}]}
blanchet@44399
  1897
blanchet@42685
  1898
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1899
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@44399
  1900
fun add_iterm_mononotonicity_info _ _ (SOME false) _ mono = mono
blanchet@44399
  1901
  | add_iterm_mononotonicity_info ctxt level _
blanchet@44399
  1902
        (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2))
blanchet@44399
  1903
        (mono as {maybe_finite_Ts, surely_finite_Ts, maybe_infinite_Ts,
blanchet@44399
  1904
                  surely_infinite_Ts, maybe_nonmono_Ts}) =
blanchet@44403
  1905
    if is_tptp_equal s andalso exists is_maybe_universal_var [tm1, tm2] then
blanchet@44399
  1906
      case level of
blanchet@44397
  1907
        Noninf_Nonmono_Types soundness =>
blanchet@44399
  1908
        if exists (type_instance ctxt T) surely_infinite_Ts orelse
blanchet@44399
  1909
           member (type_aconv ctxt) maybe_finite_Ts T then
blanchet@44399
  1910
          mono
blanchet@44500
  1911
        else if is_type_kind_of_surely_infinite ctxt soundness
blanchet@44500
  1912
                                                surely_infinite_Ts T then
blanchet@44399
  1913
          {maybe_finite_Ts = maybe_finite_Ts,
blanchet@44399
  1914
           surely_finite_Ts = surely_finite_Ts,
blanchet@44399
  1915
           maybe_infinite_Ts = maybe_infinite_Ts,
blanchet@44399
  1916
           surely_infinite_Ts = surely_infinite_Ts |> insert_type ctxt I T,
blanchet@44399
  1917
           maybe_nonmono_Ts = maybe_nonmono_Ts}
blanchet@44399
  1918
        else
blanchet@44399
  1919
          {maybe_finite_Ts = maybe_finite_Ts |> insert (type_aconv ctxt) T,
blanchet@44399
  1920
           surely_finite_Ts = surely_finite_Ts,
blanchet@44399
  1921
           maybe_infinite_Ts = maybe_infinite_Ts,
blanchet@44399
  1922
           surely_infinite_Ts = surely_infinite_Ts,
blanchet@44399
  1923
           maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
blanchet@44399
  1924
      | Fin_Nonmono_Types =>
blanchet@44399
  1925
        if exists (type_instance ctxt T) surely_finite_Ts orelse
blanchet@44399
  1926
           member (type_aconv ctxt) maybe_infinite_Ts T then
blanchet@44399
  1927
          mono
blanchet@44399
  1928
        else if is_type_surely_finite ctxt T then
blanchet@44399
  1929
          {maybe_finite_Ts = maybe_finite_Ts,
blanchet@44399
  1930
           surely_finite_Ts = surely_finite_Ts |> insert_type ctxt I T,
blanchet@44399
  1931
           maybe_infinite_Ts = maybe_infinite_Ts,
blanchet@44399
  1932
           surely_infinite_Ts = surely_infinite_Ts,
blanchet@44399
  1933
           maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
blanchet@44399
  1934
        else
blanchet@44399
  1935
          {maybe_finite_Ts = maybe_finite_Ts,
blanchet@44399
  1936
           surely_finite_Ts = surely_finite_Ts,
blanchet@44399
  1937
           maybe_infinite_Ts = maybe_infinite_Ts |> insert (type_aconv ctxt) T,
blanchet@44399
  1938
           surely_infinite_Ts = surely_infinite_Ts,
blanchet@44399
  1939
           maybe_nonmono_Ts = maybe_nonmono_Ts}
blanchet@44399
  1940
      | _ => mono
blanchet@44399
  1941
    else
blanchet@44399
  1942
      mono
blanchet@44399
  1943
  | add_iterm_mononotonicity_info _ _ _ _ mono = mono
blanchet@44399
  1944
fun add_fact_mononotonicity_info ctxt level
blanchet@44399
  1945
        ({kind, iformula, ...} : translated_formula) =
blanchet@42834
  1946
  formula_fold (SOME (kind <> Conjecture))
blanchet@44399
  1947
               (add_iterm_mononotonicity_info ctxt level) iformula
blanchet@44399
  1948
fun mononotonicity_info_for_facts ctxt type_enc facts =
blanchet@43626
  1949
  let val level = level_of_type_enc type_enc in
blanchet@44399
  1950
    default_mono
blanchet@44399
  1951
    |> is_type_level_monotonicity_based level
blanchet@44399
  1952
       ? fold (add_fact_mononotonicity_info ctxt level) facts
blanchet@42829
  1953
  end
blanchet@42677
  1954
blanchet@44501
  1955
fun add_iformula_monotonic_types ctxt mono type_enc =
blanchet@44501
  1956
  let
blanchet@44501
  1957
    val level = level_of_type_enc type_enc
blanchet@44501
  1958
    val should_encode = should_encode_type ctxt mono level
blanchet@44504
  1959
    fun add_type T = not (should_encode T) ? insert_type ctxt I T
blanchet@44506
  1960
    fun add_args (IApp (tm1, tm2)) = add_args tm1 #> add_term tm2
blanchet@44506
  1961
      | add_args _ = I
blanchet@44506
  1962
    and add_term tm = add_type (ityp_of tm) #> add_args tm
blanchet@44501
  1963
  in formula_fold NONE (K add_term) end
blanchet@44501
  1964
fun add_fact_monotonic_types ctxt mono type_enc =
blanchet@44501
  1965
  add_iformula_monotonic_types ctxt mono type_enc |> fact_lift
blanchet@44501
  1966
fun monotonic_types_for_facts ctxt mono type_enc facts =
blanchet@44501
  1967
  [] |> (polymorphism_of_type_enc type_enc = Polymorphic andalso
blanchet@44501
  1968
         is_type_level_monotonicity_based (level_of_type_enc type_enc))
blanchet@44501
  1969
        ? fold (add_fact_monotonic_types ctxt mono type_enc) facts
blanchet@44501
  1970
blanchet@44399
  1971
fun formula_line_for_guards_mono_type ctxt format mono type_enc T =
blanchet@44396
  1972
  Formula (guards_sym_formula_prefix ^
blanchet@44396
  1973
           ascii_of (mangled_type format type_enc T),
blanchet@44396
  1974
           Axiom,
blanchet@44396
  1975
           IConst (`make_bound_var "X", T, [])
blanchet@44396
  1976
           |> type_guard_iterm ctxt format type_enc T
blanchet@44396
  1977
           |> AAtom
blanchet@44399
  1978
           |> formula_from_iformula ctxt format mono type_enc
blanchet@44396
  1979
                                    (K (K (K (K true)))) (SOME true)
blanchet@44396
  1980
           |> bound_tvars type_enc (atyps_of T)
blanchet@44593
  1981
           |> close_formula_universally type_enc,
blanchet@44396
  1982
           isabelle_info introN, NONE)
blanchet@44396
  1983
blanchet@44399
  1984
fun formula_line_for_tags_mono_type ctxt format mono type_enc T =
blanchet@44396
  1985
  let val x_var = ATerm (`make_bound_var "X", []) in
blanchet@44396
  1986
    Formula (tags_sym_formula_prefix ^
blanchet@44396
  1987
             ascii_of (mangled_type format type_enc T),
blanchet@44396
  1988
             Axiom,
blanchet@44396
  1989
             eq_formula type_enc (atyps_of T) false
blanchet@44399
  1990
                        (tag_with_type ctxt format mono type_enc NONE T x_var)
blanchet@44396
  1991
                        x_var,
blanchet@44396
  1992
             isabelle_info simpN, NONE)
blanchet@44396
  1993
  end
blanchet@44396
  1994
blanchet@44399
  1995
fun problem_lines_for_mono_types ctxt format mono type_enc Ts =
blanchet@44396
  1996
  case type_enc of
blanchet@44396
  1997
    Simple_Types _ => []
blanchet@44396
  1998
  | Guards _ =>
blanchet@44399
  1999
    map (formula_line_for_guards_mono_type ctxt format mono type_enc) Ts
blanchet@44399
  2000
  | Tags _ => map (formula_line_for_tags_mono_type ctxt format mono type_enc) Ts
blanchet@44396
  2001
blanchet@44399
  2002
fun decl_line_for_sym ctxt format mono type_enc s
blanchet@42994
  2003
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  2004
  let
blanchet@44594
  2005
    val thy = Proof_Context.theory_of ctxt
blanchet@44594
  2006
    val (T, T_args) =
blanchet@44594
  2007
      if null T_args then
blanchet@44594
  2008
        (T, [])
blanchet@44594
  2009
      else case strip_prefix_and_unascii const_prefix s of
blanchet@44594
  2010
        SOME s' =>
blanchet@44594
  2011
        let
blanchet@44594
  2012
          val s' = s' |> invert_const
blanchet@44594
  2013
          val T = s' |> robust_const_type thy
blanchet@44594
  2014
        in (T, robust_const_typargs thy (s', T)) end
blanchet@44594
  2015
      | NONE =>
blanchet@44594
  2016
        case strip_prefix_and_unascii fixed_var_prefix s of
blanchet@44594
  2017
          SOME s' =>
blanchet@44594
  2018
          if String.isPrefix polymorphic_free_prefix s' then (tvar_a, [tvar_a])
blanchet@44594
  2019
          else raise Fail "unexpected type arguments to free variable"
blanchet@44594
  2020
        | NONE => raise Fail "unexpected type arguments"
blanchet@42994
  2021
  in
blanchet@42998
  2022
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@44594
  2023
          T |> fused_type ctxt mono (level_of_type_enc type_enc) ary
blanchet@44594
  2024
            |> ho_type_from_typ format type_enc pred_sym ary
blanchet@44594
  2025
            |> not (null T_args)
blanchet@44594
  2026
               ? curry ATyAbs (map (tvar_name o fst o dest_TVar) T_args))
blanchet@42994
  2027
  end
blanchet@42579
  2028
blanchet@44399
  2029
fun formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono type_enc n s
blanchet@44399
  2030
                                     j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  2031
  let
blanchet@42709
  2032
    val (kind, maybe_negate) =
blanchet@42709
  2033
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  2034
      else (Axiom, I)
blanchet@42753
  2035
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@43399
  2036
    val num_args = length arg_Ts
blanchet@42579
  2037
    val bound_names =
blanchet@43399
  2038
      1 upto num_args |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  2039
    val bounds =
blanchet@43859
  2040
      bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
blanchet@43907
  2041
    val sym_needs_arg_types = exists (curry (op =) dummyT) T_args
blanchet@43401
  2042
    fun should_keep_arg_type T =
blanchet@44393
  2043
      sym_needs_arg_types andalso
blanchet@44399
  2044
      should_guard_type ctxt mono type_enc (K true) T
blanchet@42579
  2045
    val bound_Ts =
blanchet@43401
  2046
      arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
blanchet@42579
  2047
  in
blanchet@43989
  2048
    Formula (guards_sym_formula_prefix ^ s ^
blanchet@42709
  2049
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@43859
  2050
             IConst ((s, s'), T, T_args)
blanchet@43859
  2051
             |> fold (curry (IApp o swap)) bounds
blanchet@44396
  2052
             |> type_guard_iterm ctxt format type_enc res_T
blanchet@42963
  2053
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@44399
  2054
             |> formula_from_iformula ctxt format mono type_enc
blanchet@43859
  2055
                                      (K (K (K (K true)))) (SOME true)
blanchet@43626
  2056
             |> n > 1 ? bound_tvars type_enc (atyps_of T)
blanchet@44593
  2057
             |> close_formula_universally type_enc
blanchet@42709
  2058
             |> maybe_negate,
blanchet@43693
  2059
             isabelle_info introN, NONE)
blanchet@42579
  2060
  end
blanchet@42579
  2061
blanchet@44405
  2062
fun formula_lines_for_nonuniform_tags_sym_decl ctxt format conj_sym_kind mono
blanchet@44399
  2063
        type_enc n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  2064
  let
blanchet@42829
  2065
    val ident_base =
blanchet@44396
  2066
      tags_sym_formula_prefix ^ s ^
blanchet@43125
  2067
      (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  2068
    val (kind, maybe_negate) =
blanchet@42852
  2069
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  2070
      else (Axiom, I)
blanchet@42829
  2071
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  2072
    val bound_names =
blanchet@42829
  2073
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  2074
    val bounds = bound_names |> map (fn name => ATerm (name, []))
nik@43677
  2075
    val cst = mk_aterm format type_enc (s, s') T_args
blanchet@44396
  2076
    val eq = maybe_negate oo eq_formula type_enc (atyps_of T) pred_sym
blanchet@44398
  2077
    val should_encode =
blanchet@44399
  2078
      should_encode_type ctxt mono (level_of_type_enc type_enc)
blanchet@44399
  2079
    val tag_with = tag_with_type ctxt format mono type_enc NONE
blanchet@42829
  2080
    val add_formula_for_res =
blanchet@42829
  2081
      if should_encode res_T then
blanchet@42852
  2082
        cons (Formula (ident_base ^ "_res", kind,
blanchet@44396
  2083
                       eq (tag_with res_T (cst bounds)) (cst bounds),
blanchet@43693
  2084
                       isabelle_info simpN, NONE))
blanchet@42829
  2085
      else
blanchet@42829
  2086
        I
blanchet@42829
  2087
    fun add_formula_for_arg k =
blanchet@42829
  2088
      let val arg_T = nth arg_Ts k in
blanchet@42829
  2089
        if should_encode arg_T then
blanchet@42829
  2090
          case chop k bounds of
blanchet@42829
  2091
            (bounds1, bound :: bounds2) =>
blanchet@42852
  2092
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@44396
  2093
                           eq (cst (bounds1 @ tag_with arg_T bound :: bounds2))
blanchet@44396
  2094
                              (cst bounds),
blanchet@43693
  2095
                           isabelle_info simpN, NONE))
blanchet@42829
  2096
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  2097
        else
blanchet@42829
  2098
          I
blanchet@42829
  2099
      end
blanchet@42829
  2100
  in
blanchet@42834
  2101
    [] |> not pred_sym ? add_formula_for_res
blanchet@44496
  2102
       |> Config.get ctxt type_tag_arguments
blanchet@44496
  2103
          ? fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  2104
  end
blanchet@42829
  2105
blanchet@42836
  2106
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  2107
blanchet@44399
  2108
fun problem_lines_for_sym_decls ctxt format conj_sym_kind mono type_enc
blanchet@44396
  2109
                                (s, decls) =
blanchet@43626
  2110
  case type_enc of
blanchet@42998
  2111
    Simple_Types _ =>
blanchet@44399
  2112
    decls |> map (decl_line_for_sym ctxt format mono type_enc s)
blanchet@44398
  2113
  | Guards (_, level, _) =>
blanchet@42998
  2114
    let
blanchet@42998
  2115
      val decls =
blanchet@42998
  2116
        case decls of
blanchet@42998
  2117
          decl :: (decls' as _ :: _) =>
blanchet@42998
  2118
          let val T = result_type_of_decl decl in
blanchet@44399
  2119
            if forall (type_generalization ctxt T o result_type_of_decl)
blanchet@44399
  2120
                      decls' then
blanchet@42998
  2121
              [decl]
blanchet@42998
  2122
            else
blanchet@42998
  2123
              decls
blanchet@42998
  2124
          end
blanchet@42998
  2125
        | _ => decls
blanchet@42998
  2126
      val n = length decls
blanchet@42998
  2127
      val decls =
blanchet@44399
  2128
        decls |> filter (should_encode_type ctxt mono level
blanchet@43401
  2129
                         o result_type_of_decl)
blanchet@42998
  2130
    in
blanchet@42998
  2131
      (0 upto length decls - 1, decls)
blanchet@44399
  2132
      |-> map2 (formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono
blanchet@44399
  2133
                                                 type_enc n s)
blanchet@42998
  2134
    end
blanchet@44402
  2135
  | Tags (_, _, uniformity) =>
blanchet@44402
  2136
    (case uniformity of
blanchet@44402
  2137
       Uniform => []
blanchet@44402
  2138
     | Nonuniform =>
blanchet@42998
  2139
       let val n = length decls in
blanchet@42998
  2140
         (0 upto n - 1 ~~ decls)
blanchet@44405
  2141
         |> maps (formula_lines_for_nonuniform_tags_sym_decl ctxt format
blanchet@44399
  2142
                      conj_sym_kind mono type_enc n s)
blanchet@42998
  2143
       end)
blanchet@42579
  2144
blanchet@44399
  2145
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono type_enc
blanchet@44501
  2146
                                     mono_Ts sym_decl_tab =
blanchet@44396
  2147
  let
blanchet@44396
  2148
    val syms = sym_decl_tab |> Symtab.dest |> sort_wrt fst
blanchet@44396
  2149
    val mono_lines =
blanchet@44399
  2150
      problem_lines_for_mono_types ctxt format mono type_enc mono_Ts
blanchet@44396
  2151
    val decl_lines =
blanchet@44396
  2152
      fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
blanchet@44399
  2153
                                                     mono type_enc)
blanchet@44396
  2154
               syms []
blanchet@44396
  2155
  in mono_lines @ decl_lines end
blanchet@42543
  2156
blanchet@44496
  2157
fun needs_type_tag_idempotence ctxt (Tags (poly, level, uniformity)) =
blanchet@44496
  2158
    Config.get ctxt type_tag_idempotence andalso
blanchet@43185
  2159
    poly <> Mangled_Monomorphic andalso
blanchet@44402
  2160
    ((level = All_Types andalso uniformity = Nonuniform) orelse
blanchet@44397
  2161
     is_type_level_monotonicity_based level)
blanchet@44496
  2162
  | needs_type_tag_idempotence _ _ = false
blanchet@42831
  2163
blanchet@42939
  2164
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  2165
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  2166
    if heading = needle then j
blanchet@42939
  2167
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  2168
blanchet@42998
  2169
val implicit_declsN = "Should-be-implicit typings"
blanchet@42998
  2170
val explicit_declsN = "Explicit typings"
blanchet@41157
  2171
val factsN = "Relevant facts"
blanchet@41157
  2172
val class_relsN = "Class relationships"
blanchet@42543
  2173
val aritiesN = "Arities"
blanchet@41157
  2174
val helpersN = "Helper facts"
blanchet@41157
  2175
val conjsN = "Conjectures"
blanchet@41313
  2176
val free_typesN = "Type variables"
blanchet@41157
  2177
blanchet@43828
  2178
val explicit_apply = NONE (* for experiments *)
blanchet@43259
  2179
blanchet@44397
  2180
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc exporter
blanchet@44397
  2181
        lambda_trans readable_names preproc hyp_ts concl_t facts =
blanchet@38282
  2182
  let
blanchet@44416
  2183
    val type_enc = type_enc |> adjust_type_enc format
blanchet@44088
  2184
    val lambda_trans =
blanchet@44088
  2185
      if lambda_trans = smartN then
blanchet@44088
  2186
        if is_type_enc_higher_order type_enc then lambdasN else combinatorsN
blanchet@44088
  2187
      else if lambda_trans = lambdasN andalso
blanchet@44088
  2188
              not (is_type_enc_higher_order type_enc) then
blanchet@44088
  2189
        error ("Lambda translation method incompatible with first-order \
blanchet@44088
  2190
               \encoding.")
blanchet@44088
  2191
      else
blanchet@44088
  2192
        lambda_trans
blanchet@44088
  2193
    val trans_lambdas =
blanchet@44088
  2194
      if lambda_trans = no_lambdasN then
blanchet@44088
  2195
        rpair []
blanchet@44088
  2196
      else if lambda_trans = concealedN then
blanchet@44088
  2197
        lift_lambdas ctxt type_enc ##> K []
blanchet@44088
  2198
      else if lambda_trans = liftingN then
blanchet@44088
  2199
        lift_lambdas ctxt type_enc
blanchet@44088
  2200
      else if lambda_trans = combinatorsN then
blanchet@44088
  2201
        map (introduce_combinators ctxt) #> rpair []
blanchet@44088
  2202
      else if lambda_trans = hybridN then
blanchet@44088
  2203
        lift_lambdas ctxt type_enc
blanchet@44088
  2204
        ##> maps (fn t => [t, introduce_combinators ctxt
blanchet@44088
  2205
                                  (intentionalize_def t)])
blanchet@44088
  2206
      else if lambda_trans = lambdasN then
blanchet@44088
  2207
        map (Envir.eta_contract) #> rpair []
blanchet@44088
  2208
      else
blanchet@44088
  2209
        error ("Unknown lambda translation method: " ^
blanchet@44088
  2210
               quote lambda_trans ^ ".")
blanchet@44595
  2211
    val (fact_names, classes, conjs, facts, class_rel_clauses, arity_clauses) =
blanchet@43856
  2212
      translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
blanchet@43828
  2213
                         hyp_ts concl_t facts
blanchet@44496
  2214
    val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
blanchet@44399
  2215
    val mono = conjs @ facts |> mononotonicity_info_for_facts ctxt type_enc
blanchet@43626
  2216
    val repair = repair_fact ctxt format type_enc sym_tab
blanchet@42682
  2217
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@43064
  2218
    val repaired_sym_tab =
blanchet@44496
  2219
      conjs @ facts |> sym_table_for_facts ctxt (SOME false)
blanchet@42573
  2220
    val helpers =
blanchet@43858
  2221
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
blanchet@43858
  2222
                       |> map repair
blanchet@44501
  2223
    val mono_Ts =
blanchet@44501
  2224
      helpers @ conjs @ facts
blanchet@44501
  2225
      |> monotonic_types_for_facts ctxt mono type_enc
blanchet@44595
  2226
    val class_decl_lines = decl_lines_for_classes type_enc classes
blanchet@42680
  2227
    val sym_decl_lines =
blanchet@42731
  2228
      (conjs, helpers @ facts)
blanchet@43984
  2229
      |> sym_decl_table_for_facts ctxt format type_enc repaired_sym_tab
blanchet@44399
  2230
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono
blanchet@44501
  2231
                                               type_enc mono_Ts
blanchet@42881
  2232
    val helper_lines =
blanchet@42956
  2233
      0 upto length helpers - 1 ~~ helpers
blanchet@44399
  2234
      |> map (formula_line_for_fact ctxt format helper_prefix I false true mono
blanchet@44399
  2235
                                    type_enc)
blanchet@44496
  2236
      |> (if needs_type_tag_idempotence ctxt type_enc then
blanchet@44404
  2237
            cons (type_tag_idempotence_fact type_enc)
blanchet@43159
  2238
          else
blanchet@43159
  2239
            I)
blanchet@42522
  2240
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@43039
  2241
       FLOTTER hack. *)
blanchet@38282
  2242
    val problem =
blanchet@44595
  2243
      [(explicit_declsN, class_decl_lines @ sym_decl_lines),
blanchet@42956
  2244
       (factsN,
blanchet@43501
  2245
        map (formula_line_for_fact ctxt format fact_prefix ascii_of
blanchet@44595
  2246
                                   (not exporter) (not exporter) mono type_enc)
blanchet@42956
  2247
            (0 upto length facts - 1 ~~ facts)),
blanchet@44593
  2248
       (class_relsN,
blanchet@44593
  2249
        map (formula_line_for_class_rel_clause type_enc) class_rel_clauses),
blanchet@44593
  2250
       (aritiesN, map (formula_line_for_arity_clause type_enc) arity_clauses),
blanchet@42881
  2251
       (helpersN, helper_lines),
blanchet@42962
  2252
       (conjsN,
blanchet@44399
  2253
        map (formula_line_for_conjecture ctxt format mono type_enc) conjs),
blanchet@43626
  2254
       (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
blanchet@42543
  2255
    val problem =
blanchet@42561
  2256
      problem
blanchet@43092
  2257
      |> (case format of
blanchet@43092
  2258
            CNF => ensure_cnf_problem
blanchet@43092
  2259
          | CNF_UEQ => filter_cnf_ueq_problem
blanchet@44589
  2260
          | FOF => I
blanchet@44589
  2261
          | TFF (_, TFF_Implicit) => I
blanchet@44589
  2262
          | _ => declare_undeclared_syms_in_atp_problem type_decl_prefix
blanchet@44589
  2263
                                                        implicit_declsN)
blanchet@43092
  2264
    val (problem, pool) = problem |> nice_atp_problem readable_names
blanchet@42881
  2265
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  2266
    val typed_helpers =
blanchet@42881
  2267
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  2268
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  2269
                     else NONE)
blanchet@42881
  2270
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  2271
                  ~~ helpers)
blanchet@42778
  2272
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  2273
      if min_ary > 0 then
blanchet@42755
  2274
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  2275
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  2276
        | NONE => I
blanchet@42755
  2277
      else
blanchet@42755
  2278
        I
blanchet@38282
  2279
  in
blanchet@38282
  2280
    (problem,
blanchet@38282
  2281
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  2282
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  2283
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  2284
     fact_names |> Vector.fromList,
blanchet@42881
  2285
     typed_helpers,
blanchet@42755
  2286
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  2287
  end
blanchet@38282
  2288
blanchet@41313
  2289
(* FUDGE *)
blanchet@41313
  2290
val conj_weight = 0.0
blanchet@41770
  2291
val hyp_weight = 0.1
blanchet@41770
  2292
val fact_min_weight = 0.2
blanchet@41313
  2293
val fact_max_weight = 1.0
blanchet@42608
  2294
val type_info_default_weight = 0.8
blanchet@41313
  2295
blanchet@41313
  2296
fun add_term_weights weight (ATerm (s, tms)) =