src/HOL/Tools/ATP/atp_problem_generate.ML
author blanchet
Sat Feb 04 12:08:18 2012 +0100 (2012-02-04)
changeset 46409 d4754183ccce
parent 46406 0e490b9e8422
child 46410 78ff6a886b50
permissions -rw-r--r--
made option available to users (mostly for experiments)
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(*  Title:      HOL/Tools/ATP/atp_problem_generate.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_PROBLEM_GENERATE =
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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 atp_format = ATP_Problem.atp_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 scope = Global | Local | Assum | Chained
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  datatype status = General | Induct | Intro | Elim | Simp | Spec_Eq
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  type stature = scope * status
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  datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
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  datatype strictness = Strict | Non_Strict
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  datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars
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  datatype type_level =
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    All_Types |
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    Noninf_Nonmono_Types of strictness * granularity |
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    Fin_Nonmono_Types of granularity |
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    Const_Arg_Types |
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    No_Types
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  type type_enc
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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_lamsN : string
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  val hide_lamsN : string
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  val liftingN : string
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  val combsN : string
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  val combs_and_liftingN : string
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  val combs_or_liftingN : string
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  val lam_liftingN : string
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  val keep_lamsN : 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 lam_lifted_prefix : string
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  val lam_lifted_mono_prefix : string
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  val lam_lifted_poly_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 combinator_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 lam_fact_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 unprefix_and_unascii : string -> string -> string option
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  val proxy_table : (string * (string * (thm * (string * string)))) list
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  val proxify_const : string -> (string * string) option
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  val invert_const : string -> string
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  val unproxify_const : string -> string
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  val new_skolem_var_name_from_const : string -> string
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  val atp_irrelevant_consts : string list
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  val atp_schematic_consts_of : term -> typ list Symtab.table
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  val is_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 type_enc_from_string : strictness -> string -> type_enc
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  val adjust_type_enc : atp_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 list
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  val helper_table : ((string * bool) * thm list) list
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  val trans_lams_from_string :
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    Proof.context -> type_enc -> string -> term list -> term list * term list
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  val factsN : string
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  val prepare_atp_problem :
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    Proof.context -> atp_format -> formula_kind -> formula_kind -> type_enc
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    -> bool -> string -> bool -> bool -> bool -> term list -> term
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    -> ((string * stature) * term) list
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    -> string problem * string Symtab.table * (string * stature) list vector
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       * (string * term) 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_Problem_Generate : ATP_PROBLEM_GENERATE =
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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_lamsN = "no_lams" (* used internally; undocumented *)
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val hide_lamsN = "hide_lams"
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val liftingN = "lifting"
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val combsN = "combs"
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val combs_and_liftingN = "combs_and_lifting"
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val combs_or_liftingN = "combs_or_lifting"
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val keep_lamsN = "keep_lams"
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val lam_liftingN = "lam_lifting" (* legacy *)
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(* It's still unclear whether all TFF1 implementations will support type
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   signatures such as "!>[A : $tType] : $o", with ghost type variables. *)
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val avoid_first_order_ghost_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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(* Freshness almost guaranteed! *)
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val atp_prefix = "ATP" ^ Long_Name.separator
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val atp_weak_prefix = "ATP:"
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val lam_lifted_prefix = atp_weak_prefix ^ "Lam"
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val lam_lifted_mono_prefix = lam_lifted_prefix ^ "m"
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val lam_lifted_poly_prefix = lam_lifted_prefix ^ "p"
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val skolem_const_prefix = atp_prefix ^ "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 combinator_prefix = "COMB"
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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 uncurried_alias_eq_prefix = "unc_"
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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 lam_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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(*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 unprefix_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}, combinator_prefix ^ "I"),
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   (@{const_name Meson.COMBK}, combinator_prefix ^ "K"),
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   (@{const_name Meson.COMBB}, combinator_prefix ^ "B"),
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   (@{const_name Meson.COMBC}, combinator_prefix ^ "C"),
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   (@{const_name Meson.COMBS}, combinator_prefix ^ "S")]
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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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   315
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   316
fun make_schematic_type_var (x, i) =
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   317
  tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
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   318
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
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   319
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   320
(* "HOL.eq" and choice are mapped to the ATP's equivalents *)
nik@44587
   321
local
nik@44587
   322
  val choice_const = (fst o dest_Const o HOLogic.choice_const) Term.dummyT
nik@44587
   323
  fun default c = const_prefix ^ lookup_const c
nik@44587
   324
in
nik@44587
   325
  fun make_fixed_const _ @{const_name HOL.eq} = tptp_old_equal
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   326
    | make_fixed_const (SOME (THF (_, _, THF_With_Choice))) c =
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   327
      if c = choice_const then tptp_choice else default c
nik@44587
   328
    | make_fixed_const _ c = default c
nik@44587
   329
end
blanchet@43085
   330
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   331
fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
blanchet@43085
   332
blanchet@43085
   333
fun make_type_class clas = class_prefix ^ ascii_of clas
blanchet@43085
   334
blanchet@43093
   335
fun new_skolem_var_name_from_const s =
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   336
  let val ss = s |> space_explode Long_Name.separator in
blanchet@43093
   337
    nth ss (length ss - 2)
blanchet@43093
   338
  end
blanchet@43093
   339
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   340
(* These are either simplified away by "Meson.presimplify" (most of the time) or
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   341
   handled specially via "fFalse", "fTrue", ..., "fequal". *)
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   342
val atp_irrelevant_consts =
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   343
  [@{const_name False}, @{const_name True}, @{const_name Not},
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   344
   @{const_name conj}, @{const_name disj}, @{const_name implies},
blanchet@43248
   345
   @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
blanchet@43248
   346
blanchet@43248
   347
val atp_monomorph_bad_consts =
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   348
  atp_irrelevant_consts @
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   349
  (* These are ignored anyway by the relevance filter (unless they appear in
blanchet@43248
   350
     higher-order places) but not by the monomorphizer. *)
blanchet@43248
   351
  [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
blanchet@43248
   352
   @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
blanchet@43248
   353
   @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
blanchet@43248
   354
blanchet@43258
   355
fun add_schematic_const (x as (_, T)) =
blanchet@43258
   356
  Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
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   357
val add_schematic_consts_of =
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   358
  Term.fold_aterms (fn Const (x as (s, _)) =>
blanchet@43258
   359
                       not (member (op =) atp_monomorph_bad_consts s)
blanchet@43258
   360
                       ? add_schematic_const x
blanchet@43258
   361
                      | _ => I)
blanchet@43258
   362
fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
blanchet@43248
   363
blanchet@43085
   364
(** Definitions and functions for FOL clauses and formulas for TPTP **)
blanchet@43085
   365
blanchet@43085
   366
(** Isabelle arities **)
blanchet@43085
   367
blanchet@44625
   368
type arity_atom = name * name * name list
blanchet@43085
   369
blanchet@43263
   370
val type_class = the_single @{sort type}
blanchet@43263
   371
blanchet@43086
   372
type arity_clause =
blanchet@43496
   373
  {name : string,
blanchet@44625
   374
   prem_atoms : arity_atom list,
blanchet@44625
   375
   concl_atom : arity_atom}
blanchet@44625
   376
blanchet@44625
   377
fun add_prem_atom tvar =
blanchet@44625
   378
  fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar, []))
blanchet@43085
   379
blanchet@43085
   380
(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
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   381
fun make_axiom_arity_clause (tcons, name, (cls, args)) =
blanchet@43085
   382
  let
blanchet@44595
   383
    val tvars = map (prefix tvar_prefix o string_of_int) (1 upto length args)
blanchet@43085
   384
    val tvars_srts = ListPair.zip (tvars, args)
blanchet@43085
   385
  in
blanchet@43086
   386
    {name = name,
blanchet@44625
   387
     prem_atoms = [] |> fold (uncurry add_prem_atom) tvars_srts,
blanchet@44625
   388
     concl_atom = (`make_type_class cls, `make_fixed_type_const tcons,
blanchet@44625
   389
                   tvars ~~ tvars)}
blanchet@43085
   390
  end
blanchet@43085
   391
blanchet@43085
   392
fun arity_clause _ _ (_, []) = []
blanchet@43495
   393
  | arity_clause seen n (tcons, ("HOL.type", _) :: ars) =  (* ignore *)
blanchet@43495
   394
    arity_clause seen n (tcons, ars)
blanchet@43495
   395
  | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
blanchet@43495
   396
    if member (op =) seen class then
blanchet@43495
   397
      (* multiple arities for the same (tycon, class) pair *)
blanchet@43495
   398
      make_axiom_arity_clause (tcons,
blanchet@43495
   399
          lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
blanchet@43495
   400
          ar) ::
blanchet@43495
   401
      arity_clause seen (n + 1) (tcons, ars)
blanchet@43495
   402
    else
blanchet@43495
   403
      make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
blanchet@43495
   404
                               ascii_of class, ar) ::
blanchet@43495
   405
      arity_clause (class :: seen) n (tcons, ars)
blanchet@43085
   406
blanchet@43085
   407
fun multi_arity_clause [] = []
blanchet@43085
   408
  | multi_arity_clause ((tcons, ars) :: tc_arlists) =
blanchet@44772
   409
    arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
blanchet@43085
   410
blanchet@43622
   411
(* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
blanchet@43622
   412
   theory thy provided its arguments have the corresponding sorts. *)
blanchet@43085
   413
fun type_class_pairs thy tycons classes =
blanchet@43093
   414
  let
blanchet@43093
   415
    val alg = Sign.classes_of thy
blanchet@43093
   416
    fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
blanchet@43093
   417
    fun add_class tycon class =
blanchet@43093
   418
      cons (class, domain_sorts tycon class)
blanchet@43093
   419
      handle Sorts.CLASS_ERROR _ => I
blanchet@43093
   420
    fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
blanchet@43093
   421
  in map try_classes tycons end
blanchet@43085
   422
blanchet@43085
   423
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
blanchet@43085
   424
fun iter_type_class_pairs _ _ [] = ([], [])
blanchet@43085
   425
  | iter_type_class_pairs thy tycons classes =
blanchet@43263
   426
      let
blanchet@43263
   427
        fun maybe_insert_class s =
blanchet@43263
   428
          (s <> type_class andalso not (member (op =) classes s))
blanchet@43263
   429
          ? insert (op =) s
blanchet@43263
   430
        val cpairs = type_class_pairs thy tycons classes
blanchet@43263
   431
        val newclasses =
blanchet@43263
   432
          [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
blanchet@43263
   433
        val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
blanchet@43266
   434
      in (classes' @ classes, union (op =) cpairs' cpairs) end
blanchet@43085
   435
blanchet@43085
   436
fun make_arity_clauses thy tycons =
blanchet@43085
   437
  iter_type_class_pairs thy tycons ##> multi_arity_clause
blanchet@43085
   438
blanchet@43085
   439
blanchet@43085
   440
(** Isabelle class relations **)
blanchet@43085
   441
blanchet@43086
   442
type class_rel_clause =
blanchet@43496
   443
  {name : string,
blanchet@43496
   444
   subclass : name,
blanchet@43496
   445
   superclass : name}
blanchet@43085
   446
blanchet@43622
   447
(* Generate all pairs (sub, super) such that sub is a proper subclass of super
blanchet@43622
   448
   in theory "thy". *)
blanchet@43085
   449
fun class_pairs _ [] _ = []
blanchet@43085
   450
  | class_pairs thy subs supers =
blanchet@43085
   451
      let
blanchet@43085
   452
        val class_less = Sorts.class_less (Sign.classes_of thy)
blanchet@43085
   453
        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
blanchet@43085
   454
        fun add_supers sub = fold (add_super sub) supers
blanchet@43085
   455
      in fold add_supers subs [] end
blanchet@43085
   456
blanchet@43622
   457
fun make_class_rel_clause (sub, super) =
blanchet@43622
   458
  {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
blanchet@43086
   459
   superclass = `make_type_class super}
blanchet@43085
   460
blanchet@43085
   461
fun make_class_rel_clauses thy subs supers =
blanchet@43093
   462
  map make_class_rel_clause (class_pairs thy subs supers)
blanchet@43085
   463
blanchet@43859
   464
(* intermediate terms *)
blanchet@43859
   465
datatype iterm =
blanchet@43859
   466
  IConst of name * typ * typ list |
blanchet@43859
   467
  IVar of name * typ |
blanchet@43859
   468
  IApp of iterm * iterm |
blanchet@43859
   469
  IAbs of (name * typ) * iterm
blanchet@43085
   470
blanchet@43859
   471
fun ityp_of (IConst (_, T, _)) = T
blanchet@43859
   472
  | ityp_of (IVar (_, T)) = T
blanchet@43859
   473
  | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
blanchet@43859
   474
  | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
blanchet@43085
   475
blanchet@43085
   476
(*gets the head of a combinator application, along with the list of arguments*)
blanchet@43859
   477
fun strip_iterm_comb u =
blanchet@43496
   478
  let
blanchet@43859
   479
    fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
blanchet@43496
   480
      | stripc x = x
blanchet@43496
   481
  in stripc (u, []) end
blanchet@43085
   482
blanchet@45316
   483
fun atomic_types_of T = fold_atyps (insert (op =)) T []
blanchet@43085
   484
blanchet@45509
   485
val tvar_a_str = "'a"
blanchet@45509
   486
val tvar_a = TVar ((tvar_a_str, 0), HOLogic.typeS)
blanchet@45509
   487
val tvar_a_name = (make_schematic_type_var (tvar_a_str, 0), tvar_a_str)
blanchet@45509
   488
val itself_name = `make_fixed_type_const @{type_name itself}
blanchet@45509
   489
val TYPE_name = `(make_fixed_const NONE) @{const_name TYPE}
blanchet@45509
   490
val tvar_a_atype = AType (tvar_a_name, [])
blanchet@45509
   491
val a_itself_atype = AType (itself_name, [tvar_a_atype])
blanchet@45509
   492
blanchet@43085
   493
fun new_skolem_const_name s num_T_args =
blanchet@43085
   494
  [new_skolem_const_prefix, s, string_of_int num_T_args]
blanchet@43085
   495
  |> space_implode Long_Name.separator
blanchet@43085
   496
blanchet@44594
   497
fun robust_const_type thy s =
blanchet@45509
   498
  if s = app_op_name then
blanchet@45509
   499
    Logic.varifyT_global @{typ "('a => 'b) => 'a => 'b"}
blanchet@45554
   500
  else if String.isPrefix lam_lifted_prefix s then
blanchet@45509
   501
    Logic.varifyT_global @{typ "'a => 'b"}
blanchet@45509
   502
  else
blanchet@45509
   503
    (* Old Skolems throw a "TYPE" exception here, which will be caught. *)
blanchet@45509
   504
    s |> Sign.the_const_type thy
blanchet@44594
   505
blanchet@44594
   506
(* This function only makes sense if "T" is as general as possible. *)
blanchet@44594
   507
fun robust_const_typargs thy (s, T) =
blanchet@45509
   508
  if s = app_op_name then
blanchet@45509
   509
    let val (T1, T2) = T |> domain_type |> dest_funT in [T1, T2] end
blanchet@45509
   510
  else if String.isPrefix old_skolem_const_prefix s then
blanchet@45509
   511
    [] |> Term.add_tvarsT T |> rev |> map TVar
blanchet@45554
   512
  else if String.isPrefix lam_lifted_prefix s then
blanchet@45554
   513
    if String.isPrefix lam_lifted_poly_prefix s then
blanchet@45511
   514
      let val (T1, T2) = T |> dest_funT in [T1, T2] end
blanchet@45511
   515
    else
blanchet@45511
   516
      []
blanchet@45509
   517
  else
blanchet@45509
   518
    (s, T) |> Sign.const_typargs thy
blanchet@44594
   519
blanchet@43859
   520
(* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
blanchet@43859
   521
   Also accumulates sort infomation. *)
nik@44495
   522
fun iterm_from_term thy format bs (P $ Q) =
blanchet@43085
   523
    let
nik@44495
   524
      val (P', P_atomics_Ts) = iterm_from_term thy format bs P
nik@44495
   525
      val (Q', Q_atomics_Ts) = iterm_from_term thy format bs Q
blanchet@43859
   526
    in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
nik@44495
   527
  | iterm_from_term thy format _ (Const (c, T)) =
nik@44495
   528
    (IConst (`(make_fixed_const (SOME format)) c, T,
blanchet@44594
   529
             robust_const_typargs thy (c, T)),
blanchet@45316
   530
     atomic_types_of T)
nik@44495
   531
  | iterm_from_term _ _ _ (Free (s, T)) =
blanchet@45509
   532
    (IConst (`make_fixed_var s, T, []), atomic_types_of T)
nik@44495
   533
  | iterm_from_term _ format _ (Var (v as (s, _), T)) =
blanchet@43085
   534
    (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
blanchet@43085
   535
       let
blanchet@43085
   536
         val Ts = T |> strip_type |> swap |> op ::
blanchet@43085
   537
         val s' = new_skolem_const_name s (length Ts)
nik@44495
   538
       in IConst (`(make_fixed_const (SOME format)) s', T, Ts) end
blanchet@43085
   539
     else
blanchet@45316
   540
       IVar ((make_schematic_var v, s), T), atomic_types_of T)
nik@44495
   541
  | iterm_from_term _ _ bs (Bound j) =
blanchet@45316
   542
    nth bs j |> (fn (_, (name, T)) => (IConst (name, T, []), atomic_types_of T))
nik@44495
   543
  | iterm_from_term thy format bs (Abs (s, T, t)) =
nik@43678
   544
    let
nik@43678
   545
      fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
nik@43678
   546
      val s = vary s
blanchet@44403
   547
      val name = `make_bound_var s
nik@44495
   548
      val (tm, atomic_Ts) = iterm_from_term thy format ((s, (name, T)) :: bs) t
blanchet@45316
   549
    in (IAbs ((name, T), tm), union (op =) atomic_Ts (atomic_types_of T)) end
blanchet@43085
   550
blanchet@46340
   551
datatype scope = Global | Local | Assum | Chained
blanchet@46393
   552
datatype status = General | Induct | Intro | Elim | Simp | Spec_Eq
blanchet@46340
   553
type stature = scope * status
blanchet@43085
   554
blanchet@43624
   555
datatype order = First_Order | Higher_Order
blanchet@44494
   556
datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
blanchet@46301
   557
datatype strictness = Strict | Non_Strict
blanchet@44811
   558
datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars
blanchet@42613
   559
datatype type_level =
blanchet@44397
   560
  All_Types |
blanchet@46301
   561
  Noninf_Nonmono_Types of strictness * granularity |
blanchet@44811
   562
  Fin_Nonmono_Types of granularity |
blanchet@44397
   563
  Const_Arg_Types |
blanchet@43362
   564
  No_Types
blanchet@42613
   565
blanchet@43626
   566
datatype type_enc =
blanchet@44591
   567
  Simple_Types of order * polymorphism * type_level |
blanchet@44768
   568
  Guards of polymorphism * type_level |
blanchet@44768
   569
  Tags of polymorphism * type_level
blanchet@44768
   570
blanchet@44768
   571
fun is_type_enc_higher_order (Simple_Types (Higher_Order, _, _)) = true
blanchet@44768
   572
  | is_type_enc_higher_order _ = false
blanchet@44768
   573
blanchet@44768
   574
fun polymorphism_of_type_enc (Simple_Types (_, poly, _)) = poly
blanchet@44768
   575
  | polymorphism_of_type_enc (Guards (poly, _)) = poly
blanchet@44768
   576
  | polymorphism_of_type_enc (Tags (poly, _)) = poly
blanchet@44768
   577
blanchet@44768
   578
fun level_of_type_enc (Simple_Types (_, _, level)) = level
blanchet@44768
   579
  | level_of_type_enc (Guards (_, level)) = level
blanchet@44768
   580
  | level_of_type_enc (Tags (_, level)) = level
blanchet@44768
   581
blanchet@44811
   582
fun granularity_of_type_level (Noninf_Nonmono_Types (_, grain)) = grain
blanchet@44811
   583
  | granularity_of_type_level (Fin_Nonmono_Types grain) = grain
blanchet@44811
   584
  | granularity_of_type_level _ = All_Vars
blanchet@44768
   585
blanchet@44768
   586
fun is_type_level_quasi_sound All_Types = true
blanchet@44768
   587
  | is_type_level_quasi_sound (Noninf_Nonmono_Types _) = true
blanchet@44768
   588
  | is_type_level_quasi_sound _ = false
blanchet@44768
   589
val is_type_enc_quasi_sound = is_type_level_quasi_sound o level_of_type_enc
blanchet@44768
   590
blanchet@44768
   591
fun is_type_level_fairly_sound (Fin_Nonmono_Types _) = true
blanchet@44768
   592
  | is_type_level_fairly_sound level = is_type_level_quasi_sound level
blanchet@44768
   593
val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
blanchet@44768
   594
blanchet@44768
   595
fun is_type_level_monotonicity_based (Noninf_Nonmono_Types _) = true
blanchet@44768
   596
  | is_type_level_monotonicity_based (Fin_Nonmono_Types _) = true
blanchet@44768
   597
  | is_type_level_monotonicity_based _ = false
blanchet@42613
   598
blanchet@44785
   599
(* "_query", "_bang", and "_at" are for the ASCII-challenged Metis and
blanchet@44785
   600
   Mirabelle. *)
blanchet@44785
   601
val queries = ["?", "_query"]
blanchet@44785
   602
val bangs = ["!", "_bang"]
blanchet@44785
   603
val ats = ["@", "_at"]
blanchet@44785
   604
blanchet@42689
   605
fun try_unsuffixes ss s =
blanchet@42689
   606
  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
blanchet@42689
   607
blanchet@44785
   608
fun try_nonmono constr suffixes fallback s =
blanchet@44785
   609
  case try_unsuffixes suffixes s of
blanchet@44785
   610
    SOME s =>
blanchet@44785
   611
    (case try_unsuffixes suffixes s of
blanchet@44811
   612
       SOME s => (constr Positively_Naked_Vars, s)
blanchet@44785
   613
     | NONE =>
blanchet@44785
   614
       case try_unsuffixes ats s of
blanchet@44811
   615
         SOME s => (constr Ghost_Type_Arg_Vars, s)
blanchet@44811
   616
       | NONE => (constr All_Vars, s))
blanchet@44785
   617
  | NONE => fallback s
blanchet@44768
   618
blanchet@46301
   619
fun type_enc_from_string strictness s =
blanchet@42722
   620
  (case try (unprefix "poly_") s of
blanchet@42722
   621
     SOME s => (SOME Polymorphic, s)
blanchet@42613
   622
   | NONE =>
blanchet@44494
   623
     case try (unprefix "raw_mono_") s of
blanchet@44494
   624
       SOME s => (SOME Raw_Monomorphic, s)
blanchet@42722
   625
     | NONE =>
blanchet@44494
   626
       case try (unprefix "mono_") s of
blanchet@42722
   627
         SOME s => (SOME Mangled_Monomorphic, s)
blanchet@42722
   628
       | NONE => (NONE, s))
blanchet@44785
   629
  ||> (pair All_Types
blanchet@44785
   630
       |> try_nonmono Fin_Nonmono_Types bangs
blanchet@46301
   631
       |> try_nonmono (curry Noninf_Nonmono_Types strictness) queries)
blanchet@44768
   632
  |> (fn (poly, (level, core)) =>
blanchet@44768
   633
         case (core, (poly, level)) of
blanchet@44768
   634
           ("simple", (SOME poly, _)) =>
blanchet@44742
   635
           (case (poly, level) of
blanchet@44742
   636
              (Polymorphic, All_Types) =>
blanchet@44742
   637
              Simple_Types (First_Order, Polymorphic, All_Types)
blanchet@44742
   638
            | (Mangled_Monomorphic, _) =>
blanchet@44811
   639
              if granularity_of_type_level level = All_Vars then
blanchet@44768
   640
                Simple_Types (First_Order, Mangled_Monomorphic, level)
blanchet@44768
   641
              else
blanchet@44768
   642
                raise Same.SAME
blanchet@44742
   643
            | _ => raise Same.SAME)
blanchet@44768
   644
         | ("simple_higher", (SOME poly, _)) =>
blanchet@44591
   645
           (case (poly, level) of
blanchet@44754
   646
              (Polymorphic, All_Types) =>
blanchet@44754
   647
              Simple_Types (Higher_Order, Polymorphic, All_Types)
blanchet@44754
   648
            | (_, Noninf_Nonmono_Types _) => raise Same.SAME
blanchet@44742
   649
            | (Mangled_Monomorphic, _) =>
blanchet@44811
   650
              if granularity_of_type_level level = All_Vars then
blanchet@44768
   651
                Simple_Types (Higher_Order, Mangled_Monomorphic, level)
blanchet@44768
   652
              else
blanchet@44768
   653
                raise Same.SAME
blanchet@44742
   654
            | _ => raise Same.SAME)
blanchet@44810
   655
         | ("guards", (SOME poly, _)) =>
blanchet@45949
   656
           if poly = Mangled_Monomorphic andalso
blanchet@45949
   657
              granularity_of_type_level level = Ghost_Type_Arg_Vars then
blanchet@45949
   658
             raise Same.SAME
blanchet@45949
   659
           else
blanchet@45949
   660
             Guards (poly, level)
blanchet@44810
   661
         | ("tags", (SOME poly, _)) =>
blanchet@45949
   662
           if granularity_of_type_level level = Ghost_Type_Arg_Vars then
blanchet@45949
   663
             raise Same.SAME
blanchet@45949
   664
           else
blanchet@45949
   665
             Tags (poly, level)
blanchet@44768
   666
         | ("args", (SOME poly, All_Types (* naja *))) =>
blanchet@44768
   667
           Guards (poly, Const_Arg_Types)
blanchet@44768
   668
         | ("erased", (NONE, All_Types (* naja *))) =>
blanchet@44768
   669
           Guards (Polymorphic, No_Types)
blanchet@42753
   670
         | _ => raise Same.SAME)
blanchet@44785
   671
  handle Same.SAME => error ("Unknown type encoding: " ^ quote s ^ ".")
blanchet@42613
   672
blanchet@44754
   673
fun adjust_type_enc (THF (TPTP_Monomorphic, _, _))
blanchet@44754
   674
                    (Simple_Types (order, _, level)) =
blanchet@44591
   675
    Simple_Types (order, Mangled_Monomorphic, level)
blanchet@44754
   676
  | adjust_type_enc (THF _) type_enc = type_enc
blanchet@44754
   677
  | adjust_type_enc (TFF (TPTP_Monomorphic, _)) (Simple_Types (_, _, level)) =
blanchet@44591
   678
    Simple_Types (First_Order, Mangled_Monomorphic, level)
blanchet@45303
   679
  | adjust_type_enc (DFG DFG_Sorted) (Simple_Types (_, _, level)) =
blanchet@45301
   680
    Simple_Types (First_Order, Mangled_Monomorphic, level)
blanchet@44754
   681
  | adjust_type_enc (TFF _) (Simple_Types (_, poly, level)) =
blanchet@44591
   682
    Simple_Types (First_Order, poly, level)
blanchet@44591
   683
  | adjust_type_enc format (Simple_Types (_, poly, level)) =
blanchet@44768
   684
    adjust_type_enc format (Guards (poly, level))
blanchet@44416
   685
  | adjust_type_enc CNF_UEQ (type_enc as Guards stuff) =
blanchet@44416
   686
    (if is_type_enc_fairly_sound type_enc then Tags else Guards) stuff
blanchet@44416
   687
  | adjust_type_enc _ type_enc = type_enc
blanchet@43101
   688
blanchet@45509
   689
fun constify_lifted (t $ u) = constify_lifted t $ constify_lifted u
blanchet@45509
   690
  | constify_lifted (Abs (s, T, t)) = Abs (s, T, constify_lifted t)
blanchet@45509
   691
  | constify_lifted (Free (x as (s, _))) =
blanchet@45554
   692
    (if String.isPrefix lam_lifted_prefix s then Const else Free) x
blanchet@45509
   693
  | constify_lifted t = t
blanchet@45509
   694
blanchet@46375
   695
(* Requires bound variables not to clash with any schematic variables (as should
blanchet@46375
   696
   be the case right after lambda-lifting). *)
blanchet@46385
   697
fun open_form unprefix (t as Const (@{const_name All}, _) $ Abs (s, T, t')) =
blanchet@46385
   698
    (case try unprefix s of
blanchet@46385
   699
       SOME s =>
blanchet@46385
   700
       let
blanchet@46385
   701
         val names = Name.make_context (map fst (Term.add_var_names t' []))
blanchet@46385
   702
         val (s, _) = Name.variant s names
blanchet@46385
   703
       in open_form unprefix (subst_bound (Var ((s, 0), T), t')) end
blanchet@46385
   704
     | NONE => t)
blanchet@46385
   705
  | open_form _ t = t
blanchet@46375
   706
blanchet@45554
   707
fun lift_lams_part_1 ctxt type_enc =
blanchet@45568
   708
  map close_form #> rpair ctxt
blanchet@44088
   709
  #-> Lambda_Lifting.lift_lambdas
blanchet@45564
   710
          (SOME ((if polymorphism_of_type_enc type_enc = Polymorphic then
blanchet@45564
   711
                    lam_lifted_poly_prefix
blanchet@45564
   712
                  else
blanchet@45564
   713
                    lam_lifted_mono_prefix) ^ "_a"))
blanchet@44088
   714
          Lambda_Lifting.is_quantifier
blanchet@45554
   715
  #> fst
blanchet@46385
   716
fun lift_lams_part_2 (facts, lifted) =
blanchet@46385
   717
  (map (open_form (unprefix close_form_prefix) o constify_lifted) facts,
blanchet@46385
   718
   map (open_form I o constify_lifted) lifted)
blanchet@45554
   719
val lift_lams = lift_lams_part_2 ooo lift_lams_part_1
blanchet@44088
   720
blanchet@44088
   721
fun intentionalize_def (Const (@{const_name All}, _) $ Abs (_, _, t)) =
blanchet@44088
   722
    intentionalize_def t
blanchet@44088
   723
  | intentionalize_def (Const (@{const_name HOL.eq}, _) $ t $ u) =
blanchet@44088
   724
    let
blanchet@44088
   725
      fun lam T t = Abs (Name.uu, T, t)
blanchet@44088
   726
      val (head, args) = strip_comb t ||> rev
blanchet@44088
   727
      val head_T = fastype_of head
blanchet@44088
   728
      val n = length args
blanchet@44088
   729
      val arg_Ts = head_T |> binder_types |> take n |> rev
blanchet@44088
   730
      val u = u |> subst_atomic (args ~~ map Bound (0 upto n - 1))
blanchet@44088
   731
    in HOLogic.eq_const head_T $ head $ fold lam arg_Ts u end
blanchet@44088
   732
  | intentionalize_def t = t
blanchet@44088
   733
blanchet@40114
   734
type translated_formula =
blanchet@43496
   735
  {name : string,
blanchet@46340
   736
   stature : stature,
blanchet@43496
   737
   kind : formula_kind,
blanchet@43859
   738
   iformula : (name, typ, iterm) formula,
blanchet@43496
   739
   atomic_types : typ list}
blanchet@38282
   740
blanchet@46340
   741
fun update_iformula f ({name, stature, kind, iformula, atomic_types}
blanchet@43859
   742
                       : translated_formula) =
blanchet@46340
   743
  {name = name, stature = stature, kind = kind, iformula = f iformula,
blanchet@42562
   744
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   745
blanchet@43859
   746
fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
blanchet@42558
   747
blanchet@43064
   748
fun insert_type ctxt get_T x xs =
blanchet@43064
   749
  let val T = get_T x in
blanchet@44399
   750
    if exists (type_instance ctxt T o get_T) xs then xs
blanchet@44399
   751
    else x :: filter_out (type_generalization ctxt T o get_T) xs
blanchet@43064
   752
  end
blanchet@42677
   753
blanchet@42753
   754
(* The Booleans indicate whether all type arguments should be kept. *)
blanchet@42753
   755
datatype type_arg_policy =
blanchet@45937
   756
  Explicit_Type_Args of bool (* infer_from_term_args *) |
blanchet@44771
   757
  Mangled_Type_Args |
blanchet@42753
   758
  No_Type_Args
blanchet@41136
   759
blanchet@45945
   760
fun type_arg_policy monom_constrs type_enc s =
blanchet@45315
   761
  let val poly = polymorphism_of_type_enc type_enc in
blanchet@44774
   762
    if s = type_tag_name then
blanchet@45315
   763
      if poly = Mangled_Monomorphic then Mangled_Type_Args
blanchet@45315
   764
      else Explicit_Type_Args false
blanchet@44774
   765
    else case type_enc of
blanchet@45315
   766
      Simple_Types (_, Polymorphic, _) => Explicit_Type_Args false
blanchet@45315
   767
    | Tags (_, All_Types) => No_Type_Args
blanchet@44774
   768
    | _ =>
blanchet@44774
   769
      let val level = level_of_type_enc type_enc in
blanchet@44774
   770
        if level = No_Types orelse s = @{const_name HOL.eq} orelse
blanchet@44774
   771
           (s = app_op_name andalso level = Const_Arg_Types) then
blanchet@44774
   772
          No_Type_Args
blanchet@45315
   773
        else if poly = Mangled_Monomorphic then
blanchet@44774
   774
          Mangled_Type_Args
blanchet@45945
   775
        else if member (op =) monom_constrs s andalso
blanchet@45945
   776
                granularity_of_type_level level = Positively_Naked_Vars then
blanchet@45945
   777
          No_Type_Args
blanchet@44774
   778
        else
blanchet@44811
   779
          Explicit_Type_Args
blanchet@44811
   780
              (level = All_Types orelse
blanchet@44811
   781
               granularity_of_type_level level = Ghost_Type_Arg_Vars)
blanchet@44774
   782
      end
blanchet@44774
   783
  end
blanchet@42227
   784
blanchet@44625
   785
(* Make atoms for sorted type variables. *)
blanchet@43263
   786
fun generic_add_sorts_on_type (_, []) = I
blanchet@43263
   787
  | generic_add_sorts_on_type ((x, i), s :: ss) =
blanchet@43263
   788
    generic_add_sorts_on_type ((x, i), ss)
blanchet@43263
   789
    #> (if s = the_single @{sort HOL.type} then
blanchet@43093
   790
          I
blanchet@43093
   791
        else if i = ~1 then
blanchet@44623
   792
          insert (op =) (`make_type_class s, `make_fixed_type_var x)
blanchet@43093
   793
        else
blanchet@44623
   794
          insert (op =) (`make_type_class s,
blanchet@44623
   795
                         (make_schematic_type_var (x, i), x)))
blanchet@43263
   796
fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
blanchet@43263
   797
  | add_sorts_on_tfree _ = I
blanchet@43263
   798
fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
blanchet@43263
   799
  | add_sorts_on_tvar _ = I
blanchet@43085
   800
blanchet@44625
   801
fun type_class_formula type_enc class arg =
blanchet@44625
   802
  AAtom (ATerm (class, arg ::
blanchet@44625
   803
      (case type_enc of
blanchet@44754
   804
         Simple_Types (First_Order, Polymorphic, _) =>
blanchet@45301
   805
         if avoid_first_order_ghost_type_vars then [ATerm (TYPE_name, [arg])]
blanchet@44754
   806
         else []
blanchet@44625
   807
       | _ => [])))
blanchet@44625
   808
fun formulas_for_types type_enc add_sorts_on_typ Ts =
blanchet@43626
   809
  [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
blanchet@44625
   810
     |> map (fn (class, name) =>
blanchet@44625
   811
                type_class_formula type_enc class (ATerm (name, [])))
blanchet@41137
   812
blanchet@42534
   813
fun mk_aconns c phis =
blanchet@42534
   814
  let val (phis', phi') = split_last phis in
blanchet@42534
   815
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   816
  end
blanchet@38282
   817
fun mk_ahorn [] phi = phi
blanchet@42534
   818
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   819
fun mk_aquant _ [] phi = phi
blanchet@42522
   820
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   821
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   822
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   823
blanchet@45315
   824
fun close_universally add_term_vars phi =
blanchet@41145
   825
  let
blanchet@45315
   826
    fun add_formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@45315
   827
        add_formula_vars (map fst xs @ bounds) phi
blanchet@45315
   828
      | add_formula_vars bounds (AConn (_, phis)) =
blanchet@45315
   829
        fold (add_formula_vars bounds) phis
blanchet@45315
   830
      | add_formula_vars bounds (AAtom tm) = add_term_vars bounds tm
blanchet@45315
   831
  in mk_aquant AForall (add_formula_vars [] phi []) phi end
blanchet@42522
   832
blanchet@45377
   833
fun add_term_vars bounds (ATerm (name as (s, _), tms)) =
blanchet@45377
   834
    (if is_tptp_variable s andalso
blanchet@45377
   835
        not (String.isPrefix tvar_prefix s) andalso
blanchet@45377
   836
        not (member (op =) bounds name) then
blanchet@45377
   837
       insert (op =) (name, NONE)
blanchet@45377
   838
     else
blanchet@45377
   839
       I)
blanchet@45377
   840
    #> fold (add_term_vars bounds) tms
blanchet@45377
   841
  | add_term_vars bounds (AAbs ((name, _), tm)) =
blanchet@45377
   842
    add_term_vars (name :: bounds) tm
blanchet@45401
   843
fun close_formula_universally phi = close_universally add_term_vars phi
blanchet@45315
   844
blanchet@45315
   845
fun add_iterm_vars bounds (IApp (tm1, tm2)) =
blanchet@45315
   846
    fold (add_iterm_vars bounds) [tm1, tm2]
blanchet@45315
   847
  | add_iterm_vars _ (IConst _) = I
blanchet@45315
   848
  | add_iterm_vars bounds (IVar (name, T)) =
blanchet@45315
   849
    not (member (op =) bounds name) ? insert (op =) (name, SOME T)
blanchet@45315
   850
  | add_iterm_vars bounds (IAbs (_, tm)) = add_iterm_vars bounds tm
blanchet@45315
   851
fun close_iformula_universally phi = close_universally add_iterm_vars phi
blanchet@41145
   852
blanchet@46338
   853
val fused_infinite_type_name = "ATP.fused_inf" (* shouldn't clash *)
blanchet@44594
   854
val fused_infinite_type = Type (fused_infinite_type_name, [])
blanchet@44594
   855
blanchet@44594
   856
fun tvar_name (x as (s, _)) = (make_schematic_type_var x, s)
blanchet@42994
   857
nik@43676
   858
fun ho_term_from_typ format type_enc =
blanchet@42994
   859
  let
blanchet@42994
   860
    fun term (Type (s, Ts)) =
blanchet@43626
   861
      ATerm (case (is_type_enc_higher_order type_enc, s) of
blanchet@42994
   862
               (true, @{type_name bool}) => `I tptp_bool_type
blanchet@42994
   863
             | (true, @{type_name fun}) => `I tptp_fun_type
blanchet@44594
   864
             | _ => if s = fused_infinite_type_name andalso
blanchet@44235
   865
                       is_format_typed format then
blanchet@43178
   866
                      `I tptp_individual_type
blanchet@43178
   867
                    else
blanchet@43178
   868
                      `make_fixed_type_const s,
blanchet@42994
   869
             map term Ts)
blanchet@42994
   870
    | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
blanchet@44594
   871
    | term (TVar (x, _)) = ATerm (tvar_name x, [])
blanchet@42994
   872
  in term end
blanchet@42562
   873
nik@43676
   874
fun ho_term_for_type_arg format type_enc T =
nik@43676
   875
  if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
blanchet@43401
   876
blanchet@42562
   877
(* This shouldn't clash with anything else. *)
blanchet@46409
   878
val uncurried_alias_sep = "\000"
blanchet@46392
   879
val mangled_type_sep = "\001"
blanchet@46392
   880
blanchet@46409
   881
val ascii_of_uncurried_alias_sep = ascii_of uncurried_alias_sep
blanchet@42542
   882
blanchet@42562
   883
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   884
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42761
   885
    f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
blanchet@42761
   886
    ^ ")"
blanchet@43692
   887
  | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
blanchet@42542
   888
blanchet@44396
   889
fun mangled_type format type_enc =
blanchet@44396
   890
  generic_mangled_type_name fst o ho_term_from_typ format type_enc
blanchet@44396
   891
blanchet@43085
   892
fun make_simple_type s =
blanchet@43085
   893
  if s = tptp_bool_type orelse s = tptp_fun_type orelse
blanchet@43085
   894
     s = tptp_individual_type then
blanchet@43085
   895
    s
blanchet@43085
   896
  else
blanchet@43085
   897
    simple_type_prefix ^ ascii_of s
blanchet@43085
   898
nik@43676
   899
fun ho_type_from_ho_term type_enc pred_sym ary =
blanchet@42963
   900
  let
blanchet@44593
   901
    fun to_mangled_atype ty =
blanchet@42963
   902
      AType ((make_simple_type (generic_mangled_type_name fst ty),
blanchet@44593
   903
              generic_mangled_type_name snd ty), [])
blanchet@44593
   904
    fun to_poly_atype (ATerm (name, tys)) = AType (name, map to_poly_atype tys)
blanchet@44593
   905
      | to_poly_atype _ = raise Fail "unexpected type abstraction"
blanchet@44593
   906
    val to_atype =
blanchet@44593
   907
      if polymorphism_of_type_enc type_enc = Polymorphic then to_poly_atype
blanchet@44593
   908
      else to_mangled_atype
blanchet@42963
   909
    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
blanchet@42998
   910
    fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
blanchet@42994
   911
      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
blanchet@43692
   912
      | to_fo _ _ = raise Fail "unexpected type abstraction"
blanchet@42994
   913
    fun to_ho (ty as ATerm ((s, _), tys)) =
nik@43676
   914
        if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
nik@43676
   915
      | to_ho _ = raise Fail "unexpected type abstraction"
blanchet@43626
   916
  in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
blanchet@42963
   917
nik@43677
   918
fun ho_type_from_typ format type_enc pred_sym ary =
nik@43676
   919
  ho_type_from_ho_term type_enc pred_sym ary
nik@43676
   920
  o ho_term_from_typ format type_enc
blanchet@42963
   921
blanchet@46409
   922
fun aliased_uncurried ary (s, s') =
blanchet@46409
   923
  (s ^ ascii_of_uncurried_alias_sep ^ string_of_int ary, s' ^ string_of_int ary)
blanchet@46409
   924
fun unaliased_uncurried (s, s') =
blanchet@46409
   925
  case space_explode uncurried_alias_sep s of
blanchet@46392
   926
    [_] => (s, s')
blanchet@46392
   927
  | [s1, s2] => (s1, unsuffix s2 s')
blanchet@46392
   928
  | _ => raise Fail "ill-formed explicit application alias"
blanchet@46392
   929
blanchet@46392
   930
fun raw_mangled_const_name type_name ty_args (s, s') =
blanchet@42963
   931
  let
blanchet@42963
   932
    fun type_suffix f g =
blanchet@46392
   933
      fold_rev (curry (op ^) o g o prefix mangled_type_sep o type_name f)
blanchet@46392
   934
               ty_args ""
blanchet@42963
   935
  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@46392
   936
fun mangled_const_name format type_enc =
blanchet@46392
   937
  map_filter (ho_term_for_type_arg format type_enc)
blanchet@46392
   938
  #> raw_mangled_const_name generic_mangled_type_name
blanchet@42542
   939
blanchet@42542
   940
val parse_mangled_ident =
blanchet@42542
   941
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   942
blanchet@42542
   943
fun parse_mangled_type x =
blanchet@42542
   944
  (parse_mangled_ident
blanchet@42542
   945
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   946
                    [] >> ATerm) x
blanchet@42542
   947
and parse_mangled_types x =
blanchet@42542
   948
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   949
blanchet@42542
   950
fun unmangled_type s =
blanchet@42542
   951
  s |> suffix ")" |> raw_explode
blanchet@42542
   952
    |> Scan.finite Symbol.stopper
blanchet@42542
   953
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   954
                                                quote s)) parse_mangled_type))
blanchet@42542
   955
    |> fst
blanchet@42542
   956
blanchet@46392
   957
fun unmangled_const_name s =
blanchet@46409
   958
  (s, s) |> unaliased_uncurried |> fst |> space_explode mangled_type_sep
blanchet@42542
   959
fun unmangled_const s =
blanchet@46392
   960
  let val ss = unmangled_const_name s in
blanchet@42542
   961
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   962
  end
blanchet@42542
   963
blanchet@44773
   964
fun introduce_proxies_in_iterm type_enc =
blanchet@42568
   965
  let
blanchet@43987
   966
    fun tweak_ho_quant ho_quant T [IAbs _] = IConst (`I ho_quant, T, [])
blanchet@43987
   967
      | tweak_ho_quant ho_quant (T as Type (_, [p_T as Type (_, [x_T, _]), _]))
blanchet@43987
   968
                       _ =
blanchet@43987
   969
        (* Eta-expand "!!" and "??", to work around LEO-II 1.2.8 parser
blanchet@43987
   970
           limitation. This works in conjuction with special code in
blanchet@43987
   971
           "ATP_Problem" that uses the syntactic sugar "!" and "?" whenever
blanchet@43987
   972
           possible. *)
blanchet@43987
   973
        IAbs ((`I "P", p_T),
blanchet@43987
   974
              IApp (IConst (`I ho_quant, T, []),
blanchet@43987
   975
                    IAbs ((`I "X", x_T),
blanchet@43987
   976
                          IApp (IConst (`I "P", p_T, []),
blanchet@43987
   977
                                IConst (`I "X", x_T, [])))))
blanchet@43987
   978
      | tweak_ho_quant _ _ _ = raise Fail "unexpected type for quantifier"
blanchet@43987
   979
    fun intro top_level args (IApp (tm1, tm2)) =
blanchet@43987
   980
        IApp (intro top_level (tm2 :: args) tm1, intro false [] tm2)
blanchet@43987
   981
      | intro top_level args (IConst (name as (s, _), T, T_args)) =
blanchet@42570
   982
        (case proxify_const s of
blanchet@43159
   983
           SOME proxy_base =>
blanchet@43626
   984
           if top_level orelse is_type_enc_higher_order type_enc then
blanchet@43000
   985
             case (top_level, s) of
blanchet@43987
   986
               (_, "c_False") => IConst (`I tptp_false, T, [])
blanchet@43987
   987
             | (_, "c_True") => IConst (`I tptp_true, T, [])
blanchet@43987
   988
             | (false, "c_Not") => IConst (`I tptp_not, T, [])
blanchet@43987
   989
             | (false, "c_conj") => IConst (`I tptp_and, T, [])
blanchet@43987
   990
             | (false, "c_disj") => IConst (`I tptp_or, T, [])
blanchet@43987
   991
             | (false, "c_implies") => IConst (`I tptp_implies, T, [])
blanchet@43987
   992
             | (false, "c_All") => tweak_ho_quant tptp_ho_forall T args
blanchet@43987
   993
             | (false, "c_Ex") => tweak_ho_quant tptp_ho_exists T args
blanchet@43000
   994
             | (false, s) =>
blanchet@44097
   995
               if is_tptp_equal s andalso length args = 2 then
blanchet@44097
   996
                 IConst (`I tptp_equal, T, [])
blanchet@44097
   997
               else
blanchet@44589
   998
                 (* Use a proxy even for partially applied THF0 equality,
blanchet@44589
   999
                    because the LEO-II and Satallax parsers complain about not
blanchet@44589
  1000
                    being able to infer the type of "=". *)
blanchet@44097
  1001
                 IConst (proxy_base |>> prefix const_prefix, T, T_args)
blanchet@43987
  1002
             | _ => IConst (name, T, [])
blanchet@42569
  1003
           else
blanchet@43987
  1004
             IConst (proxy_base |>> prefix const_prefix, T, T_args)
blanchet@45167
  1005
          | NONE => if s = tptp_choice then tweak_ho_quant tptp_choice T args
blanchet@45167
  1006
                    else IConst (name, T, T_args))
blanchet@43987
  1007
      | intro _ _ (IAbs (bound, tm)) = IAbs (bound, intro false [] tm)
blanchet@43987
  1008
      | intro _ _ tm = tm
blanchet@43987
  1009
  in intro true [] end
blanchet@42568
  1010
blanchet@46392
  1011
fun mangle_type_args_in_const format type_enc (name as (s, _)) T_args =
blanchet@46392
  1012
  case unprefix_and_unascii const_prefix s of
blanchet@46392
  1013
    NONE => (name, T_args)
blanchet@46392
  1014
  | SOME s'' =>
blanchet@46392
  1015
    case type_arg_policy [] type_enc (invert_const s'') of
blanchet@46392
  1016
      Mangled_Type_Args => (mangled_const_name format type_enc T_args name, [])
blanchet@46392
  1017
    | _ => (name, T_args)
blanchet@44774
  1018
fun mangle_type_args_in_iterm format type_enc =
blanchet@44774
  1019
  if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
blanchet@44774
  1020
    let
blanchet@44774
  1021
      fun mangle (IApp (tm1, tm2)) = IApp (mangle tm1, mangle tm2)
blanchet@44774
  1022
        | mangle (tm as IConst (_, _, [])) = tm
blanchet@46392
  1023
        | mangle (IConst (name, T, T_args)) =
blanchet@46392
  1024
          mangle_type_args_in_const format type_enc name T_args
blanchet@46392
  1025
          |> (fn (name, T_args) => IConst (name, T, T_args))
blanchet@44774
  1026
        | mangle (IAbs (bound, tm)) = IAbs (bound, mangle tm)
blanchet@44774
  1027
        | mangle tm = tm
blanchet@44774
  1028
    in mangle end
blanchet@44774
  1029
  else
blanchet@44774
  1030
    I
blanchet@44774
  1031
blanchet@44773
  1032
fun chop_fun 0 T = ([], T)
blanchet@44773
  1033
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@44773
  1034
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@44773
  1035
  | chop_fun _ T = ([], T)
blanchet@44773
  1036
blanchet@44774
  1037
fun filter_const_type_args _ _ _ [] = []
blanchet@44774
  1038
  | filter_const_type_args thy s ary T_args =
blanchet@44773
  1039
    let
blanchet@44773
  1040
      val U = robust_const_type thy s
blanchet@44773
  1041
      val arg_U_vars = fold Term.add_tvarsT (U |> chop_fun ary |> fst) []
blanchet@44773
  1042
      val U_args = (s, U) |> robust_const_typargs thy
blanchet@44773
  1043
    in
blanchet@44773
  1044
      U_args ~~ T_args
blanchet@44773
  1045
      |> map (fn (U, T) =>
blanchet@44773
  1046
                 if member (op =) arg_U_vars (dest_TVar U) then dummyT else T)
blanchet@44773
  1047
    end
blanchet@44773
  1048
    handle TYPE _ => T_args
blanchet@44773
  1049
blanchet@46392
  1050
fun filter_type_args_in_const _ _ _ _ _ [] = []
blanchet@46392
  1051
  | filter_type_args_in_const thy monom_constrs type_enc ary s T_args =
blanchet@46392
  1052
    case unprefix_and_unascii const_prefix s of
blanchet@46392
  1053
      NONE =>
blanchet@46392
  1054
      if level_of_type_enc type_enc = No_Types orelse s = tptp_choice then []
blanchet@46392
  1055
      else T_args
blanchet@46392
  1056
    | SOME s'' =>
blanchet@46392
  1057
      let
blanchet@46392
  1058
        val s'' = invert_const s''
blanchet@46392
  1059
        fun filter_T_args false = T_args
blanchet@46392
  1060
          | filter_T_args true = filter_const_type_args thy s'' ary T_args
blanchet@46392
  1061
      in
blanchet@46392
  1062
        case type_arg_policy monom_constrs type_enc s'' of
blanchet@46392
  1063
          Explicit_Type_Args infer_from_term_args =>
blanchet@46392
  1064
          filter_T_args infer_from_term_args
blanchet@46392
  1065
        | No_Type_Args => []
blanchet@46392
  1066
        | Mangled_Type_Args => raise Fail "unexpected (un)mangled symbol"
blanchet@46392
  1067
      end
blanchet@45945
  1068
fun filter_type_args_in_iterm thy monom_constrs type_enc =
blanchet@38282
  1069
  let
blanchet@44774
  1070
    fun filt ary (IApp (tm1, tm2)) = IApp (filt (ary + 1) tm1, filt 0 tm2)
blanchet@44774
  1071
      | filt ary (IConst (name as (s, _), T, T_args)) =
blanchet@46392
  1072
        filter_type_args_in_const thy monom_constrs type_enc ary s T_args
blanchet@46392
  1073
        |> (fn T_args => IConst (name, T, T_args))
blanchet@44774
  1074
      | filt _ (IAbs (bound, tm)) = IAbs (bound, filt 0 tm)
blanchet@44774
  1075
      | filt _ tm = tm
blanchet@44774
  1076
  in filt 0 end
blanchet@44773
  1077
blanchet@44773
  1078
fun iformula_from_prop ctxt format type_enc eq_as_iff =
blanchet@44773
  1079
  let
blanchet@44773
  1080
    val thy = Proof_Context.theory_of ctxt
blanchet@45316
  1081
    fun do_term bs t atomic_Ts =
nik@44495
  1082
      iterm_from_term thy format bs (Envir.eta_contract t)
blanchet@44773
  1083
      |>> (introduce_proxies_in_iterm type_enc
blanchet@46392
  1084
           #> mangle_type_args_in_iterm format type_enc #> AAtom)
blanchet@45316
  1085
      ||> union (op =) atomic_Ts
blanchet@44403
  1086
    fun do_quant bs q pos s T t' =
blanchet@44403
  1087
      let
blanchet@44403
  1088
        val s = singleton (Name.variant_list (map fst bs)) s
blanchet@44403
  1089
        val universal = Option.map (q = AExists ? not) pos
blanchet@44403
  1090
        val name =
blanchet@44403
  1091
          s |> `(case universal of
blanchet@44403
  1092
                   SOME true => make_all_bound_var
blanchet@44403
  1093
                 | SOME false => make_exist_bound_var
blanchet@44403
  1094
                 | NONE => make_bound_var)
blanchet@44403
  1095
      in
blanchet@44403
  1096
        do_formula ((s, (name, T)) :: bs) pos t'
blanchet@44403
  1097
        #>> mk_aquant q [(name, SOME T)]
blanchet@45316
  1098
        ##> union (op =) (atomic_types_of T)
blanchet@38518
  1099
      end
blanchet@44403
  1100
    and do_conn bs c pos1 t1 pos2 t2 =
blanchet@44403
  1101
      do_formula bs pos1 t1 ##>> do_formula bs pos2 t2 #>> uncurry (mk_aconn c)
blanchet@44403
  1102
    and do_formula bs pos t =
blanchet@38282
  1103
      case t of
blanchet@44403
  1104
        @{const Trueprop} $ t1 => do_formula bs pos t1
blanchet@44403
  1105
      | @{const Not} $ t1 => do_formula bs (Option.map not pos) t1 #>> mk_anot
blanchet@38282
  1106
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@44403
  1107
        do_quant bs AForall pos s T t'
blanchet@45167
  1108
      | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@45167
  1109
        do_formula bs pos (t0 $ eta_expand (map (snd o snd) bs) t1 1)
blanchet@38282
  1110
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@44403
  1111
        do_quant bs AExists pos s T t'
blanchet@45167
  1112
      | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@45167
  1113
        do_formula bs pos (t0 $ eta_expand (map (snd o snd) bs) t1 1)
blanchet@44403
  1114
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd pos t1 pos t2
blanchet@44403
  1115
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr pos t1 pos t2
blanchet@44403
  1116
      | @{const HOL.implies} $ t1 $ t2 =>
blanchet@44403
  1117
        do_conn bs AImplies (Option.map not pos) t1 pos t2
haftmann@38864
  1118
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@44403
  1119
        if eq_as_iff then do_conn bs AIff NONE t1 NONE t2 else do_term bs t
blanchet@41140
  1120
      | _ => do_term bs t
blanchet@38282
  1121
  in do_formula [] end
blanchet@38282
  1122
blanchet@46093
  1123
fun presimplify_term ctxt t =
blanchet@46093
  1124
  t |> exists_Const (member (op =) Meson.presimplified_consts o fst) t
blanchet@46093
  1125
       ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@46093
  1126
          #> Meson.presimplify
blanchet@46093
  1127
          #> prop_of)
blanchet@38282
  1128
blanchet@43863
  1129
fun concealed_bound_name j = atp_weak_prefix ^ string_of_int j
blanchet@38282
  1130
fun conceal_bounds Ts t =
blanchet@38282
  1131
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
  1132
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
  1133
fun reveal_bounds Ts =
blanchet@38282
  1134
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
  1135
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
  1136
blanchet@43265
  1137
fun is_fun_equality (@{const_name HOL.eq},
blanchet@43265
  1138
                     Type (_, [Type (@{type_name fun}, _), _])) = true
blanchet@43265
  1139
  | is_fun_equality _ = false
blanchet@43265
  1140
blanchet@42747
  1141
fun extensionalize_term ctxt t =
blanchet@43265
  1142
  if exists_Const is_fun_equality t then
blanchet@43265
  1143
    let val thy = Proof_Context.theory_of ctxt in
blanchet@43265
  1144
      t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@43265
  1145
        |> prop_of |> Logic.dest_equals |> snd
blanchet@43265
  1146
    end
blanchet@43265
  1147
  else
blanchet@43265
  1148
    t
blanchet@38608
  1149
blanchet@43862
  1150
fun simple_translate_lambdas do_lambdas ctxt t =
blanchet@43863
  1151
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43863
  1152
    if Meson.is_fol_term thy t then
blanchet@43863
  1153
      t
blanchet@43863
  1154
    else
blanchet@43863
  1155
      let
blanchet@44814
  1156
        fun trans Ts t =
blanchet@43863
  1157
          case t of
blanchet@44814
  1158
            @{const Not} $ t1 => @{const Not} $ trans Ts t1
blanchet@43863
  1159
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@44814
  1160
            t0 $ Abs (s, T, trans (T :: Ts) t')
blanchet@43863
  1161
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@44814
  1162
            trans Ts (t0 $ eta_expand Ts t1 1)
blanchet@43863
  1163
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@44814
  1164
            t0 $ Abs (s, T, trans (T :: Ts) t')
blanchet@43863
  1165
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@44814
  1166
            trans Ts (t0 $ eta_expand Ts t1 1)
blanchet@44814
  1167
          | (t0 as @{const HOL.conj}) $ t1 $ t2 =>
blanchet@44814
  1168
            t0 $ trans Ts t1 $ trans Ts t2
blanchet@44814
  1169
          | (t0 as @{const HOL.disj}) $ t1 $ t2 =>
blanchet@44814
  1170
            t0 $ trans Ts t1 $ trans Ts t2
blanchet@44814
  1171
          | (t0 as @{const HOL.implies}) $ t1 $ t2 =>
blanchet@44814
  1172
            t0 $ trans Ts t1 $ trans Ts t2
blanchet@43863
  1173
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@43863
  1174
              $ t1 $ t2 =>
blanchet@44814
  1175
            t0 $ trans Ts t1 $ trans Ts t2
blanchet@43863
  1176
          | _ =>
blanchet@43863
  1177
            if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
blanchet@43863
  1178
            else t |> Envir.eta_contract |> do_lambdas ctxt Ts
blanchet@43863
  1179
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@44814
  1180
      in t |> trans [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@43863
  1181
  end
blanchet@43856
  1182
blanchet@43997
  1183
fun do_cheaply_conceal_lambdas Ts (t1 $ t2) =
blanchet@43997
  1184
    do_cheaply_conceal_lambdas Ts t1
blanchet@43997
  1185
    $ do_cheaply_conceal_lambdas Ts t2
blanchet@43997
  1186
  | do_cheaply_conceal_lambdas Ts (Abs (_, T, t)) =
blanchet@45554
  1187
    Const (lam_lifted_poly_prefix ^ serial_string (),
blanchet@45509
  1188
           T --> fastype_of1 (T :: Ts, t))
blanchet@43997
  1189
  | do_cheaply_conceal_lambdas _ t = t
blanchet@43856
  1190
blanchet@43862
  1191
fun do_introduce_combinators ctxt Ts t =
wenzelm@42361
  1192
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43905
  1193
    t |> conceal_bounds Ts
blanchet@43905
  1194
      |> cterm_of thy
blanchet@43905
  1195
      |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@43905
  1196
      |> prop_of |> Logic.dest_equals |> snd
blanchet@43905
  1197
      |> reveal_bounds Ts
blanchet@38491
  1198
  end
blanchet@43862
  1199
  (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@43997
  1200
  handle THM _ => t |> do_cheaply_conceal_lambdas Ts
blanchet@43862
  1201
val introduce_combinators = simple_translate_lambdas do_introduce_combinators
blanchet@43862
  1202
blanchet@45514
  1203
fun preprocess_abstractions_in_terms trans_lams facts =
blanchet@43862
  1204
  let
blanchet@43863
  1205
    val (facts, lambda_ts) =
blanchet@45514
  1206
      facts |> map (snd o snd) |> trans_lams
blanchet@43863
  1207
            |>> map2 (fn (name, (kind, _)) => fn t => (name, (kind, t))) facts
blanchet@45554
  1208
    val lam_facts =
blanchet@43863
  1209
      map2 (fn t => fn j =>
blanchet@46393
  1210
               ((lam_fact_prefix ^ Int.toString j, (Global, Spec_Eq)),
blanchet@46393
  1211
                (Axiom, t)))
blanchet@43863
  1212
           lambda_ts (1 upto length lambda_ts)
blanchet@45554
  1213
  in (facts, lam_facts) end
blanchet@38282
  1214
blanchet@38282
  1215
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
  1216
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
  1217
fun freeze_term t =
blanchet@38282
  1218
  let
blanchet@44814
  1219
    fun freeze (t $ u) = freeze t $ freeze u
blanchet@44814
  1220
      | freeze (Abs (s, T, t)) = Abs (s, T, freeze t)
blanchet@44814
  1221
      | freeze (Var ((s, i), T)) =
blanchet@43863
  1222
        Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@44814
  1223
      | freeze t = t
blanchet@44814
  1224
  in t |> exists_subterm is_Var t ? freeze end
blanchet@38282
  1225
blanchet@46093
  1226
fun presimp_prop ctxt role t =
blanchet@45202
  1227
  (let
blanchet@45202
  1228
     val thy = Proof_Context.theory_of ctxt
blanchet@45202
  1229
     val t = t |> Envir.beta_eta_contract
blanchet@45202
  1230
               |> transform_elim_prop
blanchet@45202
  1231
               |> Object_Logic.atomize_term thy
blanchet@45202
  1232
     val need_trueprop = (fastype_of t = @{typ bool})
blanchet@45202
  1233
   in
blanchet@45202
  1234
     t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@45202
  1235
       |> extensionalize_term ctxt
blanchet@46093
  1236
       |> presimplify_term ctxt
blanchet@45202
  1237
       |> HOLogic.dest_Trueprop
blanchet@45202
  1238
   end
blanchet@45202
  1239
   handle TERM _ => if role = Conjecture then @{term False} else @{term True})
blanchet@45202
  1240
  |> pair role
blanchet@43096
  1241
blanchet@46340
  1242
fun make_formula ctxt format type_enc eq_as_iff name stature kind t =
blanchet@43096
  1243
  let
blanchet@45316
  1244
    val (iformula, atomic_Ts) =
blanchet@44773
  1245
      iformula_from_prop ctxt format type_enc eq_as_iff
blanchet@44773
  1246
                         (SOME (kind <> Conjecture)) t []
blanchet@45316
  1247
      |>> close_iformula_universally
blanchet@38282
  1248
  in
blanchet@46340
  1249
    {name = name, stature = stature, kind = kind, iformula = iformula,
blanchet@45316
  1250
     atomic_types = atomic_Ts}
blanchet@38282
  1251
  end
blanchet@38282
  1252
blanchet@46340
  1253
fun make_fact ctxt format type_enc eq_as_iff ((name, stature), t) =
blanchet@44773
  1254
  case t |> make_formula ctxt format type_enc (eq_as_iff andalso format <> CNF)
blanchet@46340
  1255
                         name stature Axiom of
blanchet@44773
  1256
    formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
blanchet@44773
  1257
    if s = tptp_true then NONE else SOME formula
blanchet@44773
  1258
  | formula => SOME formula
blanchet@42561
  1259
blanchet@46385
  1260
fun s_not_trueprop (@{const Trueprop} $ t) = @{const Trueprop} $ s_not t
blanchet@46385
  1261
  | s_not_trueprop t =
blanchet@46385
  1262
    if fastype_of t = @{typ bool} then s_not t
blanchet@46377
  1263
    else @{prop False} (* "t" is too meta *)
blanchet@44460
  1264
blanchet@44773
  1265
fun make_conjecture ctxt format type_enc =
blanchet@46340
  1266
  map (fn ((name, stature), (kind, t)) =>
blanchet@46385
  1267
          t |> kind = Conjecture ? s_not_trueprop
blanchet@46340
  1268
            |> make_formula ctxt format type_enc (format <> CNF) name stature
blanchet@46340
  1269
                            kind)
blanchet@38282
  1270
blanchet@42682
  1271
(** Finite and infinite type inference **)
blanchet@42682
  1272
blanchet@44814
  1273
fun tvar_footprint thy s ary =
blanchet@45511
  1274
  (case unprefix_and_unascii const_prefix s of
blanchet@44814
  1275
     SOME s =>
blanchet@44814
  1276
     s |> invert_const |> robust_const_type thy |> chop_fun ary |> fst
blanchet@44814
  1277
       |> map (fn T => Term.add_tvarsT T [] |> map fst)
blanchet@44814
  1278
   | NONE => [])
blanchet@44814
  1279
  handle TYPE _ => []
blanchet@44814
  1280
blanchet@44814
  1281
fun ghost_type_args thy s ary =
blanchet@45948
  1282
  if is_tptp_equal s then
blanchet@45948
  1283
    0 upto ary - 1
blanchet@45948
  1284
  else
blanchet@45948
  1285
    let
blanchet@45948
  1286
      val footprint = tvar_footprint thy s ary
blanchet@45948
  1287
      val eq = (s = @{const_name HOL.eq})
blanchet@45948
  1288
      fun ghosts _ [] = []
blanchet@45948
  1289
        | ghosts seen ((i, tvars) :: args) =
blanchet@45948
  1290
          ghosts (union (op =) seen tvars) args
blanchet@45948
  1291
          |> (eq orelse exists (fn tvar => not (member (op =) seen tvar)) tvars)
blanchet@45948
  1292
             ? cons i
blanchet@45948
  1293
    in
blanchet@45948
  1294
      if forall null footprint then
blanchet@45948
  1295
        []
blanchet@45948
  1296
      else
blanchet@45948
  1297
        0 upto length footprint - 1 ~~ footprint
blanchet@45948
  1298
        |> sort (rev_order o list_ord Term_Ord.indexname_ord o pairself snd)
blanchet@45948
  1299
        |> ghosts []
blanchet@45948
  1300
    end
blanchet@44814
  1301
blanchet@44399
  1302
type monotonicity_info =
blanchet@44399
  1303
  {maybe_finite_Ts : typ list,
blanchet@44399
  1304
   surely_finite_Ts : typ list,
blanchet@44399
  1305
   maybe_infinite_Ts : typ list,
blanchet@44399
  1306
   surely_infinite_Ts : typ list,
blanchet@44399
  1307
   maybe_nonmono_Ts : typ list}
blanchet@44399
  1308
blanchet@44397
  1309
(* These types witness that the type classes they belong to allow infinite
blanchet@44397
  1310
   models and hence that any types with these type classes is monotonic. *)
blanchet@44397
  1311
val known_infinite_types =
blanchet@44634
  1312
  [@{typ nat}, HOLogic.intT, HOLogic.realT, @{typ "nat => bool"}]
blanchet@44397
  1313
blanchet@46301
  1314
fun is_type_kind_of_surely_infinite ctxt strictness cached_Ts T =
blanchet@46301
  1315
  strictness <> Strict andalso is_type_surely_infinite ctxt true cached_Ts T
blanchet@42886
  1316
blanchet@42682
  1317
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
  1318
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
  1319
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
  1320
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
  1321
blanchet@44399
  1322
fun should_encode_type _ (_ : monotonicity_info) All_Types _ = true
blanchet@44399
  1323
  | should_encode_type ctxt {maybe_finite_Ts, surely_infinite_Ts,
blanchet@44399
  1324
                             maybe_nonmono_Ts, ...}
blanchet@46301
  1325
                       (Noninf_Nonmono_Types (strictness, grain)) T =
blanchet@44811
  1326
    grain = Ghost_Type_Arg_Vars orelse
blanchet@44811
  1327
    (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
blanchet@44811
  1328
     not (exists (type_instance ctxt T) surely_infinite_Ts orelse
blanchet@44859
  1329
          (not (member (type_equiv ctxt) maybe_finite_Ts T) andalso
blanchet@46301
  1330
           is_type_kind_of_surely_infinite ctxt strictness surely_infinite_Ts
blanchet@44811
  1331
                                           T)))
blanchet@44399
  1332
  | should_encode_type ctxt {surely_finite_Ts, maybe_infinite_Ts,
blanchet@44399
  1333
                             maybe_nonmono_Ts, ...}
blanchet@44811
  1334
                       (Fin_Nonmono_Types grain) T =
blanchet@44811
  1335
    grain = Ghost_Type_Arg_Vars orelse
blanchet@44811
  1336
    (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
blanchet@44811
  1337
     (exists (type_generalization ctxt T) surely_finite_Ts orelse
blanchet@44859
  1338
      (not (member (type_equiv ctxt) maybe_infinite_Ts T) andalso
blanchet@44811
  1339
       is_type_surely_finite ctxt T)))
blanchet@42682
  1340
  | should_encode_type _ _ _ _ = false
blanchet@42682
  1341
blanchet@44768
  1342
fun should_guard_type ctxt mono (Guards (_, level)) should_guard_var T =
blanchet@44811
  1343
    should_guard_var () andalso should_encode_type ctxt mono level T
blanchet@44399
  1344
  | should_guard_type _ _ _ _ _ = false
blanchet@42682
  1345
blanchet@44403
  1346
fun is_maybe_universal_var (IConst ((s, _), _, _)) =
blanchet@44403
  1347
    String.isPrefix bound_var_prefix s orelse
blanchet@44403
  1348
    String.isPrefix all_bound_var_prefix s
blanchet@44403
  1349
  | is_maybe_universal_var (IVar _) = true
blanchet@44403
  1350
  | is_maybe_universal_var _ = false
blanchet@42836
  1351
blanchet@45947
  1352
datatype site =
blanchet@43361
  1353
  Top_Level of bool option |
blanchet@43361
  1354
  Eq_Arg of bool option |
blanchet@43361
  1355
  Elsewhere
blanchet@42829
  1356
blanchet@45949
  1357
fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
blanchet@45949
  1358
  | should_tag_with_type ctxt mono (Tags (_, level)) site u T =
blanchet@45949
  1359
    if granularity_of_type_level level = All_Vars then
blanchet@45949
  1360
      should_encode_type ctxt mono level T
blanchet@45949
  1361
    else
blanchet@45949
  1362
      (case (site, is_maybe_universal_var u) of
blanchet@45949
  1363
         (Eq_Arg _, true) => should_encode_type ctxt mono level T
blanchet@44814
  1364
       | _ => false)
blanchet@45949
  1365
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
  1366
blanchet@44594
  1367
fun fused_type ctxt mono level =
blanchet@42994
  1368
  let
blanchet@44399
  1369
    val should_encode = should_encode_type ctxt mono level
blanchet@44594
  1370
    fun fuse 0 T = if should_encode T then T else fused_infinite_type
blanchet@44594
  1371
      | fuse ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@44594
  1372
        fuse 0 T1 --> fuse (ary - 1) T2
blanchet@44594
  1373
      | fuse _ _ = raise Fail "expected function type"
blanchet@44594
  1374
  in fuse end
blanchet@42682
  1375
blanchet@44450
  1376
(** predicators and application operators **)
blanchet@41313
  1377
blanchet@42574
  1378
type sym_info =
blanchet@44829
  1379
  {pred_sym : bool, min_ary : int, max_ary : int, types : typ list,
blanchet@44829
  1380
   in_conj : bool}
blanchet@42563
  1381
blanchet@44829
  1382
fun default_sym_tab_entries type_enc =
blanchet@44829
  1383
  (make_fixed_const NONE @{const_name undefined},
blanchet@44829
  1384
       {pred_sym = false, min_ary = 0, max_ary = 0, types = [],
blanchet@44829
  1385
        in_conj = false}) ::
blanchet@44829
  1386
  ([tptp_false, tptp_true]
blanchet@44829
  1387
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = [],
blanchet@44829
  1388
                  in_conj = false})) @
blanchet@44829
  1389
  ([tptp_equal, tptp_old_equal]
blanchet@44829
  1390
   |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = [],
blanchet@44829
  1391
                  in_conj = false}))
blanchet@44829
  1392
  |> not (is_type_enc_higher_order type_enc)
blanchet@44829
  1393
     ? cons (prefixed_predicator_name,
blanchet@44829
  1394
             {pred_sym = true, min_ary = 1, max_ary = 1, types = [],
blanchet@44829
  1395
              in_conj = false})
blanchet@44829
  1396
blanchet@46392
  1397
datatype app_op_level = Incomplete_Apply | Sufficient_Apply | Full_Apply
blanchet@46389
  1398
blanchet@46392
  1399
fun sym_table_for_facts ctxt type_enc app_op_level conjs facts =
blanchet@42558
  1400
  let
blanchet@44772
  1401
    fun consider_var_ary const_T var_T max_ary =
blanchet@43064
  1402
      let
blanchet@43064
  1403
        fun iter ary T =
blanchet@44399
  1404
          if ary = max_ary orelse type_instance ctxt var_T T orelse
blanchet@44399
  1405
             type_instance ctxt T var_T then
blanchet@43210
  1406
            ary
blanchet@43210
  1407
          else
blanchet@43210
  1408
            iter (ary + 1) (range_type T)
blanchet@43064
  1409
      in iter 0 const_T end
blanchet@44403
  1410
    fun add_universal_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@46392
  1411
      if app_op_level = Sufficient_Apply andalso
blanchet@43201
  1412
         (can dest_funT T orelse T = @{typ bool}) then
blanchet@43201
  1413
        let
blanchet@43201
  1414
          val bool_vars' = bool_vars orelse body_type T = @{typ bool}
blanchet@44829
  1415
          fun repair_min_ary {pred_sym, min_ary, max_ary, types, in_conj} =
blanchet@43201
  1416
            {pred_sym = pred_sym andalso not bool_vars',
blanchet@44772
  1417
             min_ary = fold (fn T' => consider_var_ary T' T) types min_ary,
blanchet@44829
  1418
             max_ary = max_ary, types = types, in_conj = in_conj}
blanchet@43201
  1419
          val fun_var_Ts' =
blanchet@43201
  1420
            fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
blanchet@43201
  1421
        in
blanchet@43201
  1422
          if bool_vars' = bool_vars andalso
blanchet@43201
  1423
             pointer_eq (fun_var_Ts', fun_var_Ts) then
blanchet@43201
  1424
            accum
blanchet@43167
  1425
          else
blanchet@44772
  1426
            ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_ary) sym_tab)
blanchet@43201
  1427
        end
blanchet@43201
  1428
      else
blanchet@43201
  1429
        accum
blanchet@46392
  1430
      fun add_iterm_syms conj_fact top_level tm
blanchet@46392
  1431
                         (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
blanchet@46392
  1432
        let val (head, args) = strip_iterm_comb tm in
blanchet@46392
  1433
          (case head of
blanchet@46392
  1434
             IConst ((s, _), T, _) =>
blanchet@46392
  1435
             if String.isPrefix bound_var_prefix s orelse
blanchet@46392
  1436
                String.isPrefix all_bound_var_prefix s then
blanchet@46392
  1437
               add_universal_var T accum
blanchet@46392
  1438
             else if String.isPrefix exist_bound_var_prefix s then
blanchet@46392
  1439
               accum
blanchet@46392
  1440
             else
blanchet@46392
  1441
               let val ary = length args in
blanchet@46392
  1442
                 ((bool_vars, fun_var_Ts),
blanchet@46392
  1443
                  case Symtab.lookup sym_tab s of
blanchet@46392
  1444
                    SOME {pred_sym, min_ary, max_ary, types, in_conj} =>
blanchet@46392
  1445
                    let
blanchet@46392
  1446
                      val pred_sym =
blanchet@46392
  1447
                        pred_sym andalso top_level andalso not bool_vars
blanchet@46392
  1448
                      val types' = types |> insert_type ctxt I T
blanchet@46392
  1449
                      val in_conj = in_conj orelse conj_fact
blanchet@46392
  1450
                      val min_ary =
blanchet@46392
  1451
                        if app_op_level = Sufficient_Apply andalso
blanchet@46392
  1452
                           not (pointer_eq (types', types)) then
blanchet@46392
  1453
                          fold (consider_var_ary T) fun_var_Ts min_ary
blanchet@46392
  1454
                        else
blanchet@46392
  1455
                          min_ary
blanchet@46392
  1456
                    in
blanchet@46392
  1457
                      Symtab.update (s, {pred_sym = pred_sym,
blanchet@46392
  1458
                                         min_ary = Int.min (ary, min_ary),
blanchet@46392
  1459
                                         max_ary = Int.max (ary, max_ary),
blanchet@46392
  1460
                                         types = types', in_conj = in_conj})
blanchet@46392
  1461
                                    sym_tab
blanchet@46392
  1462
                    end
blanchet@46392
  1463
                  | NONE =>
blanchet@46392
  1464
                    let
blanchet@46392
  1465
                      val pred_sym = top_level andalso not bool_vars
blanchet@46392
  1466
                      val min_ary =
blanchet@46392
  1467
                        case app_op_level of
blanchet@46392
  1468
                          Incomplete_Apply => ary
blanchet@46392
  1469
                        | Sufficient_Apply =>
blanchet@46392
  1470
                          fold (consider_var_ary T) fun_var_Ts ary
blanchet@46392
  1471
                        | Full_Apply => 0
blanchet@46392
  1472
                    in
blanchet@46392
  1473
                      Symtab.update_new (s,
blanchet@46392
  1474
                          {pred_sym = pred_sym, min_ary = min_ary,
blanchet@46392
  1475
                           max_ary = ary, types = [T], in_conj = conj_fact})
blanchet@46392
  1476
                          sym_tab
blanchet@46392
  1477
                    end)
blanchet@46392
  1478
               end
blanchet@46392
  1479
           | IVar (_, T) => add_universal_var T accum
blanchet@46392
  1480
           | IAbs ((_, T), tm) =>
blanchet@46392
  1481
             accum |> add_universal_var T |> add_iterm_syms conj_fact false tm
blanchet@46392
  1482
           | _ => accum)
blanchet@46392
  1483
          |> fold (add_iterm_syms conj_fact false) args
blanchet@46392
  1484
        end
blanchet@44829
  1485
    fun add_fact_syms conj_fact =
blanchet@46392
  1486
      K (add_iterm_syms conj_fact true) |> formula_fold NONE |> fact_lift
blanchet@44829
  1487
  in
blanchet@44829
  1488
    ((false, []), Symtab.empty)
blanchet@44829
  1489
    |> fold (add_fact_syms true) conjs
blanchet@44829
  1490
    |> fold (add_fact_syms false) facts
blanchet@44829
  1491
    |> snd
blanchet@44829
  1492
    |> fold Symtab.update (default_sym_tab_entries type_enc)
blanchet@44829
  1493
  end
blanchet@38282
  1494
blanchet@44772
  1495
fun min_ary_of sym_tab s =
blanchet@42558
  1496
  case Symtab.lookup sym_tab s of
blanchet@42574
  1497
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
  1498
  | NONE =>
blanchet@45511
  1499
    case unprefix_and_unascii const_prefix s of
blanchet@42547
  1500
      SOME s =>
blanchet@46392
  1501
      let val s = s |> unmangled_const_name |> hd |> invert_const in
blanchet@42966
  1502
        if s = predicator_name then 1
blanchet@42966
  1503
        else if s = app_op_name then 2
blanchet@44396
  1504
        else if s = type_guard_name then 1
blanchet@42557
  1505
        else 0
blanchet@42547
  1506
      end
blanchet@42544
  1507
    | NONE => 0
blanchet@38282
  1508
blanchet@38282
  1509
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
  1510
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
  1511
   type instantiations). If false, the constant always receives all of its
blanchet@38282
  1512
   arguments and is used as a predicate. *)
blanchet@42558
  1513
fun is_pred_sym sym_tab s =
blanchet@42558
  1514
  case Symtab.lookup sym_tab s of
blanchet@42574
  1515
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
  1516
    pred_sym andalso min_ary = max_ary
blanchet@42558
  1517
  | NONE => false
blanchet@38282
  1518
blanchet@44773
  1519
val app_op = `(make_fixed_const NONE) app_op_name
blanchet@42568
  1520
val predicator_combconst =
nik@44495
  1521
  IConst (`(make_fixed_const NONE) predicator_name, @{typ "bool => bool"}, [])
blanchet@42542
  1522
blanchet@43859
  1523
fun list_app head args = fold (curry (IApp o swap)) args head
blanchet@44773
  1524
fun predicator tm = IApp (predicator_combconst, tm)
blanchet@42544
  1525
blanchet@46392
  1526
fun do_app_op format type_enc head arg =
blanchet@42544
  1527
  let
blanchet@46392
  1528
    val head_T = ityp_of head
blanchet@46392
  1529
    val (arg_T, res_T) = dest_funT head_T
blanchet@46392
  1530
    val app =
blanchet@46392
  1531
      IConst (app_op, head_T --> head_T, [arg_T, res_T])
blanchet@46392
  1532
      |> mangle_type_args_in_iterm format type_enc
blanchet@46392
  1533
  in list_app app [head, arg] end
blanchet@46392
  1534
blanchet@46400
  1535
fun firstorderize_fact thy monom_constrs format type_enc sym_tab
blanchet@46409
  1536
                       uncurried_aliases =
blanchet@46392
  1537
  let
blanchet@46392
  1538
    fun do_app arg head = do_app_op format type_enc head arg
blanchet@44773
  1539
    fun list_app_ops head args = fold do_app args head
blanchet@44773
  1540
    fun introduce_app_ops tm =
blanchet@46392
  1541
      let val (head, args) = tm |> strip_iterm_comb ||> map introduce_app_ops in
blanchet@46392
  1542
        case head of
blanchet@46392
  1543
          IConst (name as (s, _), T, T_args) =>
blanchet@46409
  1544
          if uncurried_aliases andalso String.isPrefix const_prefix s then
blanchet@46392
  1545
            let
blanchet@46392
  1546
              val ary = length args
blanchet@46409
  1547
              val name = name |> ary > min_ary_of sym_tab s
blanchet@46409
  1548
                                 ? aliased_uncurried ary
blanchet@46392
  1549
            in list_app (IConst (name, T, T_args)) args end
blanchet@46392
  1550
          else
blanchet@46392
  1551
            args |> chop (min_ary_of sym_tab s)
blanchet@46392
  1552
                 |>> list_app head |-> list_app_ops
blanchet@46392
  1553
        | _ => list_app_ops head args
blanchet@46392
  1554
      end
blanchet@44773
  1555
    fun introduce_predicators tm =
blanchet@44773
  1556
      case strip_iterm_comb tm of
blanchet@44773
  1557
        (IConst ((s, _), _, _), _) =>
blanchet@44773
  1558
        if is_pred_sym sym_tab s then tm else predicator tm
blanchet@44773
  1559
      | _ => predicator tm
blanchet@44773
  1560
    val do_iterm =
blanchet@44773
  1561
      not (is_type_enc_higher_order type_enc)
blanchet@44773
  1562
      ? (introduce_app_ops #> introduce_predicators)
blanchet@45945
  1563
      #> filter_type_args_in_iterm thy monom_constrs type_enc
blanchet@44773
  1564
  in update_iformula (formula_map do_iterm) end
blanchet@42573
  1565
blanchet@42573
  1566
(** Helper facts **)
blanchet@42573
  1567
blanchet@44450
  1568
val not_ffalse = @{lemma "~ fFalse" by (unfold fFalse_def) fast}
blanchet@44450
  1569
val ftrue = @{lemma "fTrue" by (unfold fTrue_def) fast}
blanchet@44450
  1570
blanchet@43194
  1571
(* The Boolean indicates that a fairly sound type encoding is needed. *)
blanchet@43085
  1572
val helper_table =
blanchet@43194
  1573
  [(("COMBI", false), @{thms Meson.COMBI_def}),
blanchet@43194
  1574
   (("COMBK", false), @{thms Meson.COMBK_def}),
blanchet@43194
  1575
   (("COMBB", false), @{thms Meson.COMBB_def}),
blanchet@43194
  1576
   (("COMBC", false), @{thms Meson.COMBC_def}),
blanchet@43194
  1577
   (("COMBS", false), @{thms Meson.COMBS_def}),
blanchet@44450
  1578
   ((predicator_name, false), [not_ffalse, ftrue]),
blanchet@44450
  1579
   (("fFalse", false), [not_ffalse]),
blanchet@43194
  1580
   (("fFalse", true), @{thms True_or_False}),
blanchet@44450
  1581
   (("fTrue", false), [ftrue]),
blanchet@43194
  1582
   (("fTrue", true), @{thms True_or_False}),
blanchet@43194
  1583
   (("fNot", false),
blanchet@43194
  1584
    @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
blanchet@43194
  1585
           fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
blanchet@43194
  1586
   (("fconj", false),
blanchet@43194
  1587
    @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
blanchet@43194
  1588
        by (unfold fconj_def) fast+}),
blanchet@43194
  1589
   (("fdisj", false),
blanchet@43194
  1590
    @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
blanchet@43194
  1591
        by (unfold fdisj_def) fast+}),
blanchet@43194
  1592
   (("fimplies", false),
blanchet@43210
  1593
    @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
blanchet@43194
  1594
        by (unfold fimplies_def) fast+}),
nik@43678
  1595
   (("fequal", true),
nik@43678
  1596
    (* This is a lie: Higher-order equality doesn't need a sound type encoding.
nik@43678
  1597
       However, this is done so for backward compatibility: Including the
nik@43678
  1598
       equality helpers by default in Metis breaks a few existing proofs. *)
nik@43678
  1599
    @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
nik@43678
  1600
           fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
blanchet@44003
  1601
   (* Partial characterization of "fAll" and "fEx". A complete characterization
blanchet@44003
  1602
      would require the axiom of choice for replay with Metis. *)
blanchet@44003
  1603
   (("fAll", false), [@{lemma "~ fAll P | P x" by (auto simp: fAll_def)}]),
blanchet@44003
  1604
   (("fEx", false), [@{lemma "~ P x | fEx P" by (auto simp: fEx_def)}]),
blanchet@43194
  1605
   (("If", true), @{thms if_True if_False True_or_False})]
blanchet@43194
  1606
  |> map (apsnd (map zero_var_indexes))
blanchet@43085
  1607
blanchet@45364
  1608
fun atype_of_type_vars (Simple_Types (_, Polymorphic, _)) = SOME atype_of_types
blanchet@45364
  1609
  | atype_of_type_vars _ = NONE
blanchet@45364
  1610
blanchet@45920
  1611
fun bound_tvars type_enc sorts Ts =
blanchet@45920
  1612
  (sorts ? mk_ahorn (formulas_for_types type_enc add_sorts_on_tvar Ts))
blanchet@45316
  1613
  #> mk_aquant AForall
blanchet@45316
  1614
        (map_filter (fn TVar (x as (s, _), _) =>
blanchet@45316
  1615
                        SOME ((make_schematic_type_var x, s),
blanchet@45364
  1616
                              atype_of_type_vars type_enc)
blanchet@45316
  1617
                      | _ => NONE) Ts)
blanchet@44404
  1618
blanchet@46392
  1619
fun eq_formula type_enc atomic_Ts bounds pred_sym tm1 tm2 =
blanchet@44404
  1620
  (if pred_sym then AConn (AIff, [AAtom tm1, AAtom tm2])
blanchet@44404
  1621
   else AAtom (ATerm (`I tptp_equal, [tm1, tm2])))
blanchet@46392
  1622
  |> mk_aquant AForall bounds
blanchet@45377
  1623
  |> close_formula_universally
blanchet@45920
  1624
  |> bound_tvars type_enc true atomic_Ts
blanchet@44404
  1625
blanchet@46406
  1626
val helper_rank = default_rank
blanchet@46406
  1627
val min_rank = 9 * helper_rank div 10
blanchet@46406
  1628
val max_rank = 4 * min_rank
blanchet@46406
  1629
blanchet@46406
  1630
fun rank_of_fact_num n j = min_rank + (max_rank - min_rank) * j div n
blanchet@46406
  1631
nik@44495
  1632
val type_tag = `(make_fixed_const NONE) type_tag_name
blanchet@43130
  1633
blanchet@45301
  1634
fun type_tag_idempotence_fact format type_enc =
blanchet@42573
  1635
  let
blanchet@42573
  1636
    fun var s = ATerm (`I s, [])
blanchet@44408
  1637
    fun tag tm = ATerm (type_tag, [var "A", tm])
blanchet@44408
  1638
    val tagged_var = tag (var "X")
blanchet@42573
  1639
  in
blanchet@43159
  1640
    Formula (type_tag_idempotence_helper_name, Axiom,
blanchet@46392
  1641
             eq_formula type_enc [] [] false (tag tagged_var) tagged_var,
blanchet@46406
  1642
             NONE, isabelle_info format spec_eqN helper_rank)
blanchet@42573
  1643
  end
blanchet@42573
  1644
blanchet@43626
  1645
fun should_specialize_helper type_enc t =
blanchet@44493
  1646
  polymorphism_of_type_enc type_enc <> Polymorphic andalso
blanchet@43628
  1647
  level_of_type_enc type_enc <> No_Types andalso
blanchet@43628
  1648
  not (null (Term.hidden_polymorphism t))
blanchet@43159
  1649
blanchet@43858
  1650
fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
blanchet@45511
  1651
  case unprefix_and_unascii const_prefix s of
blanchet@42573
  1652
    SOME mangled_s =>
blanchet@42573
  1653
    let
blanchet@42573
  1654
      val thy = Proof_Context.theory_of ctxt
blanchet@46392
  1655
      val unmangled_s = mangled_s |> unmangled_const_name |> hd
blanchet@43628
  1656
      fun dub needs_fairly_sound j k =
blanchet@46339
  1657
        unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
blanchet@46339
  1658
        (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
blanchet@46339
  1659
        (if needs_fairly_sound then typed_helper_suffix
blanchet@46339
  1660
         else untyped_helper_suffix)
blanchet@43159
  1661
      fun dub_and_inst needs_fairly_sound (th, j) =
blanchet@43628
  1662
        let val t = prop_of th in
blanchet@43628
  1663
          if should_specialize_helper type_enc t then
blanchet@43628
  1664
            map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
blanchet@43628
  1665
                types
blanchet@43628
  1666
          else
blanchet@43628
  1667
            [t]
blanchet@43628
  1668
        end
blanchet@46339
  1669
        |> tag_list 1
blanchet@46393
  1670
        |> map (fn (k, t) =>
blanchet@46393
  1671
                   ((dub needs_fairly_sound j k, (Global, Spec_Eq)), t))
blanchet@43860
  1672
      val make_facts = map_filter (make_fact ctxt format type_enc false)
blanchet@43626
  1673
      val fairly_sound = is_type_enc_fairly_sound type_enc
blanchet@42573
  1674
    in
blanchet@43085
  1675
      helper_table
blanchet@43194
  1676
      |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
blanchet@43159
  1677
                  if helper_s <> unmangled_s orelse
blanchet@42894
  1678
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
  1679
                    []
blanchet@42573
  1680
                  else
blanchet@42573
  1681
                    ths ~~ (1 upto length ths)
blanchet@43628
  1682
                    |> maps (dub_and_inst needs_fairly_sound)
blanchet@43159
  1683
                    |> make_facts)
blanchet@42573
  1684
    end
blanchet@42573
  1685
  | NONE => []
blanchet@43858
  1686
fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
blanchet@43858
  1687
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
blanchet@43858
  1688
                  []
blanchet@42573
  1689
blanchet@43085
  1690
(***************************************************************)
blanchet@43085
  1691
(* Type Classes Present in the Axiom or Conjecture Clauses     *)
blanchet@43085
  1692
(***************************************************************)
blanchet@43085
  1693
blanchet@43085
  1694
fun set_insert (x, s) = Symtab.update (x, ()) s
blanchet@43085
  1695
blanchet@43085
  1696
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
blanchet@43085
  1697
blanchet@43085
  1698
(* Remove this trivial type class (FIXME: similar code elsewhere) *)
blanchet@43085
  1699
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
blanchet@43085
  1700
blanchet@43093
  1701
fun classes_of_terms get_Ts =
blanchet@43121
  1702
  map (map snd o get_Ts)
blanchet@43093
  1703
  #> List.foldl add_classes Symtab.empty
blanchet@43093
  1704
  #> delete_type #> Symtab.keys
blanchet@43085
  1705
wenzelm@44121
  1706
val tfree_classes_of_terms = classes_of_terms Misc_Legacy.term_tfrees
wenzelm@44121
  1707
val tvar_classes_of_terms = classes_of_terms Misc_Legacy.term_tvars
blanchet@43085
  1708
blanchet@43622
  1709
fun fold_type_constrs f (Type (s, Ts)) x =
blanchet@43622
  1710
    fold (fold_type_constrs f) Ts (f (s, x))
blanchet@43189
  1711
  | fold_type_constrs _ _ x = x
blanchet@43085
  1712
blanchet@43907
  1713
(* Type constructors used to instantiate overloaded constants are the only ones
blanchet@43907
  1714
   needed. *)
blanchet@43189
  1715
fun add_type_constrs_in_term thy =
blanchet@43085
  1716
  let
blanchet@43188
  1717
    fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
blanchet@43181
  1718
      | add (t $ u) = add t #> add u
blanchet@44738
  1719
      | add (Const x) =
blanchet@44738
  1720
        x |> robust_const_typargs thy |> fold (fold_type_constrs set_insert)
blanchet@43181
  1721
      | add (Abs (_, _, u)) = add u
blanchet@43181
  1722
      | add _ = I
blanchet@43181
  1723
  in add end
blanchet@43085
  1724
blanchet@43189
  1725
fun type_constrs_of_terms thy ts =
blanchet@43189
  1726
  Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
blanchet@43085
  1727
blanchet@45511
  1728
fun extract_lambda_def (Const (@{const_name HOL.eq}, _) $ t $ u) =
blanchet@45511
  1729
    let val (head, args) = strip_comb t in
blanchet@45511
  1730
      (head |> dest_Const |> fst,
blanchet@45511
  1731
       fold_rev (fn t as Var ((s, _), T) =>
blanchet@45511
  1732
                    (fn u => Abs (s, T, abstract_over (t, u)))
blanchet@45511
  1733
                  | _ => raise Fail "expected Var") args u)
blanchet@45511
  1734
    end
blanchet@45511
  1735
  | extract_lambda_def _ = raise Fail "malformed lifted lambda"
blanchet@45508
  1736
blanchet@45514
  1737
fun trans_lams_from_string ctxt type_enc lam_trans =
blanchet@45514
  1738
  if lam_trans = no_lamsN then
blanchet@45514
  1739
    rpair []
blanchet@45514
  1740
  else if lam_trans = hide_lamsN then
blanchet@45514
  1741
    lift_lams ctxt type_enc ##> K []
blanchet@46365
  1742
  else if lam_trans = liftingN orelse lam_trans = lam_liftingN then
blanchet@45514
  1743
    lift_lams ctxt type_enc
blanchet@46365
  1744
  else if lam_trans = combsN then
blanchet@45514
  1745
    map (introduce_combinators ctxt) #> rpair []
blanchet@46365
  1746
  else if lam_trans = combs_and_liftingN then
blanchet@46365
  1747
    lift_lams_part_1 ctxt type_enc
blanchet@46365
  1748
    ##> maps (fn t => [t, introduce_combinators ctxt (intentionalize_def t)])
blanchet@46365
  1749
    #> lift_lams_part_2
blanchet@46368
  1750
  else if lam_trans = combs_or_liftingN then
blanchet@45554
  1751
    lift_lams_part_1 ctxt type_enc
blanchet@46368
  1752
    ##> map (fn t => case head_of (strip_qnt_body @{const_name All} t) of
blanchet@46368
  1753
                       @{term "op =::bool => bool => bool"} => t
blanchet@46368
  1754
                     | _ => introduce_combinators ctxt (intentionalize_def t))
blanchet@45554
  1755
    #> lift_lams_part_2
blanchet@45514
  1756
  else if lam_trans = keep_lamsN then
blanchet@45514
  1757
    map (Envir.eta_contract) #> rpair []
blanchet@45514
  1758
  else
blanchet@45519
  1759
    error ("Unknown lambda translation scheme: " ^ quote lam_trans ^ ".")
blanchet@45514
  1760
blanchet@45514
  1761
fun translate_formulas ctxt format prem_kind type_enc lam_trans presimp hyp_ts
blanchet@45514
  1762
                       concl_t facts =
blanchet@42573
  1763
  let
blanchet@42573
  1764
    val thy = Proof_Context.theory_of ctxt
blanchet@45514
  1765
    val trans_lams = trans_lams_from_string ctxt type_enc lam_trans
blanchet@43861
  1766
    val fact_ts = facts |> map snd
blanchet@42573
  1767
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
  1768
       boost an ATP's performance (for some reason). *)
blanchet@43192
  1769
    val hyp_ts =
blanchet@43192
  1770
      hyp_ts
blanchet@43192
  1771
      |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
blanchet@43864
  1772
    val facts = facts |> map (apsnd (pair Axiom))
blanchet@43864
  1773
    val conjs =
blanchet@46385
  1774
      map (pair prem_kind) hyp_ts @ [(Conjecture, s_not_trueprop concl_t)]
blanchet@45168
  1775
      |> map (apsnd freeze_term)
blanchet@46340
  1776
      |> map2 (pair o rpair (Local, General) o string_of_int)
blanchet@46340
  1777
              (0 upto length hyp_ts)
blanchet@45554
  1778
    val ((conjs, facts), lam_facts) =
blanchet@45511
  1779
      (conjs, facts)
blanchet@46093
  1780
      |> presimp ? pairself (map (apsnd (uncurry (presimp_prop ctxt))))
blanchet@45514
  1781
      |> (if lam_trans = no_lamsN then
blanchet@45511
  1782
            rpair []
blanchet@45511
  1783
          else
blanchet@45511
  1784
            op @
blanchet@45514
  1785
            #> preprocess_abstractions_in_terms trans_lams
blanchet@45511
  1786
            #>> chop (length conjs))
blanchet@44773
  1787
    val conjs = conjs |> make_conjecture ctxt format type_enc
blanchet@43863
  1788
    val (fact_names, facts) =
blanchet@43864
  1789
      facts
blanchet@43863
  1790
      |> map_filter (fn (name, (_, t)) =>
blanchet@43863
  1791
                        make_fact ctxt format type_enc true (name, t)
blanchet@43863
  1792
                        |> Option.map (pair name))
blanchet@43861
  1793
      |> ListPair.unzip
blanchet@46375
  1794
    val lifted = lam_facts |> map (extract_lambda_def o snd o snd)
blanchet@45554
  1795
    val lam_facts =
blanchet@45554
  1796
      lam_facts |> map_filter (make_fact ctxt format type_enc true o apsnd snd)
blanchet@43861
  1797
    val all_ts = concl_t :: hyp_ts @ fact_ts
blanchet@42573
  1798
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
  1799
    val supers = tvar_classes_of_terms all_ts
blanchet@43189
  1800
    val tycons = type_constrs_of_terms thy all_ts
blanchet@43861
  1801
    val (supers, arity_clauses) =
blanchet@43626
  1802
      if level_of_type_enc type_enc = No_Types then ([], [])
blanchet@42573
  1803
      else make_arity_clauses thy tycons supers
blanchet@43861
  1804
    val class_rel_clauses = make_class_rel_clauses thy subs supers
blanchet@42573
  1805
  in
blanchet@45508
  1806
    (fact_names |> map single, union (op =) subs supers, conjs,
blanchet@45554
  1807
     facts @ lam_facts, class_rel_clauses, arity_clauses, lifted)
blanchet@42573
  1808
  end
blanchet@42573
  1809
nik@44495
  1810
val type_guard = `(make_fixed_const NONE) type_guard_name
blanchet@43130
  1811
blanchet@44774
  1812
fun type_guard_iterm format type_enc T tm =
blanchet@44396
  1813
  IApp (IConst (type_guard, T --> @{typ bool}, [T])
blanchet@44774
  1814
        |> mangle_type_args_in_iterm format type_enc, tm)
blanchet@42573
  1815
blanchet@43421
  1816
fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@43421
  1817
  | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@43000
  1818
    accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
blanchet@43692
  1819
  | is_var_positively_naked_in_term _ _ _ _ = true
blanchet@44403
  1820
blanchet@45948
  1821
fun is_var_ghost_type_arg_in_term thy polym_constrs name pos tm accum =
blanchet@44811
  1822
  is_var_positively_naked_in_term name pos tm accum orelse
blanchet@44811
  1823
  let
blanchet@44811
  1824
    val var = ATerm (name, [])
blanchet@44811
  1825
    fun is_nasty_in_term (ATerm (_, [])) = false
blanchet@44811
  1826
      | is_nasty_in_term (ATerm ((s, _), tms)) =
blanchet@45948
  1827
        let
blanchet@45948
  1828
          val ary = length tms
blanchet@45948
  1829
          val polym_constr = member (op =) polym_constrs s
blanchet@45948
  1830
          val ghosts = ghost_type_args thy s ary
blanchet@45948
  1831
        in
blanchet@45948
  1832
          exists (fn (j, tm) =>
blanchet@45948
  1833
                     if polym_constr then
blanchet@45948
  1834
                       member (op =) ghosts j andalso
blanchet@45948
  1835
                       (tm = var orelse is_nasty_in_term tm)
blanchet@45948
  1836
                     else
blanchet@45948
  1837
                       tm = var andalso member (op =) ghosts j)
blanchet@45948
  1838
                 (0 upto ary - 1 ~~ tms)
blanchet@45948
  1839
          orelse (not polym_constr andalso exists is_nasty_in_term tms)
blanchet@45948
  1840
        end
blanchet@44811
  1841
      | is_nasty_in_term _ = true
blanchet@44811
  1842
  in is_nasty_in_term tm end
blanchet@44811
  1843
blanchet@45948
  1844
fun should_guard_var_in_formula thy polym_constrs level pos phi (SOME true)
blanchet@45948
  1845
                                name =
blanchet@44811
  1846
    (case granularity_of_type_level level of
blanchet@44811
  1847
       All_Vars => true
blanchet@44811
  1848
     | Positively_Naked_Vars =>
blanchet@44811
  1849
       formula_fold pos (is_var_positively_naked_in_term name) phi false
blanchet@44811
  1850
     | Ghost_Type_Arg_Vars =>
blanchet@45948
  1851
       formula_fold pos (is_var_ghost_type_arg_in_term thy polym_constrs name)
blanchet@45948
  1852
                    phi false)
blanchet@45948
  1853
  | should_guard_var_in_formula _ _ _ _ _ _ _ = true
blanchet@45948
  1854
blanchet@45948
  1855
fun always_guard_var_in_formula _ _ _ _ _ _ _ = true
blanchet@42834
  1856
blanchet@44405
  1857
fun should_generate_tag_bound_decl _ _ _ (SOME true) _ = false
blanchet@44768
  1858
  | should_generate_tag_bound_decl ctxt mono (Tags (_, level)) _ T =
blanchet@44811
  1859
    granularity_of_type_level level <> All_Vars andalso
blanchet@44782
  1860
    should_encode_type ctxt mono level T
blanchet@44405
  1861
  | should_generate_tag_bound_decl _ _ _ _ _ = false
blanchet@44404
  1862
nik@43677
  1863
fun mk_aterm format type_enc name T_args args =
nik@43677
  1864
  ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
blanchet@42994
  1865
blanchet@46392
  1866
fun do_bound_type ctxt format mono type_enc =
blanchet@46392
  1867
  case type_enc of
blanchet@46392
  1868
    Simple_Types (_, _, level) =>
blanchet@46392
  1869
    fused_type ctxt mono level 0
blanchet@46392
  1870
    #> ho_type_from_typ format type_enc false 0 #> SOME
blanchet@46392
  1871
  | _ => K NONE
blanchet@46392
  1872
blanchet@45949
  1873
fun tag_with_type ctxt format mono type_enc pos T tm =
blanchet@43859
  1874
  IConst (type_tag, T --> T, [T])
blanchet@44774
  1875
  |> mangle_type_args_in_iterm format type_enc
blanchet@45949
  1876
  |> ho_term_from_iterm ctxt format mono type_enc pos
blanchet@43692
  1877
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
blanchet@43692
  1878
       | _ => raise Fail "unexpected lambda-abstraction")
blanchet@45949
  1879
and ho_term_from_iterm ctxt format mono type_enc =
blanchet@42573
  1880
  let
blanchet@45949
  1881
    fun term site u =
blanchet@42962
  1882
      let
blanchet@43859
  1883
        val (head, args) = strip_iterm_comb u
nik@43677
  1884
        val pos =
blanchet@45949
  1885
          case site of
nik@43677
  1886
            Top_Level pos => pos
nik@43677
  1887
          | Eq_Arg pos => pos
blanchet@44814
  1888
          | _ => NONE
nik@43677
  1889
        val t =
nik@43677
  1890
          case head of
blanchet@43859
  1891
            IConst (name as (s, _), _, T_args) =>
nik@43677
  1892
            let
blanchet@45949
  1893
              val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
nik@43677
  1894
            in
blanchet@45949
  1895
              map (term arg_site) args |> mk_aterm format type_enc name T_args
nik@43677
  1896
            end
blanchet@43859
  1897
          | IVar (name, _) =>
blanchet@45949
  1898
            map (term Elsewhere) args |> mk_aterm format type_enc name []
blanchet@43859
  1899
          | IAbs ((name, T), tm) =>
blanchet@43859
  1900
            AAbs ((name, ho_type_from_typ format type_enc true 0 T),
blanchet@45949
  1901
                  term Elsewhere tm)
blanchet@43859
  1902
          | IApp _ => raise Fail "impossible \"IApp\""
blanchet@43859
  1903
        val T = ityp_of u
blanchet@42962
  1904
      in
blanchet@45949
  1905
        if should_tag_with_type ctxt mono type_enc site u T then
blanchet@45949
  1906
          tag_with_type ctxt format mono type_enc pos T t
blanchet@45947
  1907
        else
blanchet@45947
  1908
          t
blanchet@42962
  1909
      end
blanchet@45949
  1910
  in term o Top_Level end
blanchet@45947
  1911
and formula_from_iformula ctxt polym_constrs format mono type_enc
blanchet@45947
  1912
                          should_guard_var =
blanchet@42829
  1913
  let
blanchet@44811
  1914
    val thy = Proof_Context.theory_of ctxt
blanchet@44811
  1915
    val level = level_of_type_enc type_enc
blanchet@45949
  1916
    val do_term = ho_term_from_iterm ctxt format mono type_enc
blanchet@42878
  1917
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@44399
  1918
      if should_guard_type ctxt mono type_enc
blanchet@45948
  1919
             (fn () => should_guard_var thy polym_constrs level pos phi
blanchet@45948
  1920
                                        universal name) T then
blanchet@43859
  1921
        IVar (name, T)
blanchet@44774
  1922
        |> type_guard_iterm format type_enc T
blanchet@43361
  1923
        |> do_term pos |> AAtom |> SOME
blanchet@44405
  1924
      else if should_generate_tag_bound_decl ctxt mono type_enc universal T then
blanchet@44405
  1925
        let
blanchet@44405
  1926
          val var = ATerm (name, [])
blanchet@45949
  1927
          val tagged_var = tag_with_type ctxt format mono type_enc pos T var
blanchet@44405
  1928
        in SOME (AAtom (ATerm (`I tptp_equal, [tagged_var, var]))) end
blanchet@42573
  1929
      else
blanchet@42573
  1930
        NONE
blanchet@42878
  1931
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
  1932
        let
blanchet@42878
  1933
          val phi = phi |> do_formula pos
blanchet@42878
  1934
          val universal = Option.map (q = AExists ? not) pos
blanchet@46392
  1935
          val do_bound_type = do_bound_type ctxt format mono type_enc
blanchet@42878
  1936
        in
blanchet@42834
  1937
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
  1938
                                        | SOME T => do_bound_type T)),
blanchet@42834
  1939
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
  1940
                      (map_filter
blanchet@42834
  1941
                           (fn (_, NONE) => NONE
blanchet@42834
  1942
                             | (s, SOME T) =>
blanchet@42878
  1943
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
  1944
                           xs)
blanchet@42834
  1945
                      phi)
blanchet@42834
  1946
        end
blanchet@42878
  1947
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@43361
  1948
      | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
blanchet@43493
  1949
  in do_formula end
blanchet@42573
  1950
blanchet@42573
  1951
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
  1952
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
  1953
   the remote provers might care. *)
blanchet@45947
  1954
fun formula_line_for_fact ctxt polym_constrs format prefix encode freshen pos
blanchet@46406
  1955
        mono type_enc rank (j, {name, stature, kind, iformula, atomic_types}) =
blanchet@43864
  1956
  (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name, kind,
blanchet@43859
  1957
   iformula
blanchet@45947
  1958
   |> formula_from_iformula ctxt polym_constrs format mono type_enc
blanchet@45947
  1959
          should_guard_var_in_formula (if pos then SOME true else NONE)
blanchet@45377
  1960
   |> close_formula_universally
blanchet@45920
  1961
   |> bound_tvars type_enc true atomic_types,
blanchet@43493
  1962
   NONE,
blanchet@46406
  1963
   let val rank = rank j in
blanchet@46406
  1964
     case snd stature of
blanchet@46406
  1965
       Intro => isabelle_info format introN rank
blanchet@46406
  1966
     | Elim => isabelle_info format elimN rank
blanchet@46406
  1967
     | Simp => isabelle_info format simpN rank
blanchet@46406
  1968
     | Spec_Eq => isabelle_info format spec_eqN rank
blanchet@46406
  1969
     | _ => isabelle_info format "" rank
blanchet@46406
  1970
   end)
blanchet@43493
  1971
  |> Formula
blanchet@42573
  1972
blanchet@45301
  1973
fun formula_line_for_class_rel_clause format type_enc
blanchet@44593
  1974
        ({name, subclass, superclass, ...} : class_rel_clause) =
blanchet@44622
  1975
  let val ty_arg = ATerm (tvar_a_name, []) in
blanchet@42577
  1976
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@44622
  1977
             AConn (AImplies,
blanchet@44625
  1978
                    [type_class_formula type_enc subclass ty_arg,
blanchet@44625
  1979
                     type_class_formula type_enc superclass ty_arg])
blanchet@45830
  1980
             |> mk_aquant AForall
blanchet@45830
  1981
                          [(tvar_a_name, atype_of_type_vars type_enc)],
blanchet@46406
  1982
             NONE, isabelle_info format introN helper_rank)
blanchet@42573
  1983
  end
blanchet@42573
  1984
blanchet@44625
  1985
fun formula_from_arity_atom type_enc (class, t, args) =
blanchet@44625
  1986
  ATerm (t, map (fn arg => ATerm (arg, [])) args)
blanchet@44625
  1987
  |> type_class_formula type_enc class
blanchet@42573
  1988
blanchet@45301
  1989
fun formula_line_for_arity_clause format type_enc
blanchet@45364
  1990
        ({name, prem_atoms, concl_atom} : arity_clause) =
blanchet@43495
  1991
  Formula (arity_clause_prefix ^ name, Axiom,
blanchet@44625
  1992
           mk_ahorn (map (formula_from_arity_atom type_enc) prem_atoms)
blanchet@44625
  1993
                    (formula_from_arity_atom type_enc concl_atom)
blanchet@45364
  1994
           |> mk_aquant AForall
blanchet@45364
  1995
                  (map (rpair (atype_of_type_vars type_enc)) (#3 concl_atom)),
blanchet@46406
  1996
           NONE, isabelle_info format introN helper_rank)
blanchet@42573
  1997
blanchet@45947
  1998
fun formula_line_for_conjecture ctxt polym_constrs format mono type_enc
blanchet@43859
  1999
        ({name, kind, iformula, atomic_types, ...} : translated_formula) =
blanchet@42577
  2000
  Formula (conjecture_prefix ^ name, kind,
blanchet@45316
  2001
           iformula
blanchet@45947
  2002
           |> formula_from_iformula ctxt polym_constrs format mono type_enc
blanchet@45316
  2003
                  should_guard_var_in_formula (SOME false)
blanchet@45377
  2004
           |> close_formula_universally
blanchet@46406
  2005
           |> bound_tvars type_enc true atomic_types, NONE, [])
blanchet@42573
  2006
blanchet@44625
  2007
fun formula_line_for_free_type j phi =
blanchet@46406
  2008
  Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis, phi, NONE, [])
blanchet@44626
  2009
fun formula_lines_for_free_types type_enc (facts : translated_formula list) =
blanchet@42573
  2010
  let
blanchet@44625
  2011
    val phis =
blanchet@44625
  2012
      fold (union (op =)) (map #atomic_types facts) []
blanchet@44625
  2013
      |> formulas_for_types type_enc add_sorts_on_tfree
blanchet@44625
  2014
  in map2 formula_line_for_free_type (0 upto length phis - 1) phis end
blanchet@42573
  2015
blanchet@42573
  2016
(** Symbol declarations **)
blanchet@42544
  2017
blanchet@44754
  2018
fun decl_line_for_class order s =
blanchet@44595
  2019
  let val name as (s, _) = `make_type_class s in
blanchet@44622
  2020
    Decl (sym_decl_prefix ^ s, name,
blanchet@45779
  2021
          if order = First_Order then
blanchet@45779
  2022
            ATyAbs ([tvar_a_name],
blanchet@45779
  2023
                    if avoid_first_order_ghost_type_vars then
blanchet@45779
  2024
                      AFun (a_itself_atype, bool_atype)
blanchet@45779
  2025
                    else
blanchet@45779
  2026
                      bool_atype)
blanchet@44622
  2027
          else
blanchet@44754
  2028
            AFun (atype_of_types, bool_atype))
blanchet@44595
  2029
  end
blanchet@44595
  2030
blanchet@44595
  2031
fun decl_lines_for_classes type_enc classes =
blanchet@44595
  2032
  case type_enc of
blanchet@44754
  2033
    Simple_Types (order, Polymorphic, _) =>
blanchet@44754
  2034
    map (decl_line_for_class order) classes
blanchet@44595
  2035
  | _ => []
blanchet@44595
  2036
blanchet@46392
  2037
fun sym_decl_table_for_facts ctxt format type_enc sym_tab
blanchet@46392
  2038
                             (conjs, facts, extra_tms) =
blanchet@42574
  2039
  let
blanchet@44829
  2040
    fun add_iterm_syms tm =
blanchet@43859
  2041
      let val (head, args) = strip_iterm_comb tm in
blanchet@42574
  2042
        (case head of
blanchet@43859
  2043
           IConst ((s, s'), T, T_args) =>
blanchet@44594
  2044
           let
blanchet@44829
  2045
             val (pred_sym, in_conj) =
blanchet@44829
  2046
               case Symtab.lookup sym_tab s of
blanchet@44853
  2047
                 SOME ({pred_sym, in_conj, ...} : sym_info) =>
blanchet@44853
  2048
                 (pred_sym, in_conj)
blanchet@44829
  2049
               | NONE => (false, false)
blanchet@44594
  2050
             val decl_sym =
blanchet@44594
  2051
               (case type_enc of
blanchet@44594
  2052
                  Guards _ => not pred_sym
blanchet@44594
  2053
                | _ => true) andalso
blanchet@44594
  2054
               is_tptp_user_symbol s
blanchet@44594
  2055
           in
blanchet@44594
  2056
             if decl_sym then
blanchet@42576
  2057
               Symtab.map_default (s, [])
blanchet@42886
  2058
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  2059
                                         in_conj))
blanchet@42574
  2060
             else
blanchet@42574
  2061
               I
blanchet@42574
  2062
           end
blanchet@44829
  2063
         | IAbs (_, tm) => add_iterm_syms tm
blanchet@42574
  2064
         | _ => I)
blanchet@44829
  2065
        #> fold add_iterm_syms args
blanchet@42574
  2066
      end
blanchet@44829
  2067
    val add_fact_syms = K add_iterm_syms |> formula_fold NONE |> fact_lift
blanchet@43966
  2068
    fun add_formula_var_types (AQuant (_, xs, phi)) =
blanchet@43966
  2069
        fold (fn (_, SOME T) => insert_type ctxt I T | _ => I) xs
blanchet@43966
  2070
        #> add_formula_var_types phi
blanchet@43966
  2071
      | add_formula_var_types (AConn (_, phis)) =
blanchet@43966
  2072
        fold add_formula_var_types phis
blanchet@43966
  2073
      | add_formula_var_types _ = I
blanchet@43966
  2074
    fun var_types () =
blanchet@43966
  2075
      if polymorphism_of_type_enc type_enc = Polymorphic then [tvar_a]
blanchet@43966
  2076
      else fold (fact_lift add_formula_var_types) (conjs @ facts) []
blanchet@43966
  2077
    fun add_undefined_const T =
blanchet@43984
  2078
      let
blanchet@43984
  2079
        val (s, s') =
blanchet@44622
  2080
          `(make_fixed_const NONE) @{const_name undefined}
blanchet@45945
  2081
          |> (case type_arg_policy [] type_enc @{const_name undefined} of
blanchet@44771
  2082
                Mangled_Type_Args => mangled_const_name format type_enc [T]
blanchet@44001
  2083
              | _ => I)
blanchet@43984
  2084
      in
blanchet@43984
  2085
        Symtab.map_default (s, [])
blanchet@43984
  2086
                           (insert_type ctxt #3 (s', [T], T, false, 0, false))
blanchet@43984
  2087
      end
blanchet@44622
  2088
    fun add_TYPE_const () =
blanchet@44622
  2089
      let val (s, s') = TYPE_name in
blanchet@44622
  2090
        Symtab.map_default (s, [])
blanchet@44622
  2091
            (insert_type ctxt #3
blanchet@44622
  2092
                         (s', [tvar_a], @{typ "'a itself"}, false, 0, false))
blanchet@44622
  2093
      end
blanchet@42698
  2094
  in
blanchet@42698
  2095
    Symtab.empty
blanchet@43626
  2096
    |> is_type_enc_fairly_sound type_enc
blanchet@44829
  2097
       ? (fold (fold add_fact_syms) [conjs, facts]
blanchet@46392
  2098
          #> fold add_iterm_syms extra_tms
blanchet@43985
  2099
          #> (case type_enc of
blanchet@45829
  2100
                Simple_Types (First_Order, Polymorphic, _) =>
blanchet@45829
  2101
                if avoid_first_order_ghost_type_vars then add_TYPE_const ()
blanchet@45829
  2102
                else I
blanchet@44786
  2103
              | Simple_Types _ => I
blanchet@43985
  2104
              | _ => fold add_undefined_const (var_types ())))
blanchet@42698
  2105
  end
blanchet@42533
  2106
blanchet@44399
  2107
(* We add "bool" in case the helper "True_or_False" is included later. *)
blanchet@44634
  2108
fun default_mono level =
blanchet@44399
  2109
  {maybe_finite_Ts = [@{typ bool}],
blanchet@44399
  2110
   surely_finite_Ts = [@{typ bool}],
blanchet@44399
  2111
   maybe_infinite_Ts = known_infinite_types,
blanchet@44634
  2112
   surely_infinite_Ts =
blanchet@44634
  2113
     case level of
blanchet@46301
  2114
       Noninf_Nonmono_Types (Strict, _) => []
blanchet@44634
  2115
     | _ => known_infinite_types,
blanchet@44399
  2116
   maybe_nonmono_Ts = [@{typ bool}]}
blanchet@44399
  2117
blanchet@42685
  2118
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  2119
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@44399
  2120
fun add_iterm_mononotonicity_info _ _ (SOME false) _ mono = mono
blanchet@44399
  2121
  | add_iterm_mononotonicity_info ctxt level _
blanchet@44399
  2122
        (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2))
blanchet@44399
  2123
        (mono as {maybe_finite_Ts, surely_finite_Ts, maybe_infinite_Ts,
blanchet@44399
  2124
                  surely_infinite_Ts, maybe_nonmono_Ts}) =
blanchet@44403
  2125
    if is_tptp_equal s andalso exists is_maybe_universal_var [tm1, tm2] then
blanchet@44399
  2126
      case level of
blanchet@46301
  2127
        Noninf_Nonmono_Types (strictness, _) =>
blanchet@44399
  2128
        if exists (type_instance ctxt T) surely_infinite_Ts orelse
blanchet@44859
  2129
           member (type_equiv ctxt) maybe_finite_Ts T then
blanchet@44399
  2130
          mono
blanchet@46301
  2131
        else if is_type_kind_of_surely_infinite ctxt strictness
blanchet@44500
  2132
                                                surely_infinite_Ts T then
blanchet@44399
  2133
          {maybe_finite_Ts = maybe_finite_Ts,
blanchet@44399
  2134
           surely_finite_Ts = surely_finite_Ts,
blanchet@44399
  2135
           maybe_infinite_Ts = maybe_infinite_Ts,
blanchet@44399
  2136
           surely_infinite_Ts = surely_infinite_Ts |> insert_type ctxt I T,
blanchet@44399
  2137
           maybe_nonmono_Ts = maybe_nonmono_Ts}
blanchet@44399
  2138
        else
blanchet@44859
  2139
          {maybe_finite_Ts = maybe_finite_Ts |> insert (type_equiv ctxt) T,
blanchet@44399
  2140
           surely_finite_Ts = surely_finite_Ts,
blanchet@44399
  2141
           maybe_infinite_Ts = maybe_infinite_Ts,
blanchet@44399
  2142
           surely_infinite_Ts = surely_infinite_Ts,
blanchet@44399
  2143
           maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
blanchet@44768
  2144
      | Fin_Nonmono_Types _ =>
blanchet@44399
  2145
        if exists (type_instance ctxt T) surely_finite_Ts orelse
blanchet@44859
  2146
           member (type_equiv ctxt) maybe_infinite_Ts T then
blanchet@44399
  2147
          mono
blanchet@44399
  2148
        else if is_type_surely_finite ctxt T then
blanchet@44399
  2149
          {maybe_finite_Ts = maybe_finite_Ts,
blanchet@44399
  2150
           surely_finite_Ts = surely_finite_Ts |> insert_type ctxt I T,
blanchet@44399
  2151
           maybe_infinite_Ts = maybe_infinite_Ts,
blanchet@44399
  2152
           surely_infinite_Ts = surely_infinite_Ts,
blanchet@44399
  2153
           maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
blanchet@44399
  2154
        else
blanchet@44399
  2155
          {maybe_finite_Ts = maybe_finite_Ts,
blanchet@44399
  2156
           surely_finite_Ts = surely_finite_Ts,
blanchet@44859
  2157
           maybe_infinite_Ts = maybe_infinite_Ts |> insert (type_equiv ctxt) T,
blanchet@44399
  2158
           surely_infinite_Ts = surely_infinite_Ts,
blanchet@44399
  2159
           maybe_nonmono_Ts = maybe_nonmono_Ts}
blanchet@44399
  2160
      | _ => mono
blanchet@44399
  2161
    else
blanchet@44399
  2162
      mono
blanchet@44399
  2163
  | add_iterm_mononotonicity_info _ _ _ _ mono = mono
blanchet@44399
  2164
fun add_fact_mononotonicity_info ctxt level
blanchet@44399
  2165
        ({kind, iformula, ...} : translated_formula) =
blanchet@42834
  2166
  formula_fold (SOME (kind <> Conjecture))
blanchet@44399
  2167
               (add_iterm_mononotonicity_info ctxt level) iformula
blanchet@44399
  2168
fun mononotonicity_info_for_facts ctxt type_enc facts =
blanchet@43626
  2169
  let val level = level_of_type_enc type_enc in
blanchet@44634
  2170
    default_mono level
blanchet@44399
  2171
    |> is_type_level_monotonicity_based level
blanchet@44399
  2172
       ? fold (add_fact_mononotonicity_info ctxt level) facts
blanchet@42829
  2173
  end
blanchet@42677
  2174
blanchet@44501
  2175
fun add_iformula_monotonic_types ctxt mono type_enc =
blanchet@44501
  2176
  let
blanchet@44501
  2177
    val level = level_of_type_enc type_enc
blanchet@44501
  2178
    val should_encode = should_encode_type ctxt mono level
blanchet@44504
  2179
    fun add_type T = not (should_encode T) ? insert_type ctxt I T
blanchet@44506
  2180
    fun add_args (IApp (tm1, tm2)) = add_args tm1 #> add_term tm2
blanchet@44506
  2181
      | add_args _ = I
blanchet@44506
  2182
    and add_term tm = add_type (ityp_of tm) #> add_args tm
blanchet@44501
  2183
  in formula_fold NONE (K add_term) end
blanchet@44501
  2184
fun add_fact_monotonic_types ctxt mono type_enc =
blanchet@44501
  2185
  add_iformula_monotonic_types ctxt mono type_enc |> fact_lift
blanchet@44501
  2186
fun monotonic_types_for_facts ctxt mono type_enc facts =
blanchet@44811
  2187
  let val level = level_of_type_enc type_enc in
blanchet@44811
  2188
    [] |> (polymorphism_of_type_enc type_enc = Polymorphic andalso
blanchet@44811
  2189
           is_type_level_monotonicity_based level andalso
blanchet@44811
  2190
           granularity_of_type_level level <> Ghost_Type_Arg_Vars)
blanchet@44811
  2191
          ? fold (add_fact_monotonic_types ctxt mono type_enc) facts
blanchet@44811
  2192
  end
blanchet@44501
  2193
blanchet@44399
  2194
fun formula_line_for_guards_mono_type ctxt format mono type_enc T =
blanchet@44396
  2195
  Formula (guards_sym_formula_prefix ^
blanchet@44396
  2196
           ascii_of (mangled_type format type_enc T),
blanchet@44396
  2197
           Axiom,
blanchet@44396
  2198
           IConst (`make_bound_var "X", T, [])
blanchet@44774
  2199
           |> type_guard_iterm format type_enc T
blanchet@44396
  2200
           |> AAtom
blanchet@45947
  2201
           |> formula_from_iformula ctxt [] format mono type_enc
blanchet@45948
  2202
                                    always_guard_var_in_formula (SOME true)
blanchet@45377
  2203
           |> close_formula_universally
blanchet@45920
  2204
           |> bound_tvars type_enc true (atomic_types_of T),
blanchet@46406
  2205
           NONE, isabelle_info format introN helper_rank)
blanchet@44396
  2206
blanchet@44399
  2207
fun formula_line_for_tags_mono_type ctxt format mono type_enc T =
blanchet@44396
  2208
  let val x_var = ATerm (`make_bound_var "X", []) in
blanchet@44396
  2209
    Formula (tags_sym_formula_prefix ^
blanchet@44396
  2210
             ascii_of (mangled_type format type_enc T),
blanchet@44396
  2211
             Axiom,
blanchet@46392
  2212
             eq_formula type_enc (atomic_types_of T) [] false
blanchet@45949
  2213
                  (tag_with_type ctxt format mono type_enc NONE T x_var) x_var,
blanchet@46406
  2214
             NONE, isabelle_info format spec_eqN helper_rank)
blanchet@44396
  2215
  end
blanchet@44396
  2216
blanchet@44399
  2217
fun problem_lines_for_mono_types ctxt format mono type_enc Ts =
blanchet@44396
  2218
  case type_enc of
blanchet@44396
  2219
    Simple_Types _ => []
blanchet@44396
  2220
  | Guards _ =>
blanchet@44399
  2221
    map (formula_line_for_guards_mono_type ctxt format mono type_enc) Ts
blanchet@44399
  2222
  | Tags _ => map (formula_line_for_tags_mono_type ctxt format mono type_enc) Ts
blanchet@44396
  2223
blanchet@44399
  2224
fun decl_line_for_sym ctxt format mono type_enc s
blanchet@42994
  2225
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  2226
  let
blanchet@44594
  2227
    val thy = Proof_Context.theory_of ctxt
blanchet@44594
  2228
    val (T, T_args) =
blanchet@44594
  2229
      if null T_args then
blanchet@44594
  2230
        (T, [])
blanchet@45511
  2231
      else case unprefix_and_unascii const_prefix s of
blanchet@44594
  2232
        SOME s' =>
blanchet@44594
  2233
        let
blanchet@44594
  2234
          val s' = s' |> invert_const
blanchet@44594
  2235
          val T = s' |> robust_const_type thy
blanchet@44594
  2236
        in (T, robust_const_typargs thy (s', T)) end
blanchet@45509
  2237
      | NONE => raise Fail "unexpected type arguments"
blanchet@42994
  2238
  in
blanchet@42998
  2239
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@44594
  2240
          T |> fused_type ctxt mono (level_of_type_enc type_enc) ary
blanchet@44594
  2241
            |> ho_type_from_typ format type_enc pred_sym ary
blanchet@44594
  2242
            |> not (null T_args)
blanchet@44594
  2243
               ? curry ATyAbs (map (tvar_name o fst o dest_TVar) T_args))
blanchet@42994
  2244
  end
blanchet@42579
  2245
blanchet@46392
  2246
fun honor_conj_sym_kind in_conj conj_sym_kind =
blanchet@46392
  2247
  if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@46392
  2248
  else (Axiom, I)
blanchet@46392
  2249
blanchet@44399
  2250
fun formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono type_enc n s
blanchet@44399
  2251
                                     j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  2252
  let
blanchet@44811
  2253
    val thy = Proof_Context.theory_of ctxt
blanchet@46392
  2254
    val (kind, maybe_negate) = honor_conj_sym_kind in_conj conj_sym_kind
blanchet@42753
  2255
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@44814
  2256
    val bound_names = 1 upto ary |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  2257
    val bounds =
blanchet@43859
  2258
      bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
blanchet@42579
  2259
    val bound_Ts =
blanchet@44811
  2260
      if exists (curry (op =) dummyT) T_args then
blanchet@44811
  2261
        case level_of_type_enc type_enc of
blanchet@44811
  2262
          All_Types => map SOME arg_Ts
blanchet@44811
  2263
        | level =>
blanchet@44811
  2264
          if granularity_of_type_level level = Ghost_Type_Arg_Vars then
blanchet@44811
  2265
            let val ghosts = ghost_type_args thy s ary in
blanchet@44811
  2266
              map2 (fn j => if member (op =) ghosts j then SOME else K NONE)
blanchet@44814
  2267
                   (0 upto ary - 1) arg_Ts
blanchet@44811
  2268
            end
blanchet@44811
  2269
          else
blanchet@44814
  2270
            replicate ary NONE
blanchet@44811
  2271
      else
blanchet@44814
  2272
        replicate ary NONE
blanchet@42579
  2273
  in
blanchet@43989
  2274
    Formula (guards_sym_formula_prefix ^ s ^
blanchet@42709
  2275
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@43859
  2276
             IConst ((s, s'), T, T_args)
blanchet@43859
  2277
             |> fold (curry (IApp o swap)) bounds
blanchet@44774
  2278
             |> type_guard_iterm format type_enc res_T
blanchet@42963
  2279
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@45947
  2280
             |> formula_from_iformula ctxt [] format mono type_enc
blanchet@45948
  2281
                                      always_guard_var_in_formula (SOME true)
blanchet@45377
  2282
             |> close_formula_universally
blanchet@45920
  2283
             |> bound_tvars type_enc (n > 1) (atomic_types_of T)
blanchet@42709
  2284
             |> maybe_negate,
blanchet@46406
  2285
             NONE, isabelle_info format introN helper_rank)
blanchet@42579
  2286
  end
blanchet@42579
  2287
blanchet@44811
  2288
fun formula_lines_for_tags_sym_decl ctxt format conj_sym_kind mono type_enc n s
blanchet@44811
  2289
        (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  2290
  let
blanchet@44814
  2291
    val thy = Proof_Context.theory_of ctxt
blanchet@44814
  2292
    val level = level_of_type_enc type_enc
blanchet@44814
  2293
    val grain = granularity_of_type_level level
blanchet@42829
  2294
    val ident_base =
blanchet@44396
  2295
      tags_sym_formula_prefix ^ s ^
blanchet@43125
  2296
      (if n > 1 then "_" ^ string_of_int j else "")
blanchet@46392
  2297
    val (kind, maybe_negate) = honor_conj_sym_kind in_conj conj_sym_kind
blanchet@42829
  2298
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@44814
  2299
    val bound_names = 1 upto ary |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  2300
    val bounds = bound_names |> map (fn name => ATerm (name, []))
nik@43677
  2301
    val cst = mk_aterm format type_enc (s, s') T_args
blanchet@46392
  2302
    val eq = maybe_negate oo eq_formula type_enc (atomic_types_of T) [] pred_sym
blanchet@44814
  2303
    val should_encode = should_encode_type ctxt mono level
blanchet@45949
  2304
    val tag_with = tag_with_type ctxt format mono type_enc NONE
blanchet@42829
  2305
    val add_formula_for_res =
blanchet@42829
  2306
      if should_encode res_T then
blanchet@44814
  2307
        let
blanchet@44814
  2308
          val tagged_bounds =
blanchet@44814
  2309
            if grain = Ghost_Type_Arg_Vars then
blanchet@44814
  2310
              let val ghosts = ghost_type_args thy s ary in
blanchet@44814
  2311
                map2 (fn (j, arg_T) => member (op =) ghosts j ? tag_with arg_T)
blanchet@44814
  2312
                     (0 upto ary - 1 ~~ arg_Ts) bounds
blanchet@44814
  2313
              end
blanchet@44814
  2314
            else
blanchet@44814
  2315
              bounds
blanchet@44814
  2316
        in
blanchet@44814
  2317
          cons (Formula (ident_base ^ "_res", kind,
blanchet@44814
  2318
                         eq (tag_with res_T (cst bounds)) (cst tagged_bounds),
blanchet@46406
  2319
                         NONE, isabelle_info format spec_eqN helper_rank))
blanchet@44814
  2320
        end
blanchet@42829
  2321
      else
blanchet@42829
  2322
        I
blanchet@42829
  2323
    fun add_formula_for_arg k =
blanchet@42829
  2324
      let val arg_T = nth arg_Ts k in
blanchet@42829
  2325
        if should_encode arg_T then
blanchet@42829
  2326
          case chop k bounds of
blanchet@42829
  2327
            (bounds1, bound :: bounds2) =>
blanchet@42852
  2328
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@44396
  2329
                           eq (cst (bounds1 @ tag_with arg_T bound :: bounds2))
blanchet@44396
  2330
                              (cst bounds),
blanchet@46406
  2331
                           NONE, isabelle_info format spec_eqN helper_rank))
blanchet@42829
  2332
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  2333
        else
blanchet@42829
  2334
          I
blanchet@42829
  2335
      end
blanchet@42829
  2336
  in