src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Mon Aug 09 12:40:15 2010 +0200 (2010-08-09)
changeset 38284 9f98107ad8b4
parent 38282 319c59682c51
child 38652 e063be321438
permissions -rw-r--r--
use "declaration" instead of "setup" to register Nitpick extensions
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(*  Title:      HOL/Tools/Nitpick/nitpick_hol.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2008, 2009, 2010
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Auxiliary HOL-related functions used by Nitpick.
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*)
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signature NITPICK_HOL =
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sig
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  type styp = Nitpick_Util.styp
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  type const_table = term list Symtab.table
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  type special_fun = (styp * int list * term list) * styp
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  type unrolled = styp * styp
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  type wf_cache = (styp * (bool * bool)) list
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  type hol_context =
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    {thy: theory,
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     ctxt: Proof.context,
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     max_bisim_depth: int,
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     boxes: (typ option * bool option) list,
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     stds: (typ option * bool) list,
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     wfs: (styp option * bool option) list,
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     user_axioms: bool option,
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     debug: bool,
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     whacks: term list,
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     binary_ints: bool option,
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     destroy_constrs: bool,
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     specialize: bool,
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     star_linear_preds: bool,
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     fast_descrs: bool,
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     tac_timeout: Time.time option,
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     evals: term list,
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     case_names: (string * int) list,
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     def_table: const_table,
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     nondef_table: const_table,
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     user_nondefs: term list,
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     simp_table: const_table Unsynchronized.ref,
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     psimp_table: const_table,
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     choice_spec_table: const_table,
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     intro_table: const_table,
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     ground_thm_table: term list Inttab.table,
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     ersatz_table: (string * string) list,
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     skolems: (string * string list) list Unsynchronized.ref,
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     special_funs: special_fun list Unsynchronized.ref,
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     unrolled_preds: unrolled list Unsynchronized.ref,
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     wf_cache: wf_cache Unsynchronized.ref,
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     constr_cache: (typ * styp list) list Unsynchronized.ref}
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  datatype fixpoint_kind = Lfp | Gfp | NoFp
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  datatype boxability =
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    InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
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  val name_sep : string
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  val numeral_prefix : string
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  val base_prefix : string
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  val step_prefix : string
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  val unrolled_prefix : string
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  val ubfp_prefix : string
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  val lbfp_prefix : string
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  val quot_normal_prefix : string
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  val skolem_prefix : string
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  val special_prefix : string
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  val uncurry_prefix : string
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  val eval_prefix : string
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  val iter_var_prefix : string
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  val strip_first_name_sep : string -> string * string
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  val original_name : string -> string
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  val abs_var : indexname * typ -> term -> term
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  val s_let : string -> int -> typ -> typ -> (term -> term) -> term -> term
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  val s_betapply : typ list -> term * term -> term
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  val s_betapplys : typ list -> term * term list -> term
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  val s_conj : term * term -> term
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  val s_disj : term * term -> term
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  val strip_any_connective : term -> term list * term
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  val conjuncts_of : term -> term list
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  val disjuncts_of : term -> term list
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  val unarize_unbox_etc_type : typ -> typ
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  val uniterize_unarize_unbox_etc_type : typ -> typ
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  val string_for_type : Proof.context -> typ -> string
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  val pretty_for_type : Proof.context -> typ -> Pretty.T
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  val prefix_name : string -> string -> string
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  val shortest_name : string -> string
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  val short_name : string -> string
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  val shorten_names_in_term : term -> term
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  val strict_type_match : theory -> typ * typ -> bool
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  val type_match : theory -> typ * typ -> bool
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  val const_match : theory -> styp * styp -> bool
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  val term_match : theory -> term * term -> bool
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  val frac_from_term_pair : typ -> term -> term -> term
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  val is_TFree : typ -> bool
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  val is_higher_order_type : typ -> bool
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  val is_fun_type : typ -> bool
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  val is_set_type : typ -> bool
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  val is_pair_type : typ -> bool
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  val is_lfp_iterator_type : typ -> bool
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  val is_gfp_iterator_type : typ -> bool
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  val is_fp_iterator_type : typ -> bool
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  val is_iterator_type : typ -> bool
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  val is_boolean_type : typ -> bool
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  val is_integer_type : typ -> bool
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  val is_bit_type : typ -> bool
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  val is_word_type : typ -> bool
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  val is_integer_like_type : typ -> bool
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  val is_record_type : typ -> bool
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  val is_number_type : Proof.context -> typ -> bool
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  val const_for_iterator_type : typ -> styp
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  val strip_n_binders : int -> typ -> typ list * typ
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  val nth_range_type : int -> typ -> typ
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  val num_factors_in_type : typ -> int
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  val num_binder_types : typ -> int
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  val curried_binder_types : typ -> typ list
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  val mk_flat_tuple : typ -> term list -> term
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  val dest_n_tuple : int -> term -> term list
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  val is_real_datatype : theory -> string -> bool
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  val is_standard_datatype : theory -> (typ option * bool) list -> typ -> bool
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  val is_codatatype : Proof.context -> typ -> bool
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  val is_quot_type : Proof.context -> typ -> bool
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  val is_pure_typedef : Proof.context -> typ -> bool
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  val is_univ_typedef : Proof.context -> typ -> bool
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  val is_datatype : Proof.context -> (typ option * bool) list -> typ -> bool
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  val is_record_constr : styp -> bool
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  val is_record_get : theory -> styp -> bool
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  val is_record_update : theory -> styp -> bool
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  val is_abs_fun : Proof.context -> styp -> bool
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  val is_rep_fun : Proof.context -> styp -> bool
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  val is_quot_abs_fun : Proof.context -> styp -> bool
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  val is_quot_rep_fun : Proof.context -> styp -> bool
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  val mate_of_rep_fun : Proof.context -> styp -> styp
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  val is_constr_like : Proof.context -> styp -> bool
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  val is_constr : Proof.context -> (typ option * bool) list -> styp -> bool
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  val is_sel : string -> bool
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  val is_sel_like_and_no_discr : string -> bool
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  val box_type : hol_context -> boxability -> typ -> typ
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  val binarize_nat_and_int_in_type : typ -> typ
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  val binarize_nat_and_int_in_term : term -> term
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  val discr_for_constr : styp -> styp
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  val num_sels_for_constr_type : typ -> int
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  val nth_sel_name_for_constr_name : string -> int -> string
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  val nth_sel_for_constr : styp -> int -> styp
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  val binarized_and_boxed_nth_sel_for_constr :
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    hol_context -> bool -> styp -> int -> styp
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  val sel_no_from_name : string -> int
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  val close_form : term -> term
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  val eta_expand : typ list -> term -> int -> term
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  val distinctness_formula : typ -> term list -> term
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  val register_frac_type :
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    string -> (string * string) list -> morphism -> Context.generic
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    -> Context.generic
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  val register_frac_type_global :
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    string -> (string * string) list -> theory -> theory
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  val unregister_frac_type :
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    string -> morphism -> Context.generic -> Context.generic
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  val unregister_frac_type_global : string -> theory -> theory
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  val register_codatatype :
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    typ -> string -> styp list -> morphism -> Context.generic -> Context.generic
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  val register_codatatype_global :
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    typ -> string -> styp list -> theory -> theory
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  val unregister_codatatype :
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    typ -> morphism -> Context.generic -> Context.generic
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  val unregister_codatatype_global : typ -> theory -> theory
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  val datatype_constrs : hol_context -> typ -> styp list
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  val binarized_and_boxed_datatype_constrs :
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    hol_context -> bool -> typ -> styp list
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  val num_datatype_constrs : hol_context -> typ -> int
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  val constr_name_for_sel_like : string -> string
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  val binarized_and_boxed_constr_for_sel : hol_context -> bool -> styp -> styp
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  val discriminate_value : hol_context -> styp -> term -> term
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  val select_nth_constr_arg :
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    Proof.context -> (typ option * bool) list -> styp -> term -> int -> typ
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    -> term
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  val construct_value :
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    Proof.context -> (typ option * bool) list -> styp -> term list -> term
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  val coerce_term : hol_context -> typ list -> typ -> typ -> term -> term
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  val card_of_type : (typ * int) list -> typ -> int
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  val bounded_card_of_type : int -> int -> (typ * int) list -> typ -> int
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  val bounded_exact_card_of_type :
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    hol_context -> typ list -> int -> int -> (typ * int) list -> typ -> int
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  val is_finite_type : hol_context -> typ -> bool
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  val is_small_finite_type : hol_context -> typ -> bool
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  val special_bounds : term list -> (indexname * typ) list
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  val is_funky_typedef : Proof.context -> typ -> bool
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  val all_axioms_of :
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    Proof.context -> (term * term) list -> term list * term list * term list
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  val arity_of_built_in_const :
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    theory -> (typ option * bool) list -> bool -> styp -> int option
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  val is_built_in_const :
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    theory -> (typ option * bool) list -> bool -> styp -> bool
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  val term_under_def : term -> term
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  val case_const_names :
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    Proof.context -> (typ option * bool) list -> (string * int) list
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  val unfold_defs_in_term : hol_context -> term -> term
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  val const_def_table :
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    Proof.context -> (term * term) list -> term list -> const_table
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  val const_nondef_table : term list -> const_table
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  val const_simp_table : Proof.context -> (term * term) list -> const_table
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  val const_psimp_table : Proof.context -> (term * term) list -> const_table
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  val const_choice_spec_table :
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    Proof.context -> (term * term) list -> const_table
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  val inductive_intro_table :
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    Proof.context -> (term * term) list -> const_table -> const_table
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  val ground_theorem_table : theory -> term list Inttab.table
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  val ersatz_table : Proof.context -> (string * string) list
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  val add_simps : const_table Unsynchronized.ref -> string -> term list -> unit
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  val inverse_axioms_for_rep_fun : Proof.context -> styp -> term list
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  val optimized_typedef_axioms : Proof.context -> string * typ list -> term list
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  val optimized_quot_type_axioms :
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    Proof.context -> (typ option * bool) list -> string * typ list -> term list
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  val def_of_const : theory -> const_table -> styp -> term option
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  val fixpoint_kind_of_rhs : term -> fixpoint_kind
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  val fixpoint_kind_of_const :
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    theory -> const_table -> string * typ -> fixpoint_kind
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  val is_real_inductive_pred : hol_context -> styp -> bool
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  val is_constr_pattern_lhs : Proof.context -> term -> bool
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  val is_constr_pattern_formula : Proof.context -> term -> bool
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  val nondef_props_for_const :
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    theory -> bool -> const_table -> styp -> term list
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  val is_choice_spec_fun : hol_context -> styp -> bool
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  val is_choice_spec_axiom : theory -> const_table -> term -> bool
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  val is_real_equational_fun : hol_context -> styp -> bool
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  val is_equational_fun_but_no_plain_def : hol_context -> styp -> bool
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  val codatatype_bisim_axioms : hol_context -> typ -> term list
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  val is_well_founded_inductive_pred : hol_context -> styp -> bool
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  val unrolled_inductive_pred_const : hol_context -> bool -> styp -> term
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  val equational_fun_axioms : hol_context -> styp -> term list
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  val is_equational_fun_surely_complete : hol_context -> styp -> bool
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  val merged_type_var_table_for_terms :
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    theory -> term list -> (sort * string) list
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  val merge_type_vars_in_term :
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    theory -> bool -> (sort * string) list -> term -> term
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  val ground_types_in_type : hol_context -> bool -> typ -> typ list
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  val ground_types_in_terms : hol_context -> bool -> term list -> typ list
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end;
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structure Nitpick_HOL : NITPICK_HOL =
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struct
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open Nitpick_Util
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type const_table = term list Symtab.table
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type special_fun = (styp * int list * term list) * styp
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type unrolled = styp * styp
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type wf_cache = (styp * (bool * bool)) list
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type hol_context =
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  {thy: theory,
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   ctxt: Proof.context,
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   max_bisim_depth: int,
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   boxes: (typ option * bool option) list,
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   stds: (typ option * bool) list,
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   wfs: (styp option * bool option) list,
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   user_axioms: bool option,
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   debug: bool,
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   whacks: term list,
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   binary_ints: bool option,
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   destroy_constrs: bool,
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   specialize: bool,
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   star_linear_preds: bool,
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   fast_descrs: bool,
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   tac_timeout: Time.time option,
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   evals: term list,
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   case_names: (string * int) list,
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   def_table: const_table,
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   nondef_table: const_table,
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   user_nondefs: term list,
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   simp_table: const_table Unsynchronized.ref,
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   psimp_table: const_table,
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   choice_spec_table: const_table,
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   intro_table: const_table,
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   ground_thm_table: term list Inttab.table,
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   ersatz_table: (string * string) list,
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   skolems: (string * string list) list Unsynchronized.ref,
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   special_funs: special_fun list Unsynchronized.ref,
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   unrolled_preds: unrolled list Unsynchronized.ref,
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   wf_cache: wf_cache Unsynchronized.ref,
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   constr_cache: (typ * styp list) list Unsynchronized.ref}
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datatype fixpoint_kind = Lfp | Gfp | NoFp
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datatype boxability =
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  InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
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structure Data = Generic_Data(
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  type T = {frac_types: (string * (string * string) list) list,
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            codatatypes: (string * (string * styp list)) list}
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  val empty = {frac_types = [], codatatypes = []}
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  val extend = I
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  fun merge ({frac_types = fs1, codatatypes = cs1},
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             {frac_types = fs2, codatatypes = cs2}) : T =
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    {frac_types = AList.merge (op =) (K true) (fs1, fs2),
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     codatatypes = AList.merge (op =) (K true) (cs1, cs2)})
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val name_sep = "$"
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val numeral_prefix = nitpick_prefix ^ "num" ^ name_sep
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val sel_prefix = nitpick_prefix ^ "sel"
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val discr_prefix = nitpick_prefix ^ "is" ^ name_sep
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val set_prefix = nitpick_prefix ^ "set" ^ name_sep
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val lfp_iterator_prefix = nitpick_prefix ^ "lfpit" ^ name_sep
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val gfp_iterator_prefix = nitpick_prefix ^ "gfpit" ^ name_sep
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   298
val unrolled_prefix = nitpick_prefix ^ "unroll" ^ name_sep
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   299
val base_prefix = nitpick_prefix ^ "base" ^ name_sep
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   300
val step_prefix = nitpick_prefix ^ "step" ^ name_sep
blanchet@33192
   301
val ubfp_prefix = nitpick_prefix ^ "ubfp" ^ name_sep
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   302
val lbfp_prefix = nitpick_prefix ^ "lbfp" ^ name_sep
blanchet@35311
   303
val quot_normal_prefix = nitpick_prefix ^ "qn" ^ name_sep
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   304
val skolem_prefix = nitpick_prefix ^ "sk"
blanchet@33192
   305
val special_prefix = nitpick_prefix ^ "sp"
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   306
val uncurry_prefix = nitpick_prefix ^ "unc"
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   307
val eval_prefix = nitpick_prefix ^ "eval"
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   308
val iter_var_prefix = "i"
blanchet@35718
   309
blanchet@35718
   310
(** Constant/type information and term/type manipulation **)
blanchet@33192
   311
blanchet@33192
   312
fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
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   313
fun quot_normal_name_for_type ctxt T =
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   314
  quot_normal_prefix ^ unyxml (Syntax.string_of_typ ctxt T)
blanchet@33192
   315
blanchet@33192
   316
val strip_first_name_sep =
blanchet@33192
   317
  Substring.full #> Substring.position name_sep ##> Substring.triml 1
blanchet@33192
   318
  #> pairself Substring.string
blanchet@33192
   319
fun original_name s =
blanchet@33192
   320
  if String.isPrefix nitpick_prefix s then
blanchet@33192
   321
    case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
blanchet@33192
   322
  else
blanchet@33192
   323
    s
blanchet@35718
   324
blanchet@37476
   325
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@37476
   326
blanchet@37476
   327
fun let_var s = (nitpick_prefix ^ s, 999)
blanchet@37476
   328
val let_inline_threshold = 20
blanchet@37476
   329
blanchet@37476
   330
fun s_let s n abs_T body_T f t =
blanchet@37476
   331
  if (n - 1) * (size_of_term t - 1) <= let_inline_threshold then
blanchet@37476
   332
    f t
blanchet@37476
   333
  else
blanchet@37476
   334
    let val z = (let_var s, abs_T) in
blanchet@37476
   335
      Const (@{const_name Let}, abs_T --> (abs_T --> body_T) --> body_T)
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   336
      $ t $ abs_var z (incr_boundvars 1 (f (Var z)))
blanchet@37476
   337
    end
blanchet@37476
   338
blanchet@37476
   339
fun loose_bvar1_count (Bound i, k) = if i = k then 1 else 0
blanchet@37476
   340
  | loose_bvar1_count (t1 $ t2, k) =
blanchet@37476
   341
    loose_bvar1_count (t1, k) + loose_bvar1_count (t2, k)
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   342
  | loose_bvar1_count (Abs (_, _, t), k) = loose_bvar1_count (t, k + 1)
blanchet@37476
   343
  | loose_bvar1_count _ = 0
blanchet@37476
   344
blanchet@37476
   345
fun s_betapply _ (Const (@{const_name If}, _) $ @{const True} $ t1', _) = t1'
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   346
  | s_betapply _ (Const (@{const_name If}, _) $ @{const False} $ _, t2) = t2
blanchet@37476
   347
  | s_betapply Ts (Const (@{const_name Let},
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   348
                          Type (_, [bound_T, Type (_, [_, body_T])]))
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   349
                   $ t12 $ Abs (s, T, t13'), t2) =
blanchet@37476
   350
    let val body_T' = range_type body_T in
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   351
      Const (@{const_name Let}, bound_T --> (bound_T --> body_T') --> body_T')
blanchet@37476
   352
      $ t12 $ Abs (s, T, s_betapply (T :: Ts) (t13', incr_boundvars 1 t2))
blanchet@37476
   353
    end
blanchet@37476
   354
  | s_betapply Ts (t1 as Abs (s1, T1, t1'), t2) =
blanchet@37476
   355
    (s_let s1 (loose_bvar1_count (t1', 0)) T1 (fastype_of1 (T1 :: Ts, t1'))
blanchet@37476
   356
              (curry betapply t1) t2
blanchet@37476
   357
     handle TERM _ => betapply (t1, t2)) (* FIXME: fix all uses *)
blanchet@37476
   358
  | s_betapply _ (t1, t2) = t1 $ t2
blanchet@37476
   359
fun s_betapplys Ts = Library.foldl (s_betapply Ts)
blanchet@37476
   360
blanchet@37476
   361
fun s_beta_norm Ts t =
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   362
  let
blanchet@37476
   363
    fun aux _ (Var _) = raise Same.SAME
blanchet@37476
   364
      | aux Ts (Abs (s, T, t')) = Abs (s, T, aux (T :: Ts) t')
blanchet@37476
   365
      | aux Ts ((t1 as Abs _) $ t2) =
blanchet@37476
   366
        Same.commit (aux Ts) (s_betapply Ts (t1, t2))
blanchet@37476
   367
      | aux Ts (t1 $ t2) =
blanchet@37476
   368
        ((case aux Ts t1 of
blanchet@37476
   369
           t1 as Abs _ => Same.commit (aux Ts) (s_betapply Ts (t1, t2))
blanchet@37476
   370
         | t1 => t1 $ Same.commit (aux Ts) t2)
blanchet@37476
   371
        handle Same.SAME => t1 $ aux Ts t2)
blanchet@37476
   372
      | aux _ _ = raise Same.SAME
blanchet@37476
   373
  in aux Ts t handle Same.SAME => t end
blanchet@33192
   374
blanchet@34998
   375
fun s_conj (t1, @{const True}) = t1
blanchet@34998
   376
  | s_conj (@{const True}, t2) = t2
blanchet@34998
   377
  | s_conj (t1, t2) =
blanchet@34998
   378
    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
blanchet@34998
   379
    else HOLogic.mk_conj (t1, t2)
blanchet@34998
   380
fun s_disj (t1, @{const False}) = t1
blanchet@34998
   381
  | s_disj (@{const False}, t2) = t2
blanchet@34998
   382
  | s_disj (t1, t2) =
blanchet@34998
   383
    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
blanchet@34998
   384
    else HOLogic.mk_disj (t1, t2)
blanchet@34998
   385
blanchet@34998
   386
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
blanchet@34998
   387
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
blanchet@34998
   388
  | strip_connective _ t = [t]
blanchet@35280
   389
fun strip_any_connective (t as (t0 $ _ $ _)) =
blanchet@34998
   390
    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
blanchet@34998
   391
      (strip_connective t0 t, t0)
blanchet@34998
   392
    else
blanchet@34998
   393
      ([t], @{const Not})
blanchet@34998
   394
  | strip_any_connective t = ([t], @{const Not})
blanchet@35070
   395
val conjuncts_of = strip_connective @{const "op &"}
blanchet@35070
   396
val disjuncts_of = strip_connective @{const "op |"}
blanchet@34998
   397
blanchet@33192
   398
(* When you add constants to these lists, make sure to handle them in
blanchet@33232
   399
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
blanchet@33192
   400
   well. *)
blanchet@33192
   401
val built_in_consts =
blanchet@33192
   402
  [(@{const_name all}, 1),
blanchet@33192
   403
   (@{const_name "=="}, 2),
blanchet@33192
   404
   (@{const_name "==>"}, 2),
blanchet@33192
   405
   (@{const_name Pure.conjunction}, 2),
blanchet@33192
   406
   (@{const_name Trueprop}, 1),
blanchet@33192
   407
   (@{const_name Not}, 1),
blanchet@33192
   408
   (@{const_name False}, 0),
blanchet@33192
   409
   (@{const_name True}, 0),
blanchet@33192
   410
   (@{const_name All}, 1),
blanchet@33192
   411
   (@{const_name Ex}, 1),
blanchet@37476
   412
   (@{const_name "op ="}, 1),
blanchet@33192
   413
   (@{const_name "op &"}, 2),
blanchet@33192
   414
   (@{const_name "op |"}, 2),
blanchet@33192
   415
   (@{const_name "op -->"}, 2),
blanchet@33192
   416
   (@{const_name If}, 3),
blanchet@33192
   417
   (@{const_name Let}, 2),
blanchet@33192
   418
   (@{const_name Pair}, 2),
blanchet@33192
   419
   (@{const_name fst}, 1),
blanchet@33192
   420
   (@{const_name snd}, 1),
blanchet@33192
   421
   (@{const_name Id}, 0),
blanchet@33192
   422
   (@{const_name converse}, 1),
blanchet@33192
   423
   (@{const_name trancl}, 1),
blanchet@33192
   424
   (@{const_name rel_comp}, 2),
blanchet@33192
   425
   (@{const_name image}, 2),
blanchet@33192
   426
   (@{const_name finite}, 1),
blanchet@34936
   427
   (@{const_name unknown}, 0),
blanchet@34936
   428
   (@{const_name is_unknown}, 1),
blanchet@35671
   429
   (@{const_name safe_The}, 1),
blanchet@35671
   430
   (@{const_name safe_Eps}, 1),
blanchet@33192
   431
   (@{const_name Frac}, 0),
blanchet@33192
   432
   (@{const_name norm_frac}, 0)]
blanchet@35220
   433
val built_in_nat_consts =
blanchet@35220
   434
  [(@{const_name Suc}, 0),
blanchet@35220
   435
   (@{const_name nat}, 0),
blanchet@35220
   436
   (@{const_name nat_gcd}, 0),
blanchet@35220
   437
   (@{const_name nat_lcm}, 0)]
blanchet@33192
   438
val built_in_descr_consts =
blanchet@33192
   439
  [(@{const_name The}, 1),
blanchet@33192
   440
   (@{const_name Eps}, 1)]
blanchet@33192
   441
val built_in_typed_consts =
blanchet@35220
   442
  [((@{const_name zero_class.zero}, int_T), 0),
blanchet@35220
   443
   ((@{const_name one_class.one}, int_T), 0),
blanchet@35220
   444
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   445
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   446
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
blanchet@35220
   447
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
blanchet@35220
   448
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
blanchet@35220
   449
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
blanchet@35220
   450
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
blanchet@35220
   451
val built_in_typed_nat_consts =
blanchet@35220
   452
  [((@{const_name zero_class.zero}, nat_T), 0),
blanchet@35220
   453
   ((@{const_name one_class.one}, nat_T), 0),
blanchet@35220
   454
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   455
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   456
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   457
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   458
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   459
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   460
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   461
val built_in_set_consts =
blanchet@37476
   462
  [(@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   463
blanchet@35190
   464
fun unarize_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   465
  | unarize_type @{typ "signed_bit word"} = int_T
blanchet@35190
   466
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
blanchet@35190
   467
  | unarize_type T = T
blanchet@35665
   468
fun unarize_unbox_etc_type (Type (@{type_name fin_fun}, Ts)) =
blanchet@35665
   469
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   470
  | unarize_unbox_etc_type (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   471
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   472
  | unarize_unbox_etc_type (Type (@{type_name pair_box}, Ts)) =
blanchet@38190
   473
    Type (@{type_name prod}, map unarize_unbox_etc_type Ts)
blanchet@35665
   474
  | unarize_unbox_etc_type @{typ "unsigned_bit word"} = nat_T
blanchet@35665
   475
  | unarize_unbox_etc_type @{typ "signed_bit word"} = int_T
blanchet@35665
   476
  | unarize_unbox_etc_type (Type (s, Ts as _ :: _)) =
blanchet@35665
   477
    Type (s, map unarize_unbox_etc_type Ts)
blanchet@35665
   478
  | unarize_unbox_etc_type T = T
blanchet@35280
   479
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   480
  | uniterize_type @{typ bisim_iterator} = nat_T
blanchet@35280
   481
  | uniterize_type T = T
blanchet@35665
   482
val uniterize_unarize_unbox_etc_type = uniterize_type o unarize_unbox_etc_type
blanchet@35280
   483
blanchet@35665
   484
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_unbox_etc_type
blanchet@38188
   485
fun pretty_for_type ctxt = Syntax.pretty_typ ctxt o unarize_unbox_etc_type
blanchet@33192
   486
blanchet@33192
   487
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@34121
   488
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   489
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@34121
   490
fun short_name s =
blanchet@33192
   491
  case space_explode name_sep s of
blanchet@33192
   492
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   493
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   494
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   495
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   496
  | shorten_names_in_type T = T
blanchet@34121
   497
val shorten_names_in_term =
blanchet@34121
   498
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   499
  #> map_types shorten_names_in_type
blanchet@33192
   500
blanchet@35665
   501
fun strict_type_match thy (T1, T2) =
blanchet@33192
   502
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   503
  handle Type.TYPE_MATCH => false
blanchet@35665
   504
fun type_match thy = strict_type_match thy o pairself unarize_unbox_etc_type
blanchet@33192
   505
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   506
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   507
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   508
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   509
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   510
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   511
blanchet@35711
   512
fun frac_from_term_pair T t1 t2 =
blanchet@35711
   513
  case snd (HOLogic.dest_number t1) of
blanchet@35711
   514
    0 => HOLogic.mk_number T 0
blanchet@35711
   515
  | n1 => case snd (HOLogic.dest_number t2) of
blanchet@35711
   516
            1 => HOLogic.mk_number T n1
blanchet@35711
   517
          | n2 => Const (@{const_name divide}, T --> T --> T)
blanchet@35711
   518
                  $ HOLogic.mk_number T n1 $ HOLogic.mk_number T n2
blanchet@35711
   519
blanchet@33192
   520
fun is_TFree (TFree _) = true
blanchet@33192
   521
  | is_TFree _ = false
blanchet@35665
   522
fun is_higher_order_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   523
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   524
  | is_higher_order_type _ = false
blanchet@35665
   525
fun is_fun_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   526
  | is_fun_type _ = false
blanchet@35665
   527
fun is_set_type (Type (@{type_name fun}, [_, @{typ bool}])) = true
blanchet@33192
   528
  | is_set_type _ = false
blanchet@38190
   529
fun is_pair_type (Type (@{type_name prod}, _)) = true
blanchet@33192
   530
  | is_pair_type _ = false
blanchet@33192
   531
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   532
  | is_lfp_iterator_type _ = false
blanchet@33192
   533
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   534
  | is_gfp_iterator_type _ = false
blanchet@33192
   535
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   536
fun is_iterator_type T =
blanchet@35280
   537
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   538
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   539
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   540
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   541
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   542
  | is_word_type _ = false
blanchet@35280
   543
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   544
val is_record_type = not o null o Record.dest_recTs
blanchet@38240
   545
fun is_frac_type ctxt (Type (s, [])) =
blanchet@38240
   546
    s |> AList.lookup (op =) (#frac_types (Data.get (Context.Proof ctxt)))
blanchet@38240
   547
      |> these |> null |> not
blanchet@33192
   548
  | is_frac_type _ _ = false
blanchet@38240
   549
fun is_number_type ctxt = is_integer_like_type orf is_frac_type ctxt
blanchet@33192
   550
blanchet@33192
   551
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   552
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   553
        binder_types T)
blanchet@35718
   554
fun const_for_iterator_type (Type (s, Ts)) =
blanchet@35718
   555
    (strip_first_name_sep s |> snd, Ts ---> bool_T)
blanchet@33192
   556
  | const_for_iterator_type T =
blanchet@33232
   557
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   558
blanchet@33192
   559
fun strip_n_binders 0 T = ([], T)
blanchet@35665
   560
  | strip_n_binders n (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
   561
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   562
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   563
    strip_n_binders n (Type (@{type_name fun}, Ts))
blanchet@33232
   564
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   565
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   566
blanchet@38190
   567
fun num_factors_in_type (Type (@{type_name prod}, [T1, T2])) =
blanchet@33192
   568
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   569
  | num_factors_in_type _ = 1
blanchet@35665
   570
fun num_binder_types (Type (@{type_name fun}, [_, T2])) =
blanchet@35665
   571
    1 + num_binder_types T2
blanchet@33192
   572
  | num_binder_types _ = 0
blanchet@33192
   573
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   574
fun maybe_curried_binder_types T =
blanchet@33192
   575
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   576
blanchet@33192
   577
fun mk_flat_tuple _ [t] = t
blanchet@38190
   578
  | mk_flat_tuple (Type (@{type_name prod}, [T1, T2])) (t :: ts) =
blanchet@33192
   579
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   580
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   581
fun dest_n_tuple 1 t = [t]
blanchet@33192
   582
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   583
blanchet@35220
   584
type typedef_info =
blanchet@35220
   585
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   586
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   587
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   588
blanchet@37256
   589
fun typedef_info ctxt s =
blanchet@38240
   590
  if is_frac_type ctxt (Type (s, [])) then
blanchet@38240
   591
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@38240
   592
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@38240
   593
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@38240
   594
                          |> Logic.varify_global,
blanchet@38240
   595
          set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@38240
   596
  else case Typedef.get_info ctxt s of
blanchet@38240
   597
    (* When several entries are returned, it shouldn't matter much which one
blanchet@38240
   598
       we take (according to Florian Haftmann). *)
blanchet@38240
   599
    ({abs_type, rep_type, Abs_name, Rep_name, ...},
blanchet@38240
   600
     {set_def, Rep, Abs_inverse, Rep_inverse, ...}) :: _ =>
blanchet@38240
   601
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@38240
   602
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@38240
   603
          set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@38240
   604
          Rep_inverse = SOME Rep_inverse}
blanchet@38240
   605
  | _ => NONE
blanchet@35220
   606
blanchet@35220
   607
val is_typedef = is_some oo typedef_info
blanchet@35220
   608
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   609
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   610
blanchet@34121
   611
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   612
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   613
fun is_basic_datatype thy stds s =
blanchet@38190
   614
  member (op =) [@{type_name prod}, @{type_name bool}, @{type_name int},
blanchet@38190
   615
                 "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   616
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   617
blanchet@38240
   618
(* TODO: use "Term_Subst.instantiateT" instead? *)
blanchet@33192
   619
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   620
  Same.commit (Envir.subst_type_same
blanchet@35311
   621
                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
blanchet@33192
   622
  handle Type.TYPE_MATCH =>
blanchet@33232
   623
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@38240
   624
fun varify_and_instantiate_type ctxt T1 T1' T2 =
blanchet@38240
   625
  let val thy = ProofContext.theory_of ctxt in
blanchet@38240
   626
    instantiate_type thy (varify_type ctxt T1) T1' (varify_type ctxt T2)
blanchet@38240
   627
  end
blanchet@33192
   628
blanchet@38240
   629
fun repair_constr_type ctxt body_T' T =
blanchet@38240
   630
  varify_and_instantiate_type ctxt (body_type T) body_T' T
blanchet@33192
   631
blanchet@38240
   632
fun register_frac_type_generic frac_s ersaetze generic =
blanchet@33192
   633
  let
blanchet@38240
   634
    val {frac_types, codatatypes} = Data.get generic
blanchet@33192
   635
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@38240
   636
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} generic end
blanchet@38284
   637
(* TODO: Consider morphism. *)
blanchet@38284
   638
fun register_frac_type frac_s ersaetze (_ : morphism) =
blanchet@38284
   639
  register_frac_type_generic frac_s ersaetze
blanchet@38240
   640
val register_frac_type_global = Context.theory_map oo register_frac_type_generic
blanchet@33192
   641
blanchet@38240
   642
fun unregister_frac_type_generic frac_s = register_frac_type_generic frac_s []
blanchet@38284
   643
(* TODO: Consider morphism. *)
blanchet@38284
   644
fun unregister_frac_type frac_s (_ : morphism) =
blanchet@38284
   645
  unregister_frac_type_generic frac_s
blanchet@38240
   646
val unregister_frac_type_global =
blanchet@38240
   647
  Context.theory_map o unregister_frac_type_generic
blanchet@38240
   648
blanchet@38240
   649
fun register_codatatype_generic co_T case_name constr_xs generic =
blanchet@33192
   650
  let
blanchet@38240
   651
    val ctxt = Context.proof_of generic
blanchet@38240
   652
    val thy = Context.theory_of generic
blanchet@38240
   653
    val {frac_types, codatatypes} = Data.get generic
blanchet@38240
   654
    val constr_xs = map (apsnd (repair_constr_type ctxt co_T)) constr_xs
blanchet@33192
   655
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   656
    val _ =
blanchet@34936
   657
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35665
   658
         co_s <> @{type_name fun} andalso
blanchet@35220
   659
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   660
        ()
blanchet@34121
   661
      else
blanchet@38242
   662
        raise TYPE ("Nitpick_HOL.register_codatatype_generic", [co_T], [])
blanchet@33192
   663
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   664
                                   codatatypes
blanchet@38240
   665
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} generic end
blanchet@38284
   666
(* TODO: Consider morphism. *)
blanchet@38284
   667
fun register_codatatype co_T case_name constr_xs (_ : morphism) =
blanchet@38284
   668
  register_codatatype_generic co_T case_name constr_xs
blanchet@38240
   669
val register_codatatype_global =
blanchet@38240
   670
  Context.theory_map ooo register_codatatype_generic
blanchet@33192
   671
blanchet@38240
   672
fun unregister_codatatype_generic co_T = register_codatatype_generic co_T "" []
blanchet@38284
   673
(* TODO: Consider morphism. *)
blanchet@38284
   674
fun unregister_codatatype co_T (_ : morphism) =
blanchet@38284
   675
  unregister_codatatype_generic co_T
blanchet@38240
   676
val unregister_codatatype_global =
blanchet@38240
   677
  Context.theory_map o unregister_codatatype_generic
blanchet@38240
   678
blanchet@38240
   679
fun is_codatatype ctxt (Type (s, _)) =
blanchet@38240
   680
    s |> AList.lookup (op =) (#codatatypes (Data.get (Context.Proof ctxt)))
blanchet@38240
   681
      |> Option.map snd |> these |> null |> not
blanchet@33192
   682
  | is_codatatype _ _ = false
blanchet@38215
   683
fun is_real_quot_type thy (Type (s, _)) =
blanchet@38215
   684
    is_some (Quotient_Info.quotdata_lookup_raw thy s)
blanchet@38215
   685
  | is_real_quot_type _ _ = false
blanchet@38240
   686
fun is_quot_type ctxt T =
blanchet@38240
   687
  let val thy = ProofContext.theory_of ctxt in
blanchet@38240
   688
    is_real_quot_type thy T andalso not (is_codatatype ctxt T)
blanchet@38240
   689
  end
blanchet@37256
   690
fun is_pure_typedef ctxt (T as Type (s, _)) =
blanchet@37256
   691
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   692
      is_typedef ctxt s andalso
blanchet@38215
   693
      not (is_real_datatype thy s orelse is_real_quot_type thy T orelse
blanchet@38240
   694
           is_codatatype ctxt T orelse is_record_type T orelse
blanchet@37256
   695
           is_integer_like_type T)
blanchet@37256
   696
    end
blanchet@33192
   697
  | is_pure_typedef _ _ = false
blanchet@37256
   698
fun is_univ_typedef ctxt (Type (s, _)) =
blanchet@37256
   699
    (case typedef_info ctxt s of
blanchet@33192
   700
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@35332
   701
       let
blanchet@35332
   702
         val t_opt =
blanchet@35332
   703
           case set_def of
blanchet@35332
   704
             SOME thm => try (snd o Logic.dest_equals o prop_of) thm
blanchet@35332
   705
           | NONE => try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop)
blanchet@35332
   706
                         prop_of_Rep
blanchet@35332
   707
       in
blanchet@35332
   708
         case t_opt of
blanchet@35332
   709
           SOME (Const (@{const_name top}, _)) => true
blanchet@35386
   710
           (* "Multiset.multiset" *)
blanchet@35332
   711
         | SOME (Const (@{const_name Collect}, _)
blanchet@35332
   712
                 $ Abs (_, _, Const (@{const_name finite}, _) $ _)) => true
blanchet@35386
   713
           (* "FinFun.finfun" *)
blanchet@35386
   714
         | SOME (Const (@{const_name Collect}, _) $ Abs (_, _,
blanchet@35386
   715
                     Const (@{const_name Ex}, _) $ Abs (_, _,
blanchet@35386
   716
                         Const (@{const_name finite}, _) $ _))) => true
blanchet@35332
   717
         | _ => false
blanchet@35332
   718
       end
blanchet@33192
   719
     | NONE => false)
blanchet@33192
   720
  | is_univ_typedef _ _ = false
blanchet@37256
   721
fun is_datatype ctxt stds (T as Type (s, _)) =
blanchet@37256
   722
    let val thy = ProofContext.theory_of ctxt in
blanchet@38240
   723
      (is_typedef ctxt s orelse is_codatatype ctxt T orelse
blanchet@38240
   724
       T = @{typ ind} orelse is_real_quot_type thy T) andalso
blanchet@38240
   725
      not (is_basic_datatype thy stds s)
blanchet@37256
   726
    end
blanchet@35220
   727
  | is_datatype _ _ _ = false
blanchet@33192
   728
blanchet@33192
   729
fun all_record_fields thy T =
blanchet@33192
   730
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   731
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   732
  end
blanchet@33192
   733
  handle TYPE _ => []
blanchet@35280
   734
fun is_record_constr (s, T) =
blanchet@33192
   735
  String.isSuffix Record.extN s andalso
blanchet@33192
   736
  let val dataT = body_type T in
blanchet@33192
   737
    is_record_type dataT andalso
blanchet@33192
   738
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   739
  end
blanchet@33192
   740
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   741
fun no_of_record_field thy s T1 =
blanchet@34121
   742
  find_index (curry (op =) s o fst)
blanchet@34121
   743
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@35665
   744
fun is_record_get thy (s, Type (@{type_name fun}, [T1, _])) =
blanchet@34121
   745
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   746
  | is_record_get _ _ = false
blanchet@33192
   747
fun is_record_update thy (s, T) =
blanchet@33192
   748
  String.isSuffix Record.updateN s andalso
blanchet@34121
   749
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   750
         (all_record_fields thy (body_type T))
blanchet@33192
   751
  handle TYPE _ => false
blanchet@37256
   752
fun is_abs_fun ctxt (s, Type (@{type_name fun}, [_, Type (s', _)])) =
blanchet@37256
   753
    (case typedef_info ctxt s' of
blanchet@33192
   754
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   755
     | NONE => false)
blanchet@33192
   756
  | is_abs_fun _ _ = false
blanchet@37256
   757
fun is_rep_fun ctxt (s, Type (@{type_name fun}, [Type (s', _), _])) =
blanchet@37256
   758
    (case typedef_info ctxt s' of
blanchet@33192
   759
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   760
     | NONE => false)
blanchet@33192
   761
  | is_rep_fun _ _ = false
blanchet@38215
   762
fun is_quot_abs_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@38215
   763
                                         [_, abs_T as Type (s', _)]))) =
blanchet@38240
   764
    try (Quotient_Term.absrep_const_chk Quotient_Term.AbsF ctxt) s'
blanchet@38240
   765
    = SOME (Const x) andalso not (is_codatatype ctxt abs_T)
blanchet@34936
   766
  | is_quot_abs_fun _ _ = false
blanchet@38215
   767
fun is_quot_rep_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@38215
   768
                                         [abs_T as Type (s', _), _]))) =
blanchet@38240
   769
    try (Quotient_Term.absrep_const_chk Quotient_Term.RepF ctxt) s'
blanchet@38240
   770
    = SOME (Const x) andalso not (is_codatatype ctxt abs_T)
blanchet@34936
   771
  | is_quot_rep_fun _ _ = false
blanchet@33192
   772
blanchet@37256
   773
fun mate_of_rep_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@37256
   774
                                         [T1 as Type (s', _), T2]))) =
blanchet@37256
   775
    (case typedef_info ctxt s' of
blanchet@35665
   776
       SOME {Abs_name, ...} => (Abs_name, Type (@{type_name fun}, [T2, T1]))
blanchet@33232
   777
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   778
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@35284
   779
fun rep_type_for_quot_type thy (T as Type (s, _)) =
blanchet@35284
   780
  let val {qtyp, rtyp, ...} = Quotient_Info.quotdata_lookup thy s in
blanchet@35284
   781
    instantiate_type thy qtyp T rtyp
blanchet@35284
   782
  end
blanchet@35284
   783
fun equiv_relation_for_quot_type thy (Type (s, Ts)) =
blanchet@35284
   784
    let
blanchet@38243
   785
      val {qtyp, equiv_rel, equiv_thm, ...} =
blanchet@38243
   786
        Quotient_Info.quotdata_lookup thy s
blanchet@38243
   787
      val partial =
blanchet@38243
   788
        case prop_of equiv_thm of
blanchet@38243
   789
          @{const Trueprop} $ (Const (@{const_name equivp}, _) $ _) => false
blanchet@38243
   790
        | @{const Trueprop} $ (Const (@{const_name part_equivp}, _) $ _) => true
blanchet@38243
   791
        | _ => raise NOT_SUPPORTED "Ill-formed quotient type equivalence \
blanchet@38243
   792
                                   \relation theorem"
blanchet@35284
   793
      val Ts' = qtyp |> dest_Type |> snd
blanchet@38243
   794
    in (subst_atomic_types (Ts' ~~ Ts) equiv_rel, partial) end
blanchet@34936
   795
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   796
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   797
blanchet@38240
   798
fun is_coconstr ctxt (s, T) =
blanchet@38240
   799
  case body_type T of
blanchet@38240
   800
    co_T as Type (co_s, _) =>
blanchet@38240
   801
    let val {codatatypes, ...} = Data.get (Context.Proof ctxt) in
blanchet@38240
   802
      exists (fn (s', T') => s = s' andalso repair_constr_type ctxt co_T T' = T)
blanchet@38240
   803
             (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@38240
   804
    end
blanchet@38240
   805
  | _ => false
blanchet@37256
   806
fun is_constr_like ctxt (s, T) =
blanchet@35665
   807
  member (op =) [@{const_name FinFun}, @{const_name FunBox},
blanchet@35665
   808
                 @{const_name PairBox}, @{const_name Quot},
blanchet@35665
   809
                 @{const_name Zero_Rep}, @{const_name Suc_Rep}] s orelse
blanchet@37256
   810
  let
blanchet@37256
   811
    val thy = ProofContext.theory_of ctxt
blanchet@37256
   812
    val (x as (_, T)) = (s, unarize_unbox_etc_type T)
blanchet@37256
   813
  in
blanchet@37260
   814
    is_real_constr thy x orelse is_record_constr x orelse
blanchet@37256
   815
    (is_abs_fun ctxt x andalso is_pure_typedef ctxt (range_type T)) orelse
blanchet@38240
   816
    is_coconstr ctxt x
blanchet@33192
   817
  end
blanchet@37256
   818
fun is_stale_constr ctxt (x as (_, T)) =
blanchet@38240
   819
  is_codatatype ctxt (body_type T) andalso is_constr_like ctxt x andalso
blanchet@38240
   820
  not (is_coconstr ctxt x)
blanchet@37256
   821
fun is_constr ctxt stds (x as (_, T)) =
blanchet@37256
   822
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   823
    is_constr_like ctxt x andalso
blanchet@37256
   824
    not (is_basic_datatype thy stds
blanchet@35220
   825
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@37256
   826
    not (is_stale_constr ctxt x)
blanchet@37256
   827
  end
blanchet@33192
   828
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   829
val is_sel_like_and_no_discr =
blanchet@35665
   830
  String.isPrefix sel_prefix orf
blanchet@35665
   831
  (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   832
blanchet@33192
   833
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   834
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   835
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   836
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   837
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   838
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   839
blanchet@35070
   840
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   841
  case T of
blanchet@35665
   842
    Type (@{type_name fun}, _) =>
blanchet@34936
   843
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   844
    not (is_boolean_type (body_type T))
blanchet@38190
   845
  | Type (@{type_name prod}, Ts) =>
blanchet@34936
   846
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   847
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   848
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   849
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   850
  | _ => false
blanchet@35280
   851
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   852
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   853
    SOME (SOME box_me) => box_me
blanchet@35070
   854
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   855
and box_type hol_ctxt boxy T =
blanchet@33192
   856
  case T of
blanchet@35665
   857
    Type (z as (@{type_name fun}, [T1, T2])) =>
blanchet@34936
   858
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   859
       should_box_type hol_ctxt boxy z then
blanchet@33192
   860
      Type (@{type_name fun_box},
blanchet@35070
   861
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   862
    else
blanchet@35070
   863
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   864
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@38190
   865
  | Type (z as (@{type_name prod}, Ts)) =>
blanchet@34982
   866
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   867
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   868
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   869
    else
blanchet@38190
   870
      Type (@{type_name prod},
blanchet@35665
   871
            map (box_type hol_ctxt
blanchet@34121
   872
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   873
                           else InPair)) Ts)
blanchet@33192
   874
  | _ => T
blanchet@33192
   875
blanchet@35190
   876
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   877
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   878
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   879
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   880
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   881
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   882
blanchet@33192
   883
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   884
blanchet@33192
   885
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   886
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   887
  if s = @{const_name Pair} then
blanchet@33192
   888
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   889
  else
blanchet@33192
   890
    sel_prefix_for n ^ s
blanchet@33192
   891
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   892
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   893
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   894
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   895
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   896
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   897
  oo nth_sel_for_constr
blanchet@33192
   898
blanchet@33192
   899
fun sel_no_from_name s =
blanchet@33192
   900
  if String.isPrefix discr_prefix s then
blanchet@33192
   901
    ~1
blanchet@33192
   902
  else if String.isPrefix sel_prefix s then
blanchet@33192
   903
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   904
  else if s = @{const_name snd} then
blanchet@33192
   905
    1
blanchet@33192
   906
  else
blanchet@33192
   907
    0
blanchet@33192
   908
blanchet@35078
   909
val close_form =
blanchet@35078
   910
  let
blanchet@35078
   911
    fun close_up zs zs' =
blanchet@35078
   912
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   913
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   914
           (take (length zs' - length zs) zs')
blanchet@35078
   915
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   916
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   917
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   918
        end
blanchet@35078
   919
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   920
  in aux [] end
blanchet@35078
   921
blanchet@33192
   922
fun eta_expand _ t 0 = t
blanchet@33192
   923
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   924
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   925
  | eta_expand Ts t n =
blanchet@37261
   926
    fold_rev (curry3 Abs ("x" ^ nat_subscript n))
blanchet@33192
   927
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   928
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   929
blanchet@33192
   930
fun distinctness_formula T =
blanchet@33192
   931
  all_distinct_unordered_pairs_of
blanchet@33192
   932
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   933
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   934
blanchet@35220
   935
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   936
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   937
blanchet@37256
   938
fun uncached_datatype_constrs ({thy, ctxt, stds, ...} : hol_context)
blanchet@35220
   939
                              (T as Type (s, Ts)) =
blanchet@38240
   940
    (case AList.lookup (op =) (#codatatypes (Data.get (Context.Proof ctxt)))
blanchet@38240
   941
                       s of
blanchet@38240
   942
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type ctxt T)) xs'
blanchet@33581
   943
     | _ =>
blanchet@37256
   944
       if is_datatype ctxt stds T then
blanchet@33581
   945
         case Datatype.get_info thy s of
blanchet@33581
   946
           SOME {index, descr, ...} =>
blanchet@33581
   947
           let
blanchet@33581
   948
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   949
           in
blanchet@37260
   950
             map (apsnd (fn Us =>
blanchet@37260
   951
                            map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@37260
   952
                 constrs
blanchet@33581
   953
           end
blanchet@33581
   954
         | NONE =>
blanchet@33581
   955
           if is_record_type T then
blanchet@33581
   956
             let
blanchet@33581
   957
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   958
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   959
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   960
             in [(s', T')] end
blanchet@38215
   961
           else if is_real_quot_type thy T then
blanchet@34936
   962
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@37256
   963
           else case typedef_info ctxt s of
blanchet@33581
   964
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@35311
   965
             [(Abs_name,
blanchet@38240
   966
               varify_and_instantiate_type ctxt abs_type T rep_type --> T)]
blanchet@33581
   967
           | NONE =>
blanchet@33581
   968
             if T = @{typ ind} then
blanchet@33581
   969
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   970
             else
blanchet@33581
   971
               []
blanchet@33581
   972
       else
blanchet@33581
   973
         [])
blanchet@33580
   974
  | uncached_datatype_constrs _ _ = []
blanchet@35220
   975
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   976
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   977
    SOME xs => xs
blanchet@33580
   978
  | NONE =>
blanchet@35220
   979
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   980
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   981
    end
blanchet@35190
   982
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   983
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   984
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@33192
   985
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   986
blanchet@33192
   987
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   988
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   989
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   990
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   991
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   992
    AList.lookup (op =)
blanchet@35190
   993
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   994
        s
blanchet@33192
   995
    |> the |> pair s
blanchet@33192
   996
  end
blanchet@34982
   997
blanchet@35070
   998
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   999
  let val dataT = body_type T in
blanchet@33192
  1000
    if s = @{const_name Suc} then
blanchet@33192
  1001
      Abs (Name.uu, dataT,
blanchet@33192
  1002
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
  1003
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
  1004
      Const (discr_for_constr x)
blanchet@33192
  1005
    else
blanchet@33192
  1006
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
  1007
  end
blanchet@37256
  1008
fun discriminate_value (hol_ctxt as {ctxt, ...}) x t =
blanchet@35280
  1009
  case head_of t of
blanchet@35280
  1010
    Const x' =>
blanchet@33192
  1011
    if x = x' then @{const True}
blanchet@37256
  1012
    else if is_constr_like ctxt x' then @{const False}
blanchet@37476
  1013
    else s_betapply [] (discr_term_for_constr hol_ctxt x, t)
blanchet@37476
  1014
  | _ => s_betapply [] (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
  1015
blanchet@35220
  1016
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
  1017
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
  1018
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
  1019
      @{term "%n::nat. n - 1"}
blanchet@33192
  1020
    else if is_pair_type dataT then
blanchet@33192
  1021
      Const (nth_sel_for_constr x n)
blanchet@33192
  1022
    else
blanchet@33192
  1023
      let
blanchet@38190
  1024
        fun aux m (Type (@{type_name prod}, [T1, T2])) =
blanchet@33192
  1025
            let
blanchet@33192
  1026
              val (m, t1) = aux m T1
blanchet@33192
  1027
              val (m, t2) = aux m T2
blanchet@33192
  1028
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
  1029
          | aux m T =
blanchet@33192
  1030
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
  1031
                    $ Bound 0)
blanchet@33192
  1032
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
  1033
                     (List.take (arg_Ts, n)) 0
blanchet@33192
  1034
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
  1035
  end
blanchet@37256
  1036
fun select_nth_constr_arg ctxt stds x t n res_T =
blanchet@37256
  1037
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
  1038
    (case strip_comb t of
blanchet@37256
  1039
       (Const x', args) =>
blanchet@37256
  1040
       if x = x' then nth args n
blanchet@37256
  1041
       else if is_constr_like ctxt x' then Const (@{const_name unknown}, res_T)
blanchet@37256
  1042
       else raise SAME ()
blanchet@37256
  1043
     | _ => raise SAME())
blanchet@37476
  1044
    handle SAME () =>
blanchet@37476
  1045
           s_betapply [] (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@37256
  1046
  end
blanchet@33192
  1047
blanchet@35220
  1048
fun construct_value _ _ x [] = Const x
blanchet@37256
  1049
  | construct_value ctxt stds (x as (s, _)) args =
blanchet@33192
  1050
    let val args = map Envir.eta_contract args in
blanchet@33192
  1051
      case hd args of
blanchet@35280
  1052
        Const (s', _) $ t =>
blanchet@34936
  1053
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
  1054
           constr_name_for_sel_like s' = s andalso
blanchet@35220
  1055
           forall (fn (n, t') =>
blanchet@37256
  1056
                      select_nth_constr_arg ctxt stds x t n dummyT = t')
blanchet@34936
  1057
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  1058
          t
blanchet@33192
  1059
        else
blanchet@33192
  1060
          list_comb (Const x, args)
blanchet@33192
  1061
      | _ => list_comb (Const x, args)
blanchet@33192
  1062
    end
blanchet@33192
  1063
blanchet@37256
  1064
fun constr_expand (hol_ctxt as {ctxt, stds, ...}) T t =
blanchet@35665
  1065
  (case head_of t of
blanchet@37256
  1066
     Const x => if is_constr_like ctxt x then t else raise SAME ()
blanchet@35665
  1067
   | _ => raise SAME ())
blanchet@35665
  1068
  handle SAME () =>
blanchet@35665
  1069
         let
blanchet@35665
  1070
           val x' as (_, T') =
blanchet@35665
  1071
             if is_pair_type T then
blanchet@35665
  1072
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@35665
  1073
                 (@{const_name Pair}, T1 --> T2 --> T)
blanchet@35665
  1074
               end
blanchet@35665
  1075
             else
blanchet@35665
  1076
               datatype_constrs hol_ctxt T |> hd
blanchet@35665
  1077
           val arg_Ts = binder_types T'
blanchet@35665
  1078
         in
blanchet@37256
  1079
           list_comb (Const x', map2 (select_nth_constr_arg ctxt stds x' t)
blanchet@35665
  1080
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@35665
  1081
         end
blanchet@35665
  1082
blanchet@35665
  1083
fun coerce_bound_no f j t =
blanchet@35665
  1084
  case t of
blanchet@35665
  1085
    t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
blanchet@35665
  1086
  | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
blanchet@35665
  1087
  | Bound j' => if j' = j then f t else t
blanchet@35665
  1088
  | _ => t
blanchet@35665
  1089
fun coerce_bound_0_in_term hol_ctxt new_T old_T =
blanchet@35665
  1090
  old_T <> new_T ? coerce_bound_no (coerce_term hol_ctxt [new_T] old_T new_T) 0
blanchet@37256
  1091
and coerce_term (hol_ctxt as {ctxt, stds, fast_descrs, ...}) Ts new_T old_T t =
blanchet@35665
  1092
  if old_T = new_T then
blanchet@35665
  1093
    t
blanchet@35665
  1094
  else
blanchet@35665
  1095
    case (new_T, old_T) of
blanchet@35665
  1096
      (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1097
       Type (@{type_name fun}, [old_T1, old_T2])) =>
blanchet@35665
  1098
      (case eta_expand Ts t 1 of
blanchet@35665
  1099
         Abs (s, _, t') =>
blanchet@35665
  1100
         Abs (s, new_T1,
blanchet@35665
  1101
              t' |> coerce_bound_0_in_term hol_ctxt new_T1 old_T1
blanchet@35665
  1102
                 |> coerce_term hol_ctxt (new_T1 :: Ts) new_T2 old_T2)
blanchet@35665
  1103
         |> Envir.eta_contract
blanchet@35665
  1104
         |> new_s <> @{type_name fun}
blanchet@37256
  1105
            ? construct_value ctxt stds
blanchet@35665
  1106
                  (if new_s = @{type_name fin_fun} then @{const_name FinFun}
blanchet@35665
  1107
                   else @{const_name FunBox},
blanchet@35665
  1108
                   Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1109
              o single
blanchet@35665
  1110
       | t' => raise TERM ("Nitpick_HOL.coerce_term", [t']))
blanchet@35665
  1111
    | (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1112
       Type (old_s, old_Ts as [old_T1, old_T2])) =>
blanchet@35665
  1113
      if old_s = @{type_name fin_fun} orelse old_s = @{type_name fun_box} orelse
blanchet@38190
  1114
         old_s = @{type_name pair_box} orelse old_s = @{type_name prod} then
blanchet@35665
  1115
        case constr_expand hol_ctxt old_T t of
blanchet@35665
  1116
          Const (old_s, _) $ t1 =>
blanchet@35665
  1117
          if new_s = @{type_name fun} then
blanchet@35665
  1118
            coerce_term hol_ctxt Ts new_T (Type (@{type_name fun}, old_Ts)) t1
blanchet@35665
  1119
          else
blanchet@37256
  1120
            construct_value ctxt stds
blanchet@35665
  1121
                (old_s, Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1122
                [coerce_term hol_ctxt Ts (Type (@{type_name fun}, new_Ts))
blanchet@35665
  1123
                             (Type (@{type_name fun}, old_Ts)) t1]
blanchet@35665
  1124
        | Const _ $ t1 $ t2 =>
blanchet@37256
  1125
          construct_value ctxt stds
blanchet@38190
  1126
              (if new_s = @{type_name prod} then @{const_name Pair}
blanchet@35665
  1127
               else @{const_name PairBox}, new_Ts ---> new_T)
blanchet@35665
  1128
              (map3 (coerce_term hol_ctxt Ts) [new_T1, new_T2] [old_T1, old_T2]
blanchet@35665
  1129
                    [t1, t2])
blanchet@35665
  1130
        | t' => raise TERM ("Nitpick_HOL.coerce_term", [t'])
blanchet@35665
  1131
      else
blanchet@35665
  1132
        raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1133
    | _ => raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1134
blanchet@35665
  1135
fun card_of_type assigns (Type (@{type_name fun}, [T1, T2])) =
blanchet@34123
  1136
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@38190
  1137
  | card_of_type assigns (Type (@{type_name prod}, [T1, T2])) =
blanchet@34123
  1138
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1139
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1140
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1141
  | card_of_type _ @{typ bool} = 2
blanchet@34123
  1142
  | card_of_type assigns T =
blanchet@34123
  1143
    case AList.lookup (op =) assigns T of
blanchet@33192
  1144
      SOME k => k
blanchet@33192
  1145
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1146
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@35665
  1147
fun bounded_card_of_type max default_card assigns
blanchet@35665
  1148
                         (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
  1149
    let
blanchet@34123
  1150
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1151
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1152
    in
blanchet@33192
  1153
      if k1 = max orelse k2 = max then max
blanchet@33192
  1154
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1155
    end
blanchet@35665
  1156
  | bounded_card_of_type max default_card assigns
blanchet@38190
  1157
                         (Type (@{type_name prod}, [T1, T2])) =
blanchet@33192
  1158
    let
blanchet@34123
  1159
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1160
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1161
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1162
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1163
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1164
                    card_of_type assigns T
blanchet@33192
  1165
                  else
blanchet@34123
  1166
                    card_of_type assigns T
blanchet@33232
  1167
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1168
                           default_card)
blanchet@35385
  1169
fun bounded_exact_card_of_type hol_ctxt finitizable_dataTs max default_card
blanchet@35385
  1170
                               assigns T =
blanchet@33192
  1171
  let
blanchet@33192
  1172
    fun aux avoid T =
blanchet@34121
  1173
      (if member (op =) avoid T then
blanchet@33192
  1174
         0
blanchet@35385
  1175
       else if member (op =) finitizable_dataTs T then
blanchet@35385
  1176
         raise SAME ()
blanchet@33192
  1177
       else case T of
blanchet@35665
  1178
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
  1179
         let
blanchet@33192
  1180
           val k1 = aux avoid T1
blanchet@33192
  1181
           val k2 = aux avoid T2
blanchet@33192
  1182
         in
blanchet@33192
  1183
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1184
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1185
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1186
         end
blanchet@38190
  1187
       | Type (@{type_name prod}, [T1, T2]) =>
blanchet@33192
  1188
         let
blanchet@33192
  1189
           val k1 = aux avoid T1
blanchet@33192
  1190
           val k2 = aux avoid T2
blanchet@33192
  1191
         in
blanchet@33192
  1192
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1193
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1194
           else Int.min (max, k1 * k2)
blanchet@33192
  1195
         end
blanchet@33192
  1196
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1197
       | @{typ prop} => 2
blanchet@33192
  1198
       | @{typ bool} => 2
blanchet@33192
  1199
       | Type _ =>
blanchet@35070
  1200
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1201
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1202
                  else raise SAME ()
blanchet@33192
  1203
          | constrs =>
blanchet@33192
  1204
            let
blanchet@33192
  1205
              val constr_cards =
blanchet@35280
  1206
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1207
                    constrs
blanchet@33192
  1208
            in
blanchet@34121
  1209
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1210
              else Integer.sum constr_cards
blanchet@33192
  1211
            end)
blanchet@33192
  1212
       | _ => raise SAME ())
blanchet@34123
  1213
      handle SAME () =>
blanchet@34123
  1214
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1215
  in Int.min (max, aux [] T) end
blanchet@33192
  1216
blanchet@35665
  1217
val small_type_max_card = 5
blanchet@35665
  1218
blanchet@35384
  1219
fun is_finite_type hol_ctxt T =
blanchet@35665
  1220
  bounded_exact_card_of_type hol_ctxt [] 1 2 [] T > 0
blanchet@35665
  1221
fun is_small_finite_type hol_ctxt T =
blanchet@35665
  1222
  let val n = bounded_exact_card_of_type hol_ctxt [] 1 2 [] T in
blanchet@35665
  1223
    n > 0 andalso n <= small_type_max_card
blanchet@35665
  1224
  end
blanchet@33192
  1225
blanchet@33192
  1226
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1227
  | is_ground_term (Const _) = true
blanchet@33192
  1228
  | is_ground_term _ = false
blanchet@33192
  1229
blanchet@36062
  1230
fun hashw_term (t1 $ t2) = hashw (hashw_term t1, hashw_term t2)
blanchet@36062
  1231
  | hashw_term (Const (s, _)) = hashw_string (s, 0w0)
blanchet@33192
  1232
  | hashw_term _ = 0w0
blanchet@33192
  1233
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1234
blanchet@33192
  1235
fun special_bounds ts =
wenzelm@35408
  1236
  fold Term.add_vars ts [] |> sort (Term_Ord.fast_indexname_ord o pairself fst)
blanchet@33192
  1237
blanchet@38190
  1238
(* FIXME: detect "rep_datatype"? *)
blanchet@38240
  1239
fun is_funky_typedef_name ctxt s =
blanchet@38190
  1240
  member (op =) [@{type_name unit}, @{type_name prod},
blanchet@38190
  1241
                 @{type_name Sum_Type.sum}, @{type_name int}] s orelse
blanchet@38240
  1242
  is_frac_type ctxt (Type (s, []))
blanchet@38240
  1243
fun is_funky_typedef ctxt (Type (s, _)) = is_funky_typedef_name ctxt s
blanchet@33571
  1244
  | is_funky_typedef _ _ = false
blanchet@33192
  1245
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1246
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1247
  | is_arity_type_axiom _ = false
blanchet@37256
  1248
fun is_typedef_axiom ctxt boring (@{const "==>"} $ _ $ t2) =
blanchet@37256
  1249
    is_typedef_axiom ctxt boring t2
blanchet@37256
  1250
  | is_typedef_axiom ctxt boring
blanchet@33192
  1251
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@35665
  1252
         $ Const (_, Type (@{type_name fun}, [Type (s, _), _]))
blanchet@35665
  1253
         $ Const _ $ _)) =
blanchet@38240
  1254
    boring <> is_funky_typedef_name ctxt s andalso is_typedef ctxt s
blanchet@33192
  1255
  | is_typedef_axiom _ _ _ = false
blanchet@36126
  1256
val is_class_axiom =
blanchet@36126
  1257
  Logic.strip_horn #> swap #> op :: #> forall (can Logic.dest_of_class)
blanchet@33192
  1258
blanchet@33192
  1259
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1260
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1261
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1262
   using "typedef_info". *)
blanchet@37256
  1263
fun partition_axioms_by_definitionality ctxt axioms def_names =
blanchet@33192
  1264
  let
blanchet@33192
  1265
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1266
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1267
    val nondefs =
blanchet@33192
  1268
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@37256
  1269
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom ctxt true) o snd)
blanchet@33192
  1270
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1271
blanchet@33197
  1272
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1273
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1274
   commands. *)
blanchet@33192
  1275
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1276
blanchet@35283
  1277
val is_trivial_definition =
blanchet@35283
  1278
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1279
val is_plain_definition =
blanchet@33192
  1280
  let
blanchet@33192
  1281
    fun do_lhs t1 =
blanchet@33192
  1282
      case strip_comb t1 of
blanchet@34936
  1283
        (Const _, args) =>
blanchet@34936
  1284
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1285
      | _ => false
blanchet@33192
  1286
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1287
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1288
        do_lhs t1
blanchet@33192
  1289
      | do_eq _ = false
blanchet@33192
  1290
  in do_eq end
blanchet@33192
  1291
blanchet@37256
  1292
fun all_axioms_of ctxt subst =
blanchet@33192
  1293
  let
blanchet@37256
  1294
    val thy = ProofContext.theory_of ctxt
blanchet@35335
  1295
    val axioms_of_thys =
blanchet@35893
  1296
      maps Thm.axioms_of
blanchet@35893
  1297
      #> map (apsnd (subst_atomic subst o prop_of))
blanchet@35893
  1298
      #> filter_out (is_class_axiom o snd)
blanchet@33192
  1299
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1300
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1301
                    |> OrdList.make fast_string_ord
blanchet@33192
  1302
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1303
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1304
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1305
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1306
    val (built_in_defs, built_in_nondefs) =
blanchet@37256
  1307
      partition_axioms_by_definitionality ctxt built_in_axioms def_names
blanchet@37256
  1308
      ||> filter (is_typedef_axiom ctxt false)
blanchet@33192
  1309
    val (user_defs, user_nondefs) =
blanchet@37256
  1310
      partition_axioms_by_definitionality ctxt user_axioms def_names
blanchet@33197
  1311
    val (built_in_nondefs, user_nondefs) =
blanchet@37256
  1312
      List.partition (is_typedef_axiom ctxt false) user_nondefs
blanchet@33197
  1313
      |>> append built_in_nondefs
blanchet@34121
  1314
    val defs =
blanchet@34121
  1315
      (thy |> PureThy.all_thms_of
blanchet@34121
  1316
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1317
           |> map (prop_of o snd)
blanchet@35283
  1318
           |> filter_out is_trivial_definition
blanchet@35283
  1319
           |> filter is_plain_definition) @
blanchet@34121
  1320
      user_defs @ built_in_defs
blanchet@33192
  1321
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1322
blanchet@35220
  1323
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1324
  if s = @{const_name If} then
blanchet@33192
  1325
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1326
  else
blanchet@35220
  1327
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1328
      case AList.lookup (op =)
blanchet@35220
  1329
                    (built_in_consts
blanchet@35220
  1330
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1331
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1332
        SOME n => SOME n
blanchet@35220
  1333
      | NONE =>
blanchet@35220
  1334
        case AList.lookup (op =)
blanchet@35220
  1335
                 (built_in_typed_consts
blanchet@35220
  1336
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1337
                 (s, unarize_type T) of
blanchet@35220
  1338
          SOME n => SOME n
blanchet@35220
  1339
        | NONE =>
blanchet@35280
  1340
          case s of
blanchet@35280
  1341
            @{const_name zero_class.zero} =>
blanchet@35280
  1342
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1343
          | @{const_name Suc} =>
blanchet@35280
  1344
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1345
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1346
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1347
                 else
blanchet@35280
  1348
                   NONE
blanchet@35220
  1349
    end
blanchet@35220
  1350
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1351
blanchet@33192
  1352
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1353
   simplification rules (equational specifications). *)
blanchet@33192
  1354
fun term_under_def t =
blanchet@33192
  1355
  case t of
blanchet@33192
  1356
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1357
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1358
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1359
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1360
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1361
  | t1 $ _ => term_under_def t1
blanchet@33192
  1362
  | _ => t
blanchet@33192
  1363
blanchet@36555
  1364
(* Here we crucially rely on "specialize_type" performing a preorder traversal
blanchet@36555
  1365
   of the term, without which the wrong occurrence of a constant could be
blanchet@36555
  1366
   matched in the face of overloading. *)
blanchet@35220
  1367
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1368
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1369
    []
blanchet@33192
  1370
  else
blanchet@33192
  1371
    these (Symtab.lookup table s)
blanchet@36555
  1372
    |> map_filter (try (specialize_type thy x))
blanchet@34121
  1373
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1374
blanchet@35280
  1375
fun normalized_rhs_of t =
blanchet@33192
  1376
  let
blanchet@33743
  1377
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1378
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1379
      | aux _ _ = NONE
blanchet@33192
  1380
    val (lhs, rhs) =
blanchet@33192
  1381
      case t of
blanchet@33192
  1382
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1383
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1384
        (t1, t2)
blanchet@33232
  1385
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1386
    val args = strip_comb lhs |> snd
blanchet@33743
  1387
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1388
blanchet@33192
  1389
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1390
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1391
     original_name s <> s then
blanchet@33192
  1392
    NONE
blanchet@33192
  1393
  else
blanchet@37476
  1394
    x |> def_props_for_const thy [(NONE, false)] false table
blanchet@37476
  1395
      |> List.last
blanchet@35280
  1396
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1397
    handle List.Empty => NONE
blanchet@33192
  1398
blanchet@33192
  1399
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1400
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1401
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1402
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1403
blanchet@33192
  1404
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1405
  let
blanchet@33192
  1406
    fun is_good_arg (Bound _) = true
blanchet@33192
  1407
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1408
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1409
        s = @{const_name undefined}
blanchet@33192
  1410
      | is_good_arg _ = false
blanchet@33192
  1411
  in
blanchet@33192
  1412
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1413
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1414
      (case def_of_const thy table x of
blanchet@38180
  1415
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso
blanchet@38180
  1416
                    forall is_good_arg ts
blanchet@33192
  1417
       | NONE => false)
blanchet@33192
  1418
    | _ => false
blanchet@33192
  1419
  end
blanchet@33192
  1420
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1421
  map_aterms (fn t as Const x =>
blanchet@33192
  1422
                 (case def_of_const thy table x of
blanchet@33192
  1423
                    SOME t' =>
blanchet@33192
  1424
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1425
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1426
                      else t
blanchet@33192
  1427
                    end
blanchet@33192
  1428
                 | NONE => t)
blanchet@33192
  1429
               | t => t)
blanchet@33192
  1430
blanchet@38240
  1431
fun case_const_names ctxt stds =
blanchet@38240
  1432
  let val thy = ProofContext.theory_of ctxt in
blanchet@38240
  1433
    Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@38240
  1434
                    if is_basic_datatype thy stds dtype_s then
blanchet@38240
  1435
                      I
blanchet@38240
  1436
                    else
blanchet@38240
  1437
                      cons (case_name, AList.lookup (op =) descr index
blanchet@38240
  1438
                                       |> the |> #3 |> length))
blanchet@38240
  1439
                (Datatype.get_all thy) [] @
blanchet@38240
  1440
    map (apsnd length o snd) (#codatatypes (Data.get (Context.Proof ctxt)))
blanchet@38240
  1441
  end
blanchet@33192
  1442
blanchet@35718
  1443
fun fixpoint_kind_of_const thy table x =
blanchet@35718
  1444
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@35718
  1445
    NoFp
blanchet@35718
  1446
  else
blanchet@35718
  1447
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@35718
  1448
    handle Option.Option => NoFp
blanchet@33192
  1449
blanchet@35718
  1450
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35718
  1451
                             ...} : hol_context) x =
blanchet@35718
  1452
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35718
  1453
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@38205
  1454
fun is_inductive_pred hol_ctxt (x as (s, _)) =
blanchet@38205
  1455
  is_real_inductive_pred hol_ctxt x orelse String.isPrefix ubfp_prefix s orelse
blanchet@38205
  1456
  String.isPrefix lbfp_prefix s
blanchet@33192
  1457
blanchet@35718
  1458
fun lhs_of_equation t =
blanchet@35718
  1459
  case t of
blanchet@35718
  1460
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1461
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1462
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1463
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@35718
  1464
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1465
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1466
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1467
  | _ => NONE
blanchet@35718
  1468
fun is_constr_pattern _ (Bound _) = true
blanchet@35718
  1469
  | is_constr_pattern _ (Var _) = true
blanchet@37256
  1470
  | is_constr_pattern ctxt t =
blanchet@35718
  1471
    case strip_comb t of
blanchet@35718
  1472
      (Const x, args) =>
blanchet@37256
  1473
      is_constr_like ctxt x andalso forall (is_constr_pattern ctxt) args
blanchet@35718
  1474
    | _ => false
blanchet@37256
  1475
fun is_constr_pattern_lhs ctxt t =
blanchet@37256
  1476
  forall (is_constr_pattern ctxt) (snd (strip_comb t))
blanchet@37256
  1477
fun is_constr_pattern_formula ctxt t =
blanchet@35718
  1478
  case lhs_of_equation t of
blanchet@37256
  1479
    SOME t' => is_constr_pattern_lhs ctxt t'
blanchet@35718
  1480
  | NONE => false
blanchet@35718
  1481
blanchet@36555
  1482
(* Similar to "specialize_type" but returns all matches rather than only the
blanchet@36555
  1483
   first (preorder) match. *)
blanchet@35807
  1484
fun multi_specialize_type thy slack (s, T) t =
blanchet@35807
  1485
  let
blanchet@35807
  1486
    fun aux (Const (s', T')) ys =
blanchet@35807
  1487
        if s = s' then
blanchet@35807
  1488
          ys |> (if AList.defined (op =) ys T' then
blanchet@35807
  1489
                   I
blanchet@35807
  1490
                 else
blanchet@36555
  1491
                   cons (T', monomorphic_term (Sign.typ_match thy (T', T)
blanchet@36555
  1492
                                                              Vartab.empty) t)
blanchet@35807
  1493
                   handle Type.TYPE_MATCH => I
blanchet@36575
  1494
                        | TERM _ =>
blanchet@35807
  1495
                          if slack then
blanchet@35807
  1496
                            I
blanchet@35807
  1497
                          else
blanchet@37253
  1498
                            raise NOT_SUPPORTED
blanchet@37253
  1499
                                      ("too much polymorphism in axiom \"" ^
blanchet@37253
  1500
                                       Syntax.string_of_term_global thy t ^
blanchet@37253
  1501
                                       "\" involving " ^ quote s))
blanchet@35807
  1502
        else
blanchet@35807
  1503
          ys
blanchet@35807
  1504
      | aux _ ys = ys
blanchet@35807
  1505
  in map snd (fold_aterms aux t []) end
blanchet@35807
  1506
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@35807
  1507
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@35807
  1508
blanchet@35807
  1509
fun unvarify_term (t1 $ t2) = unvarify_term t1 $ unvarify_term t2
blanchet@35807
  1510
  | unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@35807
  1511
  | unvarify_term (Abs (s, T, t')) = Abs (s, T, unvarify_term t')
blanchet@35807
  1512
  | unvarify_term t = t
blanchet@35807
  1513
fun axiom_for_choice_spec thy =
blanchet@35807
  1514
  unvarify_term
blanchet@35807
  1515
  #> Object_Logic.atomize_term thy
blanchet@35807
  1516
  #> Choice_Specification.close_form
blanchet@35807
  1517
  #> HOLogic.mk_Trueprop
blanchet@35807
  1518
fun is_choice_spec_fun ({thy, def_table, nondef_table, choice_spec_table, ...}
blanchet@35807
  1519
                        : hol_context) x =
blanchet@35807
  1520
  case nondef_props_for_const thy true choice_spec_table x of
blanchet@35807
  1521
    [] => false
blanchet@35807
  1522
  | ts => case def_of_const thy def_table x of
blanchet@35807
  1523
            SOME (Const (@{const_name Eps}, _) $ _) => true
blanchet@35807
  1524
          | SOME _ => false
blanchet@35807
  1525
          | NONE =>
blanchet@35807
  1526
            let val ts' = nondef_props_for_const thy true nondef_table x in
blanchet@35807
  1527
              length ts' = length ts andalso
blanchet@35807
  1528
              forall (fn t =>
blanchet@35807
  1529
                         exists (curry (op aconv) (axiom_for_choice_spec thy t))
blanchet@35807
  1530
                                ts') ts
blanchet@35807
  1531
            end
blanchet@35807
  1532
blanchet@35807
  1533
fun is_choice_spec_axiom thy choice_spec_table t =
blanchet@35807
  1534
  Symtab.exists (fn (_, ts) =>
blanchet@35807
  1535
                    exists (curry (op aconv) t o axiom_for_choice_spec thy) ts)
blanchet@35807
  1536
                choice_spec_table
blanchet@35807
  1537
blanchet@38205
  1538
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@38205
  1539
                             ...} : hol_context) x =
blanchet@38205
  1540
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@38205
  1541
                                                     x)))
blanchet@38205
  1542
         [!simp_table, psimp_table]
blanchet@38202
  1543
fun is_equational_fun_but_no_plain_def hol_ctxt =
blanchet@38205
  1544
  is_real_equational_fun hol_ctxt orf is_inductive_pred hol_ctxt
blanchet@38202
  1545
blanchet@35718
  1546
(** Constant unfolding **)
blanchet@33192
  1547
blanchet@37476
  1548
fun constr_case_body ctxt stds (func_t, (x as (_, T))) =
blanchet@33192
  1549
  let val arg_Ts = binder_types T in
blanchet@37476
  1550
    s_betapplys [] (func_t, map2 (select_nth_constr_arg ctxt stds x (Bound 0))
blanchet@37476
  1551
                                 (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1552
  end
blanchet@37476
  1553
fun add_constr_case res_T (body_t, guard_t) res_t =
blanchet@37476
  1554
  if res_T = bool_T then
blanchet@37476
  1555
    s_conj (HOLogic.mk_imp (guard_t, body_t), res_t)
blanchet@37476
  1556
  else
blanchet@37476
  1557
    Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@37476
  1558
    $ guard_t $ body_t $ res_t
blanchet@37476
  1559
fun optimized_case_def (hol_ctxt as {ctxt, stds, ...}) dataT res_T func_ts =
blanchet@33192
  1560
  let
blanchet@35070
  1561
    val xs = datatype_constrs hol_ctxt dataT
blanchet@37476
  1562
    val cases =
blanchet@37476
  1563
      func_ts ~~ xs
blanchet@37476
  1564
      |> map (fn (func_t, x) =>
blanchet@37476
  1565
                 (constr_case_body ctxt stds (incr_boundvars 1 func_t, x),
blanchet@37476
  1566
                  discriminate_value hol_ctxt x (Bound 0)))
blanchet@37476
  1567
      |> AList.group (op aconv)
blanchet@37476
  1568
      |> map (apsnd (List.foldl s_disj @{const False}))
blanchet@37482
  1569
      |> sort (int_ord o pairself (size_of_term o snd))
blanchet@37476
  1570
      |> rev
blanchet@33192
  1571
  in
blanchet@37476
  1572
    if res_T = bool_T then
blanchet@37476
  1573
      if forall (member (op =) [@{const False}, @{const True}] o fst) cases then
blanchet@37476
  1574
        case cases of
blanchet@37476
  1575
          [(body_t, _)] => body_t
blanchet@37476
  1576
        | [_, (@{const True}, head_t2)] => head_t2
blanchet@37476
  1577
        | [_, (@{const False}, head_t2)] => @{const Not} $ head_t2
blanchet@37476
  1578
        | _ => raise BAD ("Nitpick_HOL.optimized_case_def", "impossible cases")
blanchet@37476
  1579
      else 
blanchet@37476
  1580
        @{const True} |> fold_rev (add_constr_case res_T) cases
blanchet@37476
  1581
    else
blanchet@37476
  1582
      fst (hd cases) |> fold_rev (add_constr_case res_T) (tl cases)
blanchet@33192
  1583
  end
blanchet@37476
  1584
  |> curry absdummy dataT
blanchet@37476
  1585
blanchet@37256
  1586
fun optimized_record_get (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T res_T t =
blanchet@35070
  1587
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1588
    case no_of_record_field thy s rec_T of
blanchet@33192
  1589
      ~1 => (case rec_T of
blanchet@33192
  1590
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1591
               let
blanchet@33192
  1592
                 val rec_T' = List.last Ts
blanchet@33192
  1593
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1594
               in
blanchet@37256
  1595
                 select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@35070
  1596
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1597
               end
blanchet@33232
  1598
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1599
                                []))
blanchet@37256
  1600
    | j => select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@33192
  1601
  end
blanchet@37256
  1602
fun optimized_record_update (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T fun_t
blanchet@37256
  1603
                            rec_t =
blanchet@33192
  1604
  let
blanchet@35070
  1605
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1606
    val Ts = binder_types constr_T
blanchet@33192
  1607
    val n = length Ts
blanchet@33192
  1608
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1609
    val ts =
blanchet@35220
  1610
      map2 (fn j => fn T =>
blanchet@37256
  1611
               let val t = select_nth_constr_arg ctxt stds constr_x rec_t j T in
blanchet@35220
  1612
                 if j = special_j then
blanchet@37476
  1613
                   s_betapply [] (fun_t, t)
blanchet@35220
  1614
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1615
                   optimized_record_update hol_ctxt s
blanchet@35220
  1616
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1617
                 else
blanchet@35220
  1618
                   t
blanchet@35220
  1619
               end) (index_seq 0 n) Ts
blanchet@33192
  1620
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1621
blanchet@35070
  1622
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1623
val unfold_max_depth = 255
blanchet@33192
  1624
blanchet@38206
  1625
(* Inline definitions or define as an equational constant? Booleans tend to
blanchet@38206
  1626
   benefit more from inlining, due to the polarity analysis. *)
blanchet@38206
  1627
val def_inline_threshold_for_booleans = 50
blanchet@38206
  1628
val def_inline_threshold_for_non_booleans = 20
blanchet@38202
  1629
blanchet@38209
  1630
fun unfold_defs_in_term
blanchet@38209
  1631
        (hol_ctxt as {thy, ctxt, stds, whacks, fast_descrs, case_names,
blanchet@38209
  1632
                      def_table, ground_thm_table, ersatz_table, ...}) =
blanchet@33192
  1633
  let
blanchet@33192
  1634
    fun do_term depth Ts t =
blanchet@33192
  1635
      case t of
blanchet@33192
  1636
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@35665
  1637
                      Type (@{type_name fun}, [_, ran_T]))) $ t1 =>
blanchet@38240
  1638
        ((if is_number_type ctxt ran_T then
blanchet@33192
  1639
            let
blanchet@33192
  1640
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1641
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1642
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1643
            in
blanchet@35220
  1644
              if is_integer_like_type ran_T then
blanchet@35220
  1645
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1646
                  Const (s, ran_T)
blanchet@35220
  1647
                else
blanchet@35220
  1648
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1649
              else
blanchet@33192
  1650
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1651
                                  $ Const (s, int_T))
blanchet@33192
  1652
            end
blanchet@33192
  1653
            handle TERM _ => raise SAME ()
blanchet@33192
  1654
          else
blanchet@33192
  1655
            raise SAME ())
blanchet@37476
  1656
         handle SAME () =>
blanchet@37476
  1657
                s_betapply [] (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1658
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1659
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1660
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@37476
  1661
        s_betapplys Ts (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@37476
  1662
                        map (do_term depth Ts) [t1, t2])
blanchet@33192
  1663
      | Const (x as (@{const_name distinct},
blanchet@35665
  1664
               Type (@{type_name fun}, [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1665
        $ (t1 as _ $ _) =>
blanchet@33192
  1666
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1667
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1668
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1669
        if is_ground_term t1 andalso
blanchet@34936
  1670
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1671
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1672
          do_term depth Ts t2
blanchet@33192
  1673
        else
blanchet@33192
  1674
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1675
      | Const x => do_const depth Ts t x []
blanchet@37476
  1676
      | t1 $ t2 =>
blanchet@37476
  1677
        (case strip_comb t of
blanchet@37476
  1678
           (Const x, ts) => do_const depth Ts t x ts
blanchet@37476
  1679
         | _ => s_betapply [] (do_term depth Ts t1, do_term depth Ts t2))
blanchet@33192
  1680
      | Bound _ => t
blanchet@33192
  1681
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@38209
  1682
      | _ => if member (term_match thy) whacks t then
blanchet@38209
  1683
               Const (@{const_name unknown}, fastype_of1 (Ts, t))
blanchet@38209
  1684
             else
blanchet@38209
  1685
               t
blanchet@33192
  1686
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1687
        (Abs (Name.uu, body_type T,
blanchet@37256
  1688
              select_nth_constr_arg ctxt stds x (Bound 0) n res_T), [])
blanchet@33192
  1689
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@37256
  1690
        (select_nth_constr_arg ctxt stds x (do_term depth Ts t) n res_T, ts)
blanchet@38207
  1691
    and quot_rep_of depth Ts abs_T rep_T ts =
blanchet@38207
  1692
      select_nth_constr_arg_with_args depth Ts
blanchet@38207
  1693
          (@{const_name Quot}, rep_T --> abs_T) ts 0 rep_T
blanchet@33192
  1694
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@38209
  1695
      if member (term_match thy) whacks (Const x) then
blanchet@38209
  1696
        Const (@{const_name unknown}, fastype_of1 (Ts, t))
blanchet@38209
  1697
      else case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1698
        SOME s' =>
blanchet@33192
  1699
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1700
      | NONE =>
blanchet@33192
  1701
        let
blanchet@38206
  1702
          fun def_inline_threshold () =
blanchet@38206
  1703
            if is_boolean_type (nth_range_type (length ts) T) then
blanchet@38206
  1704
              def_inline_threshold_for_booleans
blanchet@38206
  1705
            else
blanchet@38206
  1706
              def_inline_threshold_for_non_booleans
blanchet@33192
  1707
          val (const, ts) =
blanchet@35220
  1708
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1709
              (Const x, ts)
blanchet@33192
  1710
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1711
              SOME n =>
blanchet@37476
  1712
              if length ts < n then
blanchet@37476
  1713
                (do_term depth Ts (eta_expand Ts t (n - length ts)), [])
blanchet@37476
  1714
              else
blanchet@37476
  1715
                let
blanchet@37476
  1716
                  val (dataT, res_T) = nth_range_type n T
blanchet@37476
  1717
                                       |> pairf domain_type range_type
blanchet@37476
  1718
                in
blanchet@37476
  1719
                  (optimized_case_def hol_ctxt dataT res_T
blanchet@37476
  1720
                                      (map (do_term depth Ts) (take n ts)),
blanchet@37476
  1721
                   drop n ts)
blanchet@37476
  1722
                end
blanchet@33192
  1723
            | _ =>
blanchet@37256
  1724
              if is_constr ctxt stds x then
blanchet@33192
  1725
                (Const x, ts)
blanchet@37256
  1726
              else if is_stale_constr ctxt x then
blanchet@34936
  1727
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1728
                                     \(\"" ^ s ^ "\")")
blanchet@35284
  1729
              else if is_quot_abs_fun ctxt x then
blanchet@34936
  1730
                let
blanchet@34936
  1731
                  val rep_T = domain_type T
blanchet@34936
  1732
                  val abs_T = range_type T
blanchet@34936
  1733
                in
blanchet@34936
  1734
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1735
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@35311
  1736
                               $ (Const (quot_normal_name_for_type ctxt abs_T,
blanchet@34936
  1737
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1738
                end
blanchet@35284
  1739
              else if is_quot_rep_fun ctxt x then
blanchet@38207
  1740
                quot_rep_of depth Ts (domain_type T) (range_type T) ts
blanchet@33192
  1741
              else if is_record_get thy x then
blanchet@33192
  1742
                case length ts of
blanchet@33192
  1743
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1744
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1745
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1746
              else if is_record_update thy x then
blanchet@33192
  1747
                case length ts of
blanchet@35070
  1748
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1749
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1750
                            (do_term depth Ts (hd ts))
blanchet@33580
  1751
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1752
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@38207
  1753
              else if is_abs_fun ctxt x andalso
blanchet@38240
  1754
                      is_quot_type ctxt (range_type T) then
blanchet@38207
  1755
                let
blanchet@38207
  1756
                  val abs_T = range_type T
blanchet@38207
  1757
                  val rep_T = domain_type (domain_type T)
blanchet@38207
  1758
                  val eps_fun = Const (@{const_name Eps},
blanchet@38207
  1759
                                       (rep_T --> bool_T) --> rep_T)
blanchet@38207
  1760
                  val normal_fun = 
blanchet@38207
  1761
                    Const (quot_normal_name_for_type ctxt abs_T,
blanchet@38207
  1762
                           rep_T --> rep_T)
blanchet@38207
  1763
                  val abs_fun = Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@38207
  1764
                in
blanchet@38207
  1765
                  (Abs (Name.uu, rep_T --> bool_T,
blanchet@38207
  1766
                        abs_fun $ (normal_fun $ (eps_fun $ Bound 0)))
blanchet@38207
  1767
                   |> do_term (depth + 1) Ts, ts)
blanchet@38207
  1768
                end
blanchet@37256
  1769
              else if is_rep_fun ctxt x then
blanchet@37256
  1770
                let val x' = mate_of_rep_fun ctxt x in
blanchet@37256
  1771
                  if is_constr ctxt stds x' then
blanchet@33192
  1772
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1773
                                                    (range_type T)
blanchet@38240
  1774
                  else if is_quot_type ctxt (domain_type T) then
blanchet@38207
  1775
                    let
blanchet@38207
  1776
                      val abs_T = domain_type T
blanchet@38207
  1777
                      val rep_T = domain_type (range_type T)
blanchet@38207
  1778
                      val (rep_fun, _) = quot_rep_of depth Ts abs_T rep_T []
blanchet@38243
  1779
                      val (equiv_rel, _) =
blanchet@38243
  1780
                        equiv_relation_for_quot_type thy abs_T
blanchet@38207
  1781
                    in
blanchet@38207
  1782
                      (Abs (Name.uu, abs_T, equiv_rel $ (rep_fun $ Bound 0)),
blanchet@38207
  1783
                       ts)
blanchet@38207
  1784
                    end
blanchet@33192
  1785
                  else
blanchet@38208
  1786
                    (Const x, ts)
blanchet@33192
  1787
                end
blanchet@38202
  1788
              else if is_equational_fun_but_no_plain_def hol_ctxt x orelse
blanchet@35807
  1789
                      is_choice_spec_fun hol_ctxt x then
blanchet@33192
  1790
                (Const x, ts)
blanchet@33192
  1791
              else case def_of_const thy def_table x of
blanchet@33192
  1792
                SOME def =>
blanchet@33192
  1793
                if depth > unfold_max_depth then
blanchet@34124
  1794
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1795
                                   "too many nested definitions (" ^
blanchet@34124
  1796
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1797
                                   quote s)
blanchet@33192
  1798
                else if s = @{const_name wfrec'} then
blanchet@37476
  1799
                  (do_term (depth + 1) Ts (s_betapplys Ts (def, ts)), [])
blanchet@38206
  1800
                else if size_of_term def > def_inline_threshold () then
blanchet@38202
  1801
                  (Const x, ts)
blanchet@33192
  1802
                else
blanchet@33192
  1803
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1804
              | NONE => (Const x, ts)
blanchet@37476
  1805
        in
blanchet@37476
  1806
          s_betapplys Ts (const, map (do_term depth Ts) ts)
blanchet@37476
  1807
          |> s_beta_norm Ts
blanchet@37476
  1808
        end
blanchet@33192
  1809
  in do_term 0 [] end
blanchet@33192
  1810
blanchet@35718
  1811
(** Axiom extraction/generation **)
blanchet@35718
  1812
blanchet@38206
  1813
fun extensional_equal j (Type (@{type_name fun}, [dom_T, ran_T])) t1 t2 =
blanchet@38206
  1814
    let val var_t = Var (("x", j), dom_T) in
blanchet@38206
  1815
      extensional_equal (j + 1) ran_T (betapply (t1, var_t))
blanchet@38206
  1816
                        (betapply (t2, var_t))
blanchet@38206
  1817
    end
blanchet@38206
  1818
  | extensional_equal _ T t1 t2 =
blanchet@38206
  1819
    Const (@{const_name "op ="}, T --> T --> bool_T) $ t1 $ t2
blanchet@38206
  1820
blanchet@38202
  1821
fun equationalize_term ctxt tag t =
blanchet@38206
  1822
  let
blanchet@38206
  1823
    val j = maxidx_of_term t + 1
blanchet@38206
  1824
    val (prems, concl) = Logic.strip_horn t
blanchet@38206
  1825
  in
blanchet@38174
  1826
    Logic.list_implies (prems,
blanchet@38200
  1827
        case concl of
blanchet@38206
  1828
          @{const Trueprop} $ (Const (@{const_name "op ="}, Type (_, [T, _]))
blanchet@38206
  1829
                               $ t1 $ t2) =>
blanchet@38206
  1830
          @{const Trueprop} $ extensional_equal j T t1 t2
blanchet@38200
  1831
        | @{const Trueprop} $ t' =>
blanchet@38200
  1832
          @{const Trueprop} $ HOLogic.mk_eq (t', @{const True})
blanchet@38201
  1833
        | Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>
blanchet@38206
  1834
          @{const Trueprop} $ extensional_equal j T t1 t2
blanchet@38201
  1835
        | _ => (warning ("Ignoring " ^ quote tag ^ " for non-equation" ^
blanchet@38201
  1836
                         quote (Syntax.string_of_term ctxt t) ^ ".");
blanchet@38201
  1837
                raise SAME ()))
blanchet@38201
  1838
    |> SOME
blanchet@38200
  1839
  end
blanchet@38201
  1840
  handle SAME () => NONE
blanchet@38172
  1841
blanchet@35807
  1842
fun pair_for_prop t =
blanchet@35807
  1843
  case term_under_def t of
blanchet@35807
  1844
    Const (s, _) => (s, t)
blanchet@35807
  1845
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@38172
  1846
blanchet@35807
  1847
fun def_table_for get ctxt subst =
blanchet@35807
  1848
  ctxt |> get |> map (pair_for_prop o subst_atomic subst)
blanchet@35807
  1849
       |> AList.group (op =) |> Symtab.make
blanchet@38172
  1850
blanchet@35718
  1851
fun const_def_table ctxt subst ts =
blanchet@35807
  1852
  def_table_for (map prop_of o Nitpick_Defs.get) ctxt subst
blanchet@35718
  1853
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@35718
  1854
          (map pair_for_prop ts)
blanchet@38172
  1855
blanchet@38172
  1856
fun paired_with_consts t = map (rpair t) (Term.add_const_names t [])
blanchet@35718
  1857
fun const_nondef_table ts =
blanchet@35807
  1858
  fold (append o paired_with_consts) ts [] |> AList.group (op =) |> Symtab.make
blanchet@38172
  1859
blanchet@38201
  1860
fun const_simp_table ctxt =
blanchet@38202
  1861
  def_table_for (map_filter (equationalize_term ctxt "nitpick_simp" o prop_of)
blanchet@38201
  1862
                 o Nitpick_Simps.get) ctxt
blanchet@38201
  1863
fun const_psimp_table ctxt =
blanchet@38202
  1864
  def_table_for (map_filter (equationalize_term ctxt "nitpick_psimp" o prop_of)
blanchet@38201
  1865
                 o Nitpick_Psimps.get) ctxt
blanchet@38172
  1866
blanchet@35807
  1867
fun const_choice_spec_table ctxt subst =
blanchet@35807
  1868
  map (subst_atomic subst o prop_of) (Nitpick_Choice_Specs.get ctxt)
blanchet@35807
  1869
  |> const_nondef_table
blanchet@38172
  1870
blanchet@35718
  1871
fun inductive_intro_table ctxt subst def_table =
blanchet@37264
  1872
  let val thy = ProofContext.theory_of ctxt in
blanchet@37264
  1873
    def_table_for
blanchet@37264
  1874
        (maps (map (unfold_mutually_inductive_preds thy def_table o prop_of)
blanchet@37264
  1875
               o snd o snd)
blanchet@37264
  1876
         o filter (fn (cat, _) => cat = Spec_Rules.Inductive orelse
blanchet@37264
  1877
                                  cat = Spec_Rules.Co_Inductive)
blanchet@37264
  1878
         o Spec_Rules.get) ctxt subst
blanchet@37264
  1879
  end
blanchet@38172
  1880
blanchet@35718
  1881
fun ground_theorem_table thy =
blanchet@35718
  1882
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@35718
  1883
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@35718
  1884
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@35718
  1885
blanchet@35807
  1886
(* TODO: Move to "Nitpick.thy" *)
blanchet@35718
  1887
val basic_ersatz_table =
blanchet@37213
  1888
  [(@{const_name card}, @{const_name card'}),
blanchet@35718
  1889
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@35718
  1890
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@35718
  1891
   (@{const_name wf}, @{const_name wf'}),
blanchet@35718
  1892
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@35718
  1893
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@35718
  1894
blanchet@38240
  1895
fun ersatz_table ctxt =
blanchet@38240
  1896
 basic_ersatz_table
blanchet@38240
  1897
 |> fold (append o snd) (#frac_types (Data.get (Context.Proof ctxt)))
blanchet@35718
  1898
blanchet@35718
  1899
fun add_simps simp_table s eqs =
blanchet@35718
  1900
  Unsynchronized.change simp_table
blanchet@35718
  1901
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@35718
  1902
blanchet@37256
  1903
fun inverse_axioms_for_rep_fun ctxt (x as (_, T)) =
blanchet@37256
  1904
  let
blanchet@37256
  1905
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1906
    val abs_T = domain_type T
blanchet@37256
  1907
  in
blanchet@37256
  1908
    typedef_info ctxt (fst (dest_Type abs_T)) |> the
blanchet@35718
  1909
    |> pairf #Abs_inverse #Rep_inverse
blanchet@36555
  1910
    |> pairself (specialize_type thy x o prop_of o the)
blanchet@35718
  1911
    ||> single |> op ::
blanchet@35718
  1912
  end
blanchet@37256
  1913
fun optimized_typedef_axioms ctxt (abs_z as (abs_s, _)) =
blanchet@37256
  1914
  let
blanchet@37256
  1915
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1916
    val abs_T = Type abs_z
blanchet@37256
  1917
  in
blanchet@37256
  1918
    if is_univ_typedef ctxt abs_T then
blanchet@35718
  1919
      []
blanchet@37256
  1920
    else case typedef_info ctxt abs_s of
blanchet@35718
  1921
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@35718
  1922
      let
blanchet@38240
  1923
        val rep_T = varify_and_instantiate_type ctxt abs_type abs_T rep_type
blanchet@35718
  1924
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@35718
  1925
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@35718
  1926
        val set_t' =
blanchet@35718
  1927
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@36555
  1928
                      |> specialize_type thy (dest_Const rep_t)
blanchet@35718
  1929
                      |> HOLogic.dest_mem |> snd
blanchet@35718
  1930
      in
blanchet@35718
  1931
        [HOLogic.all_const abs_T
blanchet@35718
  1932
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@35718
  1933
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@35718
  1934
        |> map HOLogic.mk_Trueprop
blanchet@35718
  1935
      end
blanchet@35718
  1936
    | NONE => []
blanchet@35718
  1937
  end
blanchet@35718
  1938
fun optimized_quot_type_axioms ctxt stds abs_z =
blanchet@35718
  1939
  let
blanchet@35718
  1940
    val thy = ProofContext.theory_of ctxt
blanchet@35718
  1941
    val abs_T = Type abs_z
blanchet@35718
  1942
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@38243
  1943
    val (equiv_rel, partial) = equiv_relation_for_quot_type thy abs_T
blanchet@35718
  1944
    val a_var = Var (("a", 0), abs_T)
blanchet@35718
  1945
    val x_var = Var (("x", 0), rep_T)
blanchet@35718
  1946
    val y_var = Var (("y", 0), rep_T)
blanchet@35718
  1947
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@37256
  1948
    val sel_a_t = select_nth_constr_arg ctxt stds x a_var 0 rep_T
blanchet@38207
  1949
    val normal_fun =
blanchet@38207
  1950
      Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T)
blanchet@38207
  1951
    val normal_x = normal_fun $ x_var
blanchet@38207
  1952
    val normal_y = normal_fun $ y_var
blanchet@35718
  1953
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@35718
  1954
  in
blanchet@38207
  1955
    [Logic.mk_equals (normal_fun $ sel_a_t, sel_a_t),
blanchet@35718
  1956
     Logic.list_implies
blanchet@35718
  1957
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@35718
  1958
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@35718
  1959
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@35718
  1960
           Logic.mk_equals (normal_x, normal_y)),
blanchet@35718
  1961
     Logic.list_implies
blanchet@35718
  1962
         ([HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)),
blanchet@35718
  1963
           HOLogic.mk_Trueprop (@{const Not} $ HOLogic.mk_eq (normal_x, x_var))],
blanchet@35718
  1964
          HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@38243
  1965
    |> partial ? cons (HOLogic.mk_Trueprop (equiv_rel $ sel_a_t $ sel_a_t))
blanchet@35718
  1966
  end
blanchet@35718
  1967
blanchet@38240
  1968
fun codatatype_bisim_axioms (hol_ctxt as {thy, ctxt, stds, ...}) T =
blanchet@33192
  1969
  let
blanchet@35070
  1970
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1971
    val set_T = T --> bool_T
blanchet@33192
  1972
    val iter_T = @{typ bisim_iterator}
blanchet@33192
  1973
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1974
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1975
    val n_var_minus_1 =
blanchet@35671
  1976
      Const (@{const_name safe_The}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1977
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1978
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1979
    val x_var = Var (("x", 0), T)
blanchet@33192
  1980
    val y_var = Var (("y", 0), T)
blanchet@38161
  1981
    fun bisim_const T =
blanchet@38161
  1982
      Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1983
    fun nth_sub_bisim x n nth_T =
blanchet@38240
  1984
      (if is_codatatype ctxt nth_T then bisim_const nth_T $ n_var_minus_1
blanchet@33192
  1985
       else HOLogic.eq_const nth_T)
blanchet@37256
  1986
      $ select_nth_constr_arg ctxt stds x x_var n nth_T
blanchet@37256
  1987
      $ select_nth_constr_arg ctxt stds x y_var n nth_T
blanchet@33192
  1988
    fun case_func (x as (_, T)) =
blanchet@33192
  1989
      let
blanchet@33192
  1990
        val arg_Ts = binder_types T
blanchet@33192
  1991
        val core_t =
blanchet@35070
  1992
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1993
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1994
          |> foldr1 s_conj
blanchet@33192
  1995
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1996
  in
blanchet@38163
  1997
    [HOLogic.mk_imp
blanchet@38163
  1998
       (HOLogic.mk_disj (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T,
blanchet@38163
  1999
            s_betapply [] (optimized_case_def hol_ctxt T bool_T
blanchet@38163
  2000
                                              (map case_func xs), x_var)),
blanchet@38163
  2001
        bisim_const T $ n_var $ x_var $ y_var),
blanchet@38161
  2002
     HOLogic.eq_const set_T $ (bisim_const T $ bisim_max $ x_var)
blanchet@34124
  2003
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  2004
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  2005
    |> map HOLogic.mk_Trueprop
blanchet@33192
  2006
  end
blanchet@33192
  2007
blanchet@33192
  2008
exception NO_TRIPLE of unit
blanchet@33192
  2009
blanchet@33192
  2010
fun triple_for_intro_rule thy x t =
blanchet@33192
  2011
  let
wenzelm@35625
  2012
    val prems = Logic.strip_imp_prems t |> map (Object_Logic.atomize_term thy)
wenzelm@35625
  2013
    val concl = Logic.strip_imp_concl t |> Object_Logic.atomize_term thy
blanchet@34121
  2014
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@36385
  2015
    val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  2016
  in
blanchet@33192
  2017
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  2018
  end
blanchet@33192
  2019
blanchet@33192
  2020
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  2021
fun wf_constraint_for rel side concl main =
blanchet@33192
  2022
  let
blanchet@37269
  2023
    val core = HOLogic.mk_mem (HOLogic.mk_prod
blanchet@37269
  2024
                               (pairself tuple_for_args (main, concl)), Var rel)
blanchet@33192
  2025
    val t = List.foldl HOLogic.mk_imp core side
blanchet@37269
  2026
    val vars = filter_out (curry (op =) rel) (Term.add_vars t [])
blanchet@33192
  2027
  in
blanchet@33192
  2028
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  2029
                      HOLogic.all_const T
blanchet@33192
  2030
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  2031
                  (t, vars)
blanchet@33192
  2032
  end
blanchet@33192
  2033
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  2034
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  2035
blanchet@33192
  2036
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  2037
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  2038
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  2039
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  2040
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  2041
blanchet@35181
  2042
val max_cached_wfs = 50
blanchet@35181
  2043
val cached_timeout =
blanchet@35181
  2044
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  2045
val cached_wf_props =
blanchet@35181
  2046
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  2047
krauss@33351
  2048
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  2049
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  2050
blanchet@33580
  2051
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  2052
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  2053
         : hol_context) (x as (_, T)) =
blanchet@35220
  2054
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  2055
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  2056
                      [Const x])
blanchet@33192
  2057
  | intro_ts =>
blanchet@33192
  2058
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  2059
          |> filter_out (null o #2) of
blanchet@33192
  2060
       [] => true
blanchet@33192
  2061
     | triples =>
blanchet@33192
  2062
       let
blanchet@33192
  2063
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  2064
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  2065
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  2066
         val rel = (("R", j), rel_T)
blanchet@33192
  2067
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  2068
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  2069
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  2070
         val _ = if debug then
blanchet@33192
  2071
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  2072
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  2073
                 else
blanchet@33192
  2074
                   ()
blanchet@33192
  2075
       in
blanchet@35181
  2076
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  2077
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  2078
           ()
blanchet@33557
  2079
         else
blanchet@35181
  2080
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  2081
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  2082
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  2083
           SOME wf => wf
blanchet@33192
  2084
         | NONE =>
blanchet@33192
  2085
           let
blanchet@33192
  2086
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  2087
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  2088
                             termination_tacs
blanchet@35181
  2089
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  2090
       end)
blanchet@35309
  2091
    handle List.Empty => false | NO_TRIPLE () => false
blanchet@33192
  2092
blanchet@35070
  2093
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  2094
blanchet@33192
  2095
fun is_well_founded_inductive_pred
blanchet@35070
  2096
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  2097
        (x as (s, _)) =
blanchet@33192
  2098
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  2099
    SOME (SOME b) => b
blanchet@34936
  2100
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  2101
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  2102
           SOME (_, wf) => wf
blanchet@35181
  2103
         | NONE =>
blanchet@35181
  2104
           let
blanchet@35181
  2105
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  2106
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  2107
           in
blanchet@35181
  2108
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  2109
           end
blanchet@33192
  2110
blanchet@35280
  2111
fun ap_curry [_] _ t = t
blanchet@35280
  2112
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  2113
    let val n = length arg_Ts in
blanchet@33192
  2114
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  2115
                incr_boundvars n t
blanchet@33192
  2116
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  2117
    end
blanchet@33192
  2118
blanchet@33192
  2119
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  2120
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  2121
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  2122
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  2123
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  2124
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  2125
blanchet@33192
  2126
val is_linear_inductive_pred_def =
blanchet@33192
  2127
  let
blanchet@33192
  2128
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  2129
        do_disjunct (j + 1) t2
blanchet@33192
  2130
      | do_disjunct j t =
blanchet@33192
  2131
        case num_occs_of_bound_in_term j t of
blanchet@33192
  2132
          0 => true
blanchet@35070
  2133
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  2134
        | _ => false
blanchet@33192
  2135
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2136
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  2137
          case length xs of
blanchet@33192
  2138
            1 => false
blanchet@35070
  2139
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  2140
        end
blanchet@33192
  2141
      | do_lfp_def _ = false
blanchet@33192
  2142
  in do_lfp_def o strip_abs_body end
blanchet@33192
  2143
blanchet@33851
  2144
fun n_ptuple_paths 0 = []
blanchet@33851
  2145
  | n_ptuple_paths 1 = []
blanchet@33851
  2146
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  2147
<