src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Sat Sep 11 10:13:51 2010 +0200 (2010-09-11)
changeset 39315 27f7b7748425
parent 38864 4abe644fcea5
child 39345 062c10ff848c
permissions -rw-r--r--
always handle type variables in typedefs as global
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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 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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val unrolled_prefix = nitpick_prefix ^ "unroll" ^ name_sep
blanchet@33192
   298
val base_prefix = nitpick_prefix ^ "base" ^ name_sep
blanchet@33192
   299
val step_prefix = nitpick_prefix ^ "step" ^ name_sep
blanchet@33192
   300
val ubfp_prefix = nitpick_prefix ^ "ubfp" ^ name_sep
blanchet@33192
   301
val lbfp_prefix = nitpick_prefix ^ "lbfp" ^ name_sep
blanchet@35311
   302
val quot_normal_prefix = nitpick_prefix ^ "qn" ^ name_sep
blanchet@33192
   303
val skolem_prefix = nitpick_prefix ^ "sk"
blanchet@33192
   304
val special_prefix = nitpick_prefix ^ "sp"
blanchet@33192
   305
val uncurry_prefix = nitpick_prefix ^ "unc"
blanchet@33192
   306
val eval_prefix = nitpick_prefix ^ "eval"
blanchet@33192
   307
val iter_var_prefix = "i"
blanchet@35718
   308
blanchet@35718
   309
(** Constant/type information and term/type manipulation **)
blanchet@33192
   310
blanchet@33192
   311
fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
blanchet@35311
   312
fun quot_normal_name_for_type ctxt T =
blanchet@35311
   313
  quot_normal_prefix ^ unyxml (Syntax.string_of_typ ctxt T)
blanchet@33192
   314
blanchet@33192
   315
val strip_first_name_sep =
blanchet@33192
   316
  Substring.full #> Substring.position name_sep ##> Substring.triml 1
blanchet@33192
   317
  #> pairself Substring.string
blanchet@33192
   318
fun original_name s =
blanchet@33192
   319
  if String.isPrefix nitpick_prefix s then
blanchet@33192
   320
    case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
blanchet@33192
   321
  else
blanchet@33192
   322
    s
blanchet@35718
   323
blanchet@37476
   324
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@37476
   325
blanchet@37476
   326
fun let_var s = (nitpick_prefix ^ s, 999)
blanchet@37476
   327
val let_inline_threshold = 20
blanchet@37476
   328
blanchet@37476
   329
fun s_let s n abs_T body_T f t =
blanchet@37476
   330
  if (n - 1) * (size_of_term t - 1) <= let_inline_threshold then
blanchet@37476
   331
    f t
blanchet@37476
   332
  else
blanchet@37476
   333
    let val z = (let_var s, abs_T) in
blanchet@37476
   334
      Const (@{const_name Let}, abs_T --> (abs_T --> body_T) --> body_T)
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   335
      $ t $ abs_var z (incr_boundvars 1 (f (Var z)))
blanchet@37476
   336
    end
blanchet@37476
   337
blanchet@37476
   338
fun loose_bvar1_count (Bound i, k) = if i = k then 1 else 0
blanchet@37476
   339
  | loose_bvar1_count (t1 $ t2, k) =
blanchet@37476
   340
    loose_bvar1_count (t1, k) + loose_bvar1_count (t2, k)
blanchet@37476
   341
  | loose_bvar1_count (Abs (_, _, t), k) = loose_bvar1_count (t, k + 1)
blanchet@37476
   342
  | loose_bvar1_count _ = 0
blanchet@37476
   343
blanchet@37476
   344
fun s_betapply _ (Const (@{const_name If}, _) $ @{const True} $ t1', _) = t1'
blanchet@37476
   345
  | s_betapply _ (Const (@{const_name If}, _) $ @{const False} $ _, t2) = t2
blanchet@37476
   346
  | s_betapply Ts (Const (@{const_name Let},
blanchet@37476
   347
                          Type (_, [bound_T, Type (_, [_, body_T])]))
blanchet@37476
   348
                   $ t12 $ Abs (s, T, t13'), t2) =
blanchet@37476
   349
    let val body_T' = range_type body_T in
blanchet@37476
   350
      Const (@{const_name Let}, bound_T --> (bound_T --> body_T') --> body_T')
blanchet@37476
   351
      $ t12 $ Abs (s, T, s_betapply (T :: Ts) (t13', incr_boundvars 1 t2))
blanchet@37476
   352
    end
blanchet@37476
   353
  | s_betapply Ts (t1 as Abs (s1, T1, t1'), t2) =
blanchet@37476
   354
    (s_let s1 (loose_bvar1_count (t1', 0)) T1 (fastype_of1 (T1 :: Ts, t1'))
blanchet@37476
   355
              (curry betapply t1) t2
blanchet@37476
   356
     handle TERM _ => betapply (t1, t2)) (* FIXME: fix all uses *)
blanchet@37476
   357
  | s_betapply _ (t1, t2) = t1 $ t2
blanchet@37476
   358
fun s_betapplys Ts = Library.foldl (s_betapply Ts)
blanchet@37476
   359
blanchet@37476
   360
fun s_beta_norm Ts t =
blanchet@37476
   361
  let
blanchet@37476
   362
    fun aux _ (Var _) = raise Same.SAME
blanchet@37476
   363
      | aux Ts (Abs (s, T, t')) = Abs (s, T, aux (T :: Ts) t')
blanchet@37476
   364
      | aux Ts ((t1 as Abs _) $ t2) =
blanchet@37476
   365
        Same.commit (aux Ts) (s_betapply Ts (t1, t2))
blanchet@37476
   366
      | aux Ts (t1 $ t2) =
blanchet@37476
   367
        ((case aux Ts t1 of
blanchet@37476
   368
           t1 as Abs _ => Same.commit (aux Ts) (s_betapply Ts (t1, t2))
blanchet@37476
   369
         | t1 => t1 $ Same.commit (aux Ts) t2)
blanchet@37476
   370
        handle Same.SAME => t1 $ aux Ts t2)
blanchet@37476
   371
      | aux _ _ = raise Same.SAME
blanchet@37476
   372
  in aux Ts t handle Same.SAME => t end
blanchet@33192
   373
blanchet@34998
   374
fun s_conj (t1, @{const True}) = t1
blanchet@34998
   375
  | s_conj (@{const True}, t2) = t2
blanchet@34998
   376
  | s_conj (t1, t2) =
blanchet@34998
   377
    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
blanchet@34998
   378
    else HOLogic.mk_conj (t1, t2)
blanchet@34998
   379
fun s_disj (t1, @{const False}) = t1
blanchet@34998
   380
  | s_disj (@{const False}, t2) = t2
blanchet@34998
   381
  | s_disj (t1, t2) =
blanchet@34998
   382
    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
blanchet@34998
   383
    else HOLogic.mk_disj (t1, t2)
blanchet@34998
   384
blanchet@34998
   385
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
blanchet@34998
   386
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
blanchet@34998
   387
  | strip_connective _ t = [t]
blanchet@35280
   388
fun strip_any_connective (t as (t0 $ _ $ _)) =
haftmann@38795
   389
    if t0 = @{const HOL.conj} orelse t0 = @{const HOL.disj} then
blanchet@34998
   390
      (strip_connective t0 t, t0)
blanchet@34998
   391
    else
blanchet@34998
   392
      ([t], @{const Not})
blanchet@34998
   393
  | strip_any_connective t = ([t], @{const Not})
haftmann@38795
   394
val conjuncts_of = strip_connective @{const HOL.conj}
haftmann@38795
   395
val disjuncts_of = strip_connective @{const HOL.disj}
blanchet@34998
   396
blanchet@33192
   397
(* When you add constants to these lists, make sure to handle them in
blanchet@33232
   398
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
blanchet@33192
   399
   well. *)
blanchet@33192
   400
val built_in_consts =
blanchet@33192
   401
  [(@{const_name all}, 1),
blanchet@33192
   402
   (@{const_name "=="}, 2),
blanchet@33192
   403
   (@{const_name "==>"}, 2),
blanchet@33192
   404
   (@{const_name Pure.conjunction}, 2),
blanchet@33192
   405
   (@{const_name Trueprop}, 1),
blanchet@33192
   406
   (@{const_name Not}, 1),
blanchet@33192
   407
   (@{const_name False}, 0),
blanchet@33192
   408
   (@{const_name True}, 0),
blanchet@33192
   409
   (@{const_name All}, 1),
blanchet@33192
   410
   (@{const_name Ex}, 1),
haftmann@38864
   411
   (@{const_name HOL.eq}, 1),
haftmann@38795
   412
   (@{const_name HOL.conj}, 2),
haftmann@38795
   413
   (@{const_name HOL.disj}, 2),
haftmann@38786
   414
   (@{const_name HOL.implies}, 2),
blanchet@33192
   415
   (@{const_name If}, 3),
blanchet@33192
   416
   (@{const_name Let}, 2),
blanchet@33192
   417
   (@{const_name Pair}, 2),
blanchet@33192
   418
   (@{const_name fst}, 1),
blanchet@33192
   419
   (@{const_name snd}, 1),
blanchet@33192
   420
   (@{const_name Id}, 0),
blanchet@33192
   421
   (@{const_name converse}, 1),
blanchet@33192
   422
   (@{const_name trancl}, 1),
blanchet@33192
   423
   (@{const_name rel_comp}, 2),
blanchet@33192
   424
   (@{const_name image}, 2),
blanchet@33192
   425
   (@{const_name finite}, 1),
blanchet@34936
   426
   (@{const_name unknown}, 0),
blanchet@34936
   427
   (@{const_name is_unknown}, 1),
blanchet@35671
   428
   (@{const_name safe_The}, 1),
blanchet@35671
   429
   (@{const_name safe_Eps}, 1),
blanchet@33192
   430
   (@{const_name Frac}, 0),
blanchet@33192
   431
   (@{const_name norm_frac}, 0)]
blanchet@35220
   432
val built_in_nat_consts =
blanchet@35220
   433
  [(@{const_name Suc}, 0),
blanchet@35220
   434
   (@{const_name nat}, 0),
blanchet@35220
   435
   (@{const_name nat_gcd}, 0),
blanchet@35220
   436
   (@{const_name nat_lcm}, 0)]
blanchet@33192
   437
val built_in_descr_consts =
blanchet@33192
   438
  [(@{const_name The}, 1),
blanchet@33192
   439
   (@{const_name Eps}, 1)]
blanchet@33192
   440
val built_in_typed_consts =
blanchet@35220
   441
  [((@{const_name zero_class.zero}, int_T), 0),
blanchet@35220
   442
   ((@{const_name one_class.one}, int_T), 0),
blanchet@35220
   443
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   444
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   445
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
blanchet@35220
   446
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
blanchet@35220
   447
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
blanchet@35220
   448
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
blanchet@35220
   449
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
blanchet@35220
   450
val built_in_typed_nat_consts =
blanchet@35220
   451
  [((@{const_name zero_class.zero}, nat_T), 0),
blanchet@35220
   452
   ((@{const_name one_class.one}, nat_T), 0),
blanchet@35220
   453
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   454
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   455
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   456
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   457
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   458
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   459
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   460
val built_in_set_consts =
blanchet@37476
   461
  [(@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   462
blanchet@35190
   463
fun unarize_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   464
  | unarize_type @{typ "signed_bit word"} = int_T
blanchet@35190
   465
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
blanchet@35190
   466
  | unarize_type T = T
blanchet@35665
   467
fun unarize_unbox_etc_type (Type (@{type_name fin_fun}, Ts)) =
blanchet@35665
   468
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   469
  | unarize_unbox_etc_type (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   470
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   471
  | unarize_unbox_etc_type (Type (@{type_name pair_box}, Ts)) =
blanchet@38190
   472
    Type (@{type_name prod}, map unarize_unbox_etc_type Ts)
blanchet@35665
   473
  | unarize_unbox_etc_type @{typ "unsigned_bit word"} = nat_T
blanchet@35665
   474
  | unarize_unbox_etc_type @{typ "signed_bit word"} = int_T
blanchet@35665
   475
  | unarize_unbox_etc_type (Type (s, Ts as _ :: _)) =
blanchet@35665
   476
    Type (s, map unarize_unbox_etc_type Ts)
blanchet@35665
   477
  | unarize_unbox_etc_type T = T
blanchet@35280
   478
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   479
  | uniterize_type @{typ bisim_iterator} = nat_T
blanchet@35280
   480
  | uniterize_type T = T
blanchet@35665
   481
val uniterize_unarize_unbox_etc_type = uniterize_type o unarize_unbox_etc_type
blanchet@35280
   482
blanchet@35665
   483
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_unbox_etc_type
blanchet@38188
   484
fun pretty_for_type ctxt = Syntax.pretty_typ ctxt o unarize_unbox_etc_type
blanchet@33192
   485
blanchet@33192
   486
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@34121
   487
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   488
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@34121
   489
fun short_name s =
blanchet@33192
   490
  case space_explode name_sep s of
blanchet@33192
   491
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   492
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   493
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   494
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   495
  | shorten_names_in_type T = T
blanchet@34121
   496
val shorten_names_in_term =
blanchet@34121
   497
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   498
  #> map_types shorten_names_in_type
blanchet@33192
   499
blanchet@35665
   500
fun strict_type_match thy (T1, T2) =
blanchet@33192
   501
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   502
  handle Type.TYPE_MATCH => false
blanchet@35665
   503
fun type_match thy = strict_type_match thy o pairself unarize_unbox_etc_type
blanchet@33192
   504
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   505
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   506
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   507
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   508
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   509
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   510
blanchet@35711
   511
fun frac_from_term_pair T t1 t2 =
blanchet@35711
   512
  case snd (HOLogic.dest_number t1) of
blanchet@35711
   513
    0 => HOLogic.mk_number T 0
blanchet@35711
   514
  | n1 => case snd (HOLogic.dest_number t2) of
blanchet@35711
   515
            1 => HOLogic.mk_number T n1
blanchet@35711
   516
          | n2 => Const (@{const_name divide}, T --> T --> T)
blanchet@35711
   517
                  $ HOLogic.mk_number T n1 $ HOLogic.mk_number T n2
blanchet@35711
   518
blanchet@33192
   519
fun is_TFree (TFree _) = true
blanchet@33192
   520
  | is_TFree _ = false
blanchet@35665
   521
fun is_higher_order_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   522
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   523
  | is_higher_order_type _ = false
blanchet@35665
   524
fun is_fun_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   525
  | is_fun_type _ = false
blanchet@35665
   526
fun is_set_type (Type (@{type_name fun}, [_, @{typ bool}])) = true
blanchet@33192
   527
  | is_set_type _ = false
blanchet@38190
   528
fun is_pair_type (Type (@{type_name prod}, _)) = true
blanchet@33192
   529
  | is_pair_type _ = false
blanchet@33192
   530
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   531
  | is_lfp_iterator_type _ = false
blanchet@33192
   532
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   533
  | is_gfp_iterator_type _ = false
blanchet@33192
   534
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   535
fun is_iterator_type T =
blanchet@35280
   536
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   537
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   538
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   539
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   540
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   541
  | is_word_type _ = false
blanchet@35280
   542
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   543
val is_record_type = not o null o Record.dest_recTs
blanchet@38240
   544
fun is_frac_type ctxt (Type (s, [])) =
blanchet@38240
   545
    s |> AList.lookup (op =) (#frac_types (Data.get (Context.Proof ctxt)))
blanchet@38240
   546
      |> these |> null |> not
blanchet@33192
   547
  | is_frac_type _ _ = false
blanchet@38240
   548
fun is_number_type ctxt = is_integer_like_type orf is_frac_type ctxt
blanchet@33192
   549
blanchet@33192
   550
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   551
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   552
        binder_types T)
blanchet@35718
   553
fun const_for_iterator_type (Type (s, Ts)) =
blanchet@35718
   554
    (strip_first_name_sep s |> snd, Ts ---> bool_T)
blanchet@33192
   555
  | const_for_iterator_type T =
blanchet@33232
   556
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   557
blanchet@33192
   558
fun strip_n_binders 0 T = ([], T)
blanchet@35665
   559
  | strip_n_binders n (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
   560
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   561
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   562
    strip_n_binders n (Type (@{type_name fun}, Ts))
blanchet@33232
   563
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   564
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   565
blanchet@38190
   566
fun num_factors_in_type (Type (@{type_name prod}, [T1, T2])) =
blanchet@33192
   567
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   568
  | num_factors_in_type _ = 1
blanchet@35665
   569
fun num_binder_types (Type (@{type_name fun}, [_, T2])) =
blanchet@35665
   570
    1 + num_binder_types T2
blanchet@33192
   571
  | num_binder_types _ = 0
blanchet@33192
   572
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   573
fun maybe_curried_binder_types T =
blanchet@33192
   574
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   575
blanchet@33192
   576
fun mk_flat_tuple _ [t] = t
blanchet@38190
   577
  | mk_flat_tuple (Type (@{type_name prod}, [T1, T2])) (t :: ts) =
blanchet@33192
   578
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   579
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   580
fun dest_n_tuple 1 t = [t]
blanchet@33192
   581
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   582
blanchet@35220
   583
type typedef_info =
blanchet@35220
   584
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   585
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   586
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   587
blanchet@37256
   588
fun typedef_info ctxt s =
blanchet@38240
   589
  if is_frac_type ctxt (Type (s, [])) then
blanchet@38240
   590
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@38240
   591
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@38240
   592
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@38240
   593
                          |> Logic.varify_global,
blanchet@38240
   594
          set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@38240
   595
  else case Typedef.get_info ctxt s of
blanchet@38240
   596
    (* When several entries are returned, it shouldn't matter much which one
blanchet@38240
   597
       we take (according to Florian Haftmann). *)
blanchet@39315
   598
    (* The "Logic.varifyT_global" calls are a temporary hack because these
blanchet@39315
   599
       types's type variables sometimes clash with locally fixed type variables.
blanchet@39315
   600
       Remove these calls once "Typedef" is fully localized. *)
blanchet@38240
   601
    ({abs_type, rep_type, Abs_name, Rep_name, ...},
blanchet@38240
   602
     {set_def, Rep, Abs_inverse, Rep_inverse, ...}) :: _ =>
blanchet@39315
   603
    SOME {abs_type = Logic.varifyT_global abs_type,
blanchet@39315
   604
          rep_type = Logic.varifyT_global rep_type, Abs_name = Abs_name,
blanchet@38240
   605
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@38240
   606
          set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@38240
   607
          Rep_inverse = SOME Rep_inverse}
blanchet@38240
   608
  | _ => NONE
blanchet@35220
   609
blanchet@35220
   610
val is_typedef = is_some oo typedef_info
blanchet@35220
   611
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   612
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   613
blanchet@34121
   614
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   615
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   616
fun is_basic_datatype thy stds s =
blanchet@38190
   617
  member (op =) [@{type_name prod}, @{type_name bool}, @{type_name int},
blanchet@38190
   618
                 "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   619
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   620
blanchet@38240
   621
(* TODO: use "Term_Subst.instantiateT" instead? *)
blanchet@33192
   622
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   623
  Same.commit (Envir.subst_type_same
blanchet@35311
   624
                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
blanchet@33192
   625
  handle Type.TYPE_MATCH =>
blanchet@33232
   626
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@38240
   627
fun varify_and_instantiate_type ctxt T1 T1' T2 =
blanchet@38240
   628
  let val thy = ProofContext.theory_of ctxt in
blanchet@38240
   629
    instantiate_type thy (varify_type ctxt T1) T1' (varify_type ctxt T2)
blanchet@38240
   630
  end
blanchet@33192
   631
blanchet@38240
   632
fun repair_constr_type ctxt body_T' T =
blanchet@38240
   633
  varify_and_instantiate_type ctxt (body_type T) body_T' T
blanchet@33192
   634
blanchet@38240
   635
fun register_frac_type_generic frac_s ersaetze generic =
blanchet@33192
   636
  let
blanchet@38240
   637
    val {frac_types, codatatypes} = Data.get generic
blanchet@33192
   638
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@38240
   639
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} generic end
blanchet@38284
   640
(* TODO: Consider morphism. *)
blanchet@38284
   641
fun register_frac_type frac_s ersaetze (_ : morphism) =
blanchet@38284
   642
  register_frac_type_generic frac_s ersaetze
blanchet@38240
   643
val register_frac_type_global = Context.theory_map oo register_frac_type_generic
blanchet@33192
   644
blanchet@38240
   645
fun unregister_frac_type_generic frac_s = register_frac_type_generic frac_s []
blanchet@38284
   646
(* TODO: Consider morphism. *)
blanchet@38284
   647
fun unregister_frac_type frac_s (_ : morphism) =
blanchet@38284
   648
  unregister_frac_type_generic frac_s
blanchet@38240
   649
val unregister_frac_type_global =
blanchet@38240
   650
  Context.theory_map o unregister_frac_type_generic
blanchet@38240
   651
blanchet@38240
   652
fun register_codatatype_generic co_T case_name constr_xs generic =
blanchet@33192
   653
  let
blanchet@38240
   654
    val ctxt = Context.proof_of generic
blanchet@38240
   655
    val thy = Context.theory_of generic
blanchet@38240
   656
    val {frac_types, codatatypes} = Data.get generic
blanchet@38240
   657
    val constr_xs = map (apsnd (repair_constr_type ctxt co_T)) constr_xs
blanchet@33192
   658
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   659
    val _ =
blanchet@34936
   660
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35665
   661
         co_s <> @{type_name fun} andalso
blanchet@35220
   662
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   663
        ()
blanchet@34121
   664
      else
blanchet@38242
   665
        raise TYPE ("Nitpick_HOL.register_codatatype_generic", [co_T], [])
blanchet@33192
   666
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   667
                                   codatatypes
blanchet@38240
   668
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} generic end
blanchet@38284
   669
(* TODO: Consider morphism. *)
blanchet@38284
   670
fun register_codatatype co_T case_name constr_xs (_ : morphism) =
blanchet@38284
   671
  register_codatatype_generic co_T case_name constr_xs
blanchet@38240
   672
val register_codatatype_global =
blanchet@38240
   673
  Context.theory_map ooo register_codatatype_generic
blanchet@33192
   674
blanchet@38240
   675
fun unregister_codatatype_generic co_T = register_codatatype_generic co_T "" []
blanchet@38284
   676
(* TODO: Consider morphism. *)
blanchet@38284
   677
fun unregister_codatatype co_T (_ : morphism) =
blanchet@38284
   678
  unregister_codatatype_generic co_T
blanchet@38240
   679
val unregister_codatatype_global =
blanchet@38240
   680
  Context.theory_map o unregister_codatatype_generic
blanchet@38240
   681
blanchet@38240
   682
fun is_codatatype ctxt (Type (s, _)) =
blanchet@38240
   683
    s |> AList.lookup (op =) (#codatatypes (Data.get (Context.Proof ctxt)))
blanchet@38240
   684
      |> Option.map snd |> these |> null |> not
blanchet@33192
   685
  | is_codatatype _ _ = false
blanchet@38215
   686
fun is_real_quot_type thy (Type (s, _)) =
blanchet@38215
   687
    is_some (Quotient_Info.quotdata_lookup_raw thy s)
blanchet@38215
   688
  | is_real_quot_type _ _ = false
blanchet@38240
   689
fun is_quot_type ctxt T =
blanchet@38240
   690
  let val thy = ProofContext.theory_of ctxt in
blanchet@38240
   691
    is_real_quot_type thy T andalso not (is_codatatype ctxt T)
blanchet@38240
   692
  end
blanchet@37256
   693
fun is_pure_typedef ctxt (T as Type (s, _)) =
blanchet@37256
   694
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   695
      is_typedef ctxt s andalso
blanchet@38215
   696
      not (is_real_datatype thy s orelse is_real_quot_type thy T orelse
blanchet@38240
   697
           is_codatatype ctxt T orelse is_record_type T orelse
blanchet@37256
   698
           is_integer_like_type T)
blanchet@37256
   699
    end
blanchet@33192
   700
  | is_pure_typedef _ _ = false
blanchet@37256
   701
fun is_univ_typedef ctxt (Type (s, _)) =
blanchet@37256
   702
    (case typedef_info ctxt s of
blanchet@33192
   703
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@35332
   704
       let
blanchet@35332
   705
         val t_opt =
blanchet@35332
   706
           case set_def of
blanchet@35332
   707
             SOME thm => try (snd o Logic.dest_equals o prop_of) thm
blanchet@35332
   708
           | NONE => try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop)
blanchet@35332
   709
                         prop_of_Rep
blanchet@35332
   710
       in
blanchet@35332
   711
         case t_opt of
blanchet@35332
   712
           SOME (Const (@{const_name top}, _)) => true
blanchet@35386
   713
           (* "Multiset.multiset" *)
blanchet@35332
   714
         | SOME (Const (@{const_name Collect}, _)
blanchet@35332
   715
                 $ Abs (_, _, Const (@{const_name finite}, _) $ _)) => true
blanchet@35386
   716
           (* "FinFun.finfun" *)
blanchet@35386
   717
         | SOME (Const (@{const_name Collect}, _) $ Abs (_, _,
blanchet@35386
   718
                     Const (@{const_name Ex}, _) $ Abs (_, _,
blanchet@35386
   719
                         Const (@{const_name finite}, _) $ _))) => true
blanchet@35332
   720
         | _ => false
blanchet@35332
   721
       end
blanchet@33192
   722
     | NONE => false)
blanchet@33192
   723
  | is_univ_typedef _ _ = false
blanchet@37256
   724
fun is_datatype ctxt stds (T as Type (s, _)) =
blanchet@37256
   725
    let val thy = ProofContext.theory_of ctxt in
blanchet@38240
   726
      (is_typedef ctxt s orelse is_codatatype ctxt T orelse
blanchet@38240
   727
       T = @{typ ind} orelse is_real_quot_type thy T) andalso
blanchet@38240
   728
      not (is_basic_datatype thy stds s)
blanchet@37256
   729
    end
blanchet@35220
   730
  | is_datatype _ _ _ = false
blanchet@33192
   731
blanchet@33192
   732
fun all_record_fields thy T =
blanchet@33192
   733
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   734
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   735
  end
blanchet@33192
   736
  handle TYPE _ => []
blanchet@35280
   737
fun is_record_constr (s, T) =
blanchet@33192
   738
  String.isSuffix Record.extN s andalso
blanchet@33192
   739
  let val dataT = body_type T in
blanchet@33192
   740
    is_record_type dataT andalso
blanchet@33192
   741
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   742
  end
blanchet@33192
   743
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   744
fun no_of_record_field thy s T1 =
blanchet@34121
   745
  find_index (curry (op =) s o fst)
blanchet@34121
   746
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@35665
   747
fun is_record_get thy (s, Type (@{type_name fun}, [T1, _])) =
blanchet@34121
   748
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   749
  | is_record_get _ _ = false
blanchet@33192
   750
fun is_record_update thy (s, T) =
blanchet@33192
   751
  String.isSuffix Record.updateN s andalso
blanchet@34121
   752
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   753
         (all_record_fields thy (body_type T))
blanchet@33192
   754
  handle TYPE _ => false
blanchet@37256
   755
fun is_abs_fun ctxt (s, Type (@{type_name fun}, [_, Type (s', _)])) =
blanchet@37256
   756
    (case typedef_info ctxt s' of
blanchet@33192
   757
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   758
     | NONE => false)
blanchet@33192
   759
  | is_abs_fun _ _ = false
blanchet@37256
   760
fun is_rep_fun ctxt (s, Type (@{type_name fun}, [Type (s', _), _])) =
blanchet@37256
   761
    (case typedef_info ctxt s' of
blanchet@33192
   762
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   763
     | NONE => false)
blanchet@33192
   764
  | is_rep_fun _ _ = false
blanchet@38215
   765
fun is_quot_abs_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@38215
   766
                                         [_, abs_T as Type (s', _)]))) =
blanchet@38240
   767
    try (Quotient_Term.absrep_const_chk Quotient_Term.AbsF ctxt) s'
blanchet@38240
   768
    = SOME (Const x) andalso not (is_codatatype ctxt abs_T)
blanchet@34936
   769
  | is_quot_abs_fun _ _ = false
blanchet@38215
   770
fun is_quot_rep_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@38215
   771
                                         [abs_T as Type (s', _), _]))) =
blanchet@38240
   772
    try (Quotient_Term.absrep_const_chk Quotient_Term.RepF ctxt) s'
blanchet@38240
   773
    = SOME (Const x) andalso not (is_codatatype ctxt abs_T)
blanchet@34936
   774
  | is_quot_rep_fun _ _ = false
blanchet@33192
   775
blanchet@37256
   776
fun mate_of_rep_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@37256
   777
                                         [T1 as Type (s', _), T2]))) =
blanchet@37256
   778
    (case typedef_info ctxt s' of
blanchet@35665
   779
       SOME {Abs_name, ...} => (Abs_name, Type (@{type_name fun}, [T2, T1]))
blanchet@33232
   780
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   781
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@35284
   782
fun rep_type_for_quot_type thy (T as Type (s, _)) =
blanchet@35284
   783
  let val {qtyp, rtyp, ...} = Quotient_Info.quotdata_lookup thy s in
blanchet@35284
   784
    instantiate_type thy qtyp T rtyp
blanchet@35284
   785
  end
blanchet@35284
   786
fun equiv_relation_for_quot_type thy (Type (s, Ts)) =
blanchet@35284
   787
    let
blanchet@38243
   788
      val {qtyp, equiv_rel, equiv_thm, ...} =
blanchet@38243
   789
        Quotient_Info.quotdata_lookup thy s
blanchet@38243
   790
      val partial =
blanchet@38243
   791
        case prop_of equiv_thm of
blanchet@38243
   792
          @{const Trueprop} $ (Const (@{const_name equivp}, _) $ _) => false
blanchet@38243
   793
        | @{const Trueprop} $ (Const (@{const_name part_equivp}, _) $ _) => true
blanchet@38243
   794
        | _ => raise NOT_SUPPORTED "Ill-formed quotient type equivalence \
blanchet@38243
   795
                                   \relation theorem"
blanchet@35284
   796
      val Ts' = qtyp |> dest_Type |> snd
blanchet@38243
   797
    in (subst_atomic_types (Ts' ~~ Ts) equiv_rel, partial) end
blanchet@34936
   798
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   799
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   800
blanchet@38240
   801
fun is_coconstr ctxt (s, T) =
blanchet@38240
   802
  case body_type T of
blanchet@38240
   803
    co_T as Type (co_s, _) =>
blanchet@38240
   804
    let val {codatatypes, ...} = Data.get (Context.Proof ctxt) in
blanchet@38240
   805
      exists (fn (s', T') => s = s' andalso repair_constr_type ctxt co_T T' = T)
blanchet@38240
   806
             (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@38240
   807
    end
blanchet@38240
   808
  | _ => false
blanchet@37256
   809
fun is_constr_like ctxt (s, T) =
blanchet@35665
   810
  member (op =) [@{const_name FinFun}, @{const_name FunBox},
blanchet@35665
   811
                 @{const_name PairBox}, @{const_name Quot},
blanchet@35665
   812
                 @{const_name Zero_Rep}, @{const_name Suc_Rep}] s orelse
blanchet@37256
   813
  let
blanchet@37256
   814
    val thy = ProofContext.theory_of ctxt
blanchet@37256
   815
    val (x as (_, T)) = (s, unarize_unbox_etc_type T)
blanchet@37256
   816
  in
blanchet@37260
   817
    is_real_constr thy x orelse is_record_constr x orelse
blanchet@37256
   818
    (is_abs_fun ctxt x andalso is_pure_typedef ctxt (range_type T)) orelse
blanchet@38240
   819
    is_coconstr ctxt x
blanchet@33192
   820
  end
blanchet@37256
   821
fun is_stale_constr ctxt (x as (_, T)) =
blanchet@38240
   822
  is_codatatype ctxt (body_type T) andalso is_constr_like ctxt x andalso
blanchet@38240
   823
  not (is_coconstr ctxt x)
blanchet@37256
   824
fun is_constr ctxt stds (x as (_, T)) =
blanchet@37256
   825
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   826
    is_constr_like ctxt x andalso
blanchet@37256
   827
    not (is_basic_datatype thy stds
blanchet@35220
   828
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@37256
   829
    not (is_stale_constr ctxt x)
blanchet@37256
   830
  end
blanchet@33192
   831
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   832
val is_sel_like_and_no_discr =
blanchet@35665
   833
  String.isPrefix sel_prefix orf
blanchet@35665
   834
  (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   835
blanchet@33192
   836
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   837
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   838
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   839
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   840
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   841
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   842
blanchet@35070
   843
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   844
  case T of
blanchet@35665
   845
    Type (@{type_name fun}, _) =>
blanchet@34936
   846
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   847
    not (is_boolean_type (body_type T))
blanchet@38190
   848
  | Type (@{type_name prod}, Ts) =>
blanchet@34936
   849
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   850
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   851
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   852
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   853
  | _ => false
blanchet@35280
   854
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   855
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   856
    SOME (SOME box_me) => box_me
blanchet@35070
   857
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   858
and box_type hol_ctxt boxy T =
blanchet@33192
   859
  case T of
blanchet@35665
   860
    Type (z as (@{type_name fun}, [T1, T2])) =>
blanchet@34936
   861
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   862
       should_box_type hol_ctxt boxy z then
blanchet@33192
   863
      Type (@{type_name fun_box},
blanchet@35070
   864
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   865
    else
blanchet@35070
   866
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   867
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@38190
   868
  | Type (z as (@{type_name prod}, Ts)) =>
blanchet@34982
   869
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   870
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   871
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   872
    else
blanchet@38190
   873
      Type (@{type_name prod},
blanchet@35665
   874
            map (box_type hol_ctxt
blanchet@34121
   875
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   876
                           else InPair)) Ts)
blanchet@33192
   877
  | _ => T
blanchet@33192
   878
blanchet@35190
   879
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   880
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   881
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   882
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   883
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   884
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   885
blanchet@33192
   886
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   887
blanchet@33192
   888
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   889
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   890
  if s = @{const_name Pair} then
blanchet@33192
   891
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   892
  else
blanchet@33192
   893
    sel_prefix_for n ^ s
blanchet@33192
   894
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   895
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   896
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   897
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   898
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   899
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   900
  oo nth_sel_for_constr
blanchet@33192
   901
blanchet@33192
   902
fun sel_no_from_name s =
blanchet@33192
   903
  if String.isPrefix discr_prefix s then
blanchet@33192
   904
    ~1
blanchet@33192
   905
  else if String.isPrefix sel_prefix s then
blanchet@33192
   906
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   907
  else if s = @{const_name snd} then
blanchet@33192
   908
    1
blanchet@33192
   909
  else
blanchet@33192
   910
    0
blanchet@33192
   911
blanchet@35078
   912
val close_form =
blanchet@35078
   913
  let
blanchet@35078
   914
    fun close_up zs zs' =
blanchet@35078
   915
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   916
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   917
           (take (length zs' - length zs) zs')
blanchet@35078
   918
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   919
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   920
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   921
        end
blanchet@35078
   922
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   923
  in aux [] end
blanchet@35078
   924
blanchet@33192
   925
fun distinctness_formula T =
blanchet@33192
   926
  all_distinct_unordered_pairs_of
blanchet@33192
   927
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   928
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   929
blanchet@35220
   930
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   931
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   932
blanchet@37256
   933
fun uncached_datatype_constrs ({thy, ctxt, stds, ...} : hol_context)
blanchet@35220
   934
                              (T as Type (s, Ts)) =
blanchet@38240
   935
    (case AList.lookup (op =) (#codatatypes (Data.get (Context.Proof ctxt)))
blanchet@38240
   936
                       s of
blanchet@38240
   937
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type ctxt T)) xs'
blanchet@33581
   938
     | _ =>
blanchet@37256
   939
       if is_datatype ctxt stds T then
blanchet@33581
   940
         case Datatype.get_info thy s of
blanchet@33581
   941
           SOME {index, descr, ...} =>
blanchet@33581
   942
           let
blanchet@33581
   943
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   944
           in
blanchet@37260
   945
             map (apsnd (fn Us =>
blanchet@37260
   946
                            map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@37260
   947
                 constrs
blanchet@33581
   948
           end
blanchet@33581
   949
         | NONE =>
blanchet@33581
   950
           if is_record_type T then
blanchet@33581
   951
             let
blanchet@33581
   952
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   953
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   954
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   955
             in [(s', T')] end
blanchet@38215
   956
           else if is_real_quot_type thy T then
blanchet@34936
   957
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@37256
   958
           else case typedef_info ctxt s of
blanchet@33581
   959
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@35311
   960
             [(Abs_name,
blanchet@38240
   961
               varify_and_instantiate_type ctxt abs_type T rep_type --> T)]
blanchet@33581
   962
           | NONE =>
blanchet@33581
   963
             if T = @{typ ind} then
blanchet@33581
   964
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   965
             else
blanchet@33581
   966
               []
blanchet@33581
   967
       else
blanchet@33581
   968
         [])
blanchet@33580
   969
  | uncached_datatype_constrs _ _ = []
blanchet@35220
   970
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   971
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   972
    SOME xs => xs
blanchet@33580
   973
  | NONE =>
blanchet@35220
   974
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   975
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   976
    end
blanchet@35190
   977
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   978
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   979
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@33192
   980
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   981
blanchet@33192
   982
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   983
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   984
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   985
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   986
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   987
    AList.lookup (op =)
blanchet@35190
   988
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   989
        s
blanchet@33192
   990
    |> the |> pair s
blanchet@33192
   991
  end
blanchet@34982
   992
blanchet@35070
   993
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   994
  let val dataT = body_type T in
blanchet@33192
   995
    if s = @{const_name Suc} then
blanchet@33192
   996
      Abs (Name.uu, dataT,
blanchet@33192
   997
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
   998
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
   999
      Const (discr_for_constr x)
blanchet@33192
  1000
    else
blanchet@33192
  1001
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
  1002
  end
blanchet@37256
  1003
fun discriminate_value (hol_ctxt as {ctxt, ...}) x t =
blanchet@35280
  1004
  case head_of t of
blanchet@35280
  1005
    Const x' =>
blanchet@33192
  1006
    if x = x' then @{const True}
blanchet@37256
  1007
    else if is_constr_like ctxt x' then @{const False}
blanchet@37476
  1008
    else s_betapply [] (discr_term_for_constr hol_ctxt x, t)
blanchet@37476
  1009
  | _ => s_betapply [] (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
  1010
blanchet@35220
  1011
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
  1012
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
  1013
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
  1014
      @{term "%n::nat. n - 1"}
blanchet@33192
  1015
    else if is_pair_type dataT then
blanchet@33192
  1016
      Const (nth_sel_for_constr x n)
blanchet@33192
  1017
    else
blanchet@33192
  1018
      let
blanchet@38190
  1019
        fun aux m (Type (@{type_name prod}, [T1, T2])) =
blanchet@33192
  1020
            let
blanchet@33192
  1021
              val (m, t1) = aux m T1
blanchet@33192
  1022
              val (m, t2) = aux m T2
blanchet@33192
  1023
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
  1024
          | aux m T =
blanchet@33192
  1025
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
  1026
                    $ Bound 0)
blanchet@33192
  1027
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
  1028
                     (List.take (arg_Ts, n)) 0
blanchet@33192
  1029
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
  1030
  end
blanchet@37256
  1031
fun select_nth_constr_arg ctxt stds x t n res_T =
blanchet@37256
  1032
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
  1033
    (case strip_comb t of
blanchet@37256
  1034
       (Const x', args) =>
blanchet@37256
  1035
       if x = x' then nth args n
blanchet@37256
  1036
       else if is_constr_like ctxt x' then Const (@{const_name unknown}, res_T)
blanchet@37256
  1037
       else raise SAME ()
blanchet@37256
  1038
     | _ => raise SAME())
blanchet@37476
  1039
    handle SAME () =>
blanchet@37476
  1040
           s_betapply [] (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@37256
  1041
  end
blanchet@33192
  1042
blanchet@35220
  1043
fun construct_value _ _ x [] = Const x
blanchet@37256
  1044
  | construct_value ctxt stds (x as (s, _)) args =
blanchet@33192
  1045
    let val args = map Envir.eta_contract args in
blanchet@33192
  1046
      case hd args of
blanchet@35280
  1047
        Const (s', _) $ t =>
blanchet@34936
  1048
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
  1049
           constr_name_for_sel_like s' = s andalso
blanchet@35220
  1050
           forall (fn (n, t') =>
blanchet@37256
  1051
                      select_nth_constr_arg ctxt stds x t n dummyT = t')
blanchet@34936
  1052
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  1053
          t
blanchet@33192
  1054
        else
blanchet@33192
  1055
          list_comb (Const x, args)
blanchet@33192
  1056
      | _ => list_comb (Const x, args)
blanchet@33192
  1057
    end
blanchet@33192
  1058
blanchet@37256
  1059
fun constr_expand (hol_ctxt as {ctxt, stds, ...}) T t =
blanchet@35665
  1060
  (case head_of t of
blanchet@37256
  1061
     Const x => if is_constr_like ctxt x then t else raise SAME ()
blanchet@35665
  1062
   | _ => raise SAME ())
blanchet@35665
  1063
  handle SAME () =>
blanchet@35665
  1064
         let
blanchet@35665
  1065
           val x' as (_, T') =
blanchet@35665
  1066
             if is_pair_type T then
blanchet@35665
  1067
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@35665
  1068
                 (@{const_name Pair}, T1 --> T2 --> T)
blanchet@35665
  1069
               end
blanchet@35665
  1070
             else
blanchet@35665
  1071
               datatype_constrs hol_ctxt T |> hd
blanchet@35665
  1072
           val arg_Ts = binder_types T'
blanchet@35665
  1073
         in
blanchet@37256
  1074
           list_comb (Const x', map2 (select_nth_constr_arg ctxt stds x' t)
blanchet@35665
  1075
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@35665
  1076
         end
blanchet@35665
  1077
blanchet@35665
  1078
fun coerce_bound_no f j t =
blanchet@35665
  1079
  case t of
blanchet@35665
  1080
    t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
blanchet@35665
  1081
  | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
blanchet@35665
  1082
  | Bound j' => if j' = j then f t else t
blanchet@35665
  1083
  | _ => t
blanchet@35665
  1084
fun coerce_bound_0_in_term hol_ctxt new_T old_T =
blanchet@35665
  1085
  old_T <> new_T ? coerce_bound_no (coerce_term hol_ctxt [new_T] old_T new_T) 0
blanchet@37256
  1086
and coerce_term (hol_ctxt as {ctxt, stds, fast_descrs, ...}) Ts new_T old_T t =
blanchet@35665
  1087
  if old_T = new_T then
blanchet@35665
  1088
    t
blanchet@35665
  1089
  else
blanchet@35665
  1090
    case (new_T, old_T) of
blanchet@35665
  1091
      (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1092
       Type (@{type_name fun}, [old_T1, old_T2])) =>
blanchet@35665
  1093
      (case eta_expand Ts t 1 of
blanchet@35665
  1094
         Abs (s, _, t') =>
blanchet@35665
  1095
         Abs (s, new_T1,
blanchet@35665
  1096
              t' |> coerce_bound_0_in_term hol_ctxt new_T1 old_T1
blanchet@35665
  1097
                 |> coerce_term hol_ctxt (new_T1 :: Ts) new_T2 old_T2)
blanchet@35665
  1098
         |> Envir.eta_contract
blanchet@35665
  1099
         |> new_s <> @{type_name fun}
blanchet@37256
  1100
            ? construct_value ctxt stds
blanchet@35665
  1101
                  (if new_s = @{type_name fin_fun} then @{const_name FinFun}
blanchet@35665
  1102
                   else @{const_name FunBox},
blanchet@35665
  1103
                   Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1104
              o single
blanchet@35665
  1105
       | t' => raise TERM ("Nitpick_HOL.coerce_term", [t']))
blanchet@35665
  1106
    | (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1107
       Type (old_s, old_Ts as [old_T1, old_T2])) =>
blanchet@35665
  1108
      if old_s = @{type_name fin_fun} orelse old_s = @{type_name fun_box} orelse
blanchet@38190
  1109
         old_s = @{type_name pair_box} orelse old_s = @{type_name prod} then
blanchet@35665
  1110
        case constr_expand hol_ctxt old_T t of
blanchet@35665
  1111
          Const (old_s, _) $ t1 =>
blanchet@35665
  1112
          if new_s = @{type_name fun} then
blanchet@35665
  1113
            coerce_term hol_ctxt Ts new_T (Type (@{type_name fun}, old_Ts)) t1
blanchet@35665
  1114
          else
blanchet@37256
  1115
            construct_value ctxt stds
blanchet@35665
  1116
                (old_s, Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1117
                [coerce_term hol_ctxt Ts (Type (@{type_name fun}, new_Ts))
blanchet@35665
  1118
                             (Type (@{type_name fun}, old_Ts)) t1]
blanchet@35665
  1119
        | Const _ $ t1 $ t2 =>
blanchet@37256
  1120
          construct_value ctxt stds
blanchet@38190
  1121
              (if new_s = @{type_name prod} then @{const_name Pair}
blanchet@35665
  1122
               else @{const_name PairBox}, new_Ts ---> new_T)
blanchet@35665
  1123
              (map3 (coerce_term hol_ctxt Ts) [new_T1, new_T2] [old_T1, old_T2]
blanchet@35665
  1124
                    [t1, t2])
blanchet@35665
  1125
        | t' => raise TERM ("Nitpick_HOL.coerce_term", [t'])
blanchet@35665
  1126
      else
blanchet@35665
  1127
        raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1128
    | _ => raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1129
blanchet@35665
  1130
fun card_of_type assigns (Type (@{type_name fun}, [T1, T2])) =
blanchet@34123
  1131
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@38190
  1132
  | card_of_type assigns (Type (@{type_name prod}, [T1, T2])) =
blanchet@34123
  1133
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1134
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1135
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1136
  | card_of_type _ @{typ bool} = 2
blanchet@34123
  1137
  | card_of_type assigns T =
blanchet@34123
  1138
    case AList.lookup (op =) assigns T of
blanchet@33192
  1139
      SOME k => k
blanchet@33192
  1140
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1141
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@35665
  1142
fun bounded_card_of_type max default_card assigns
blanchet@35665
  1143
                         (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
  1144
    let
blanchet@34123
  1145
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1146
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1147
    in
blanchet@33192
  1148
      if k1 = max orelse k2 = max then max
blanchet@33192
  1149
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1150
    end
blanchet@35665
  1151
  | bounded_card_of_type max default_card assigns
blanchet@38190
  1152
                         (Type (@{type_name prod}, [T1, T2])) =
blanchet@33192
  1153
    let
blanchet@34123
  1154
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1155
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1156
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1157
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1158
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1159
                    card_of_type assigns T
blanchet@33192
  1160
                  else
blanchet@34123
  1161
                    card_of_type assigns T
blanchet@33232
  1162
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1163
                           default_card)
blanchet@35385
  1164
fun bounded_exact_card_of_type hol_ctxt finitizable_dataTs max default_card
blanchet@35385
  1165
                               assigns T =
blanchet@33192
  1166
  let
blanchet@33192
  1167
    fun aux avoid T =
blanchet@34121
  1168
      (if member (op =) avoid T then
blanchet@33192
  1169
         0
blanchet@35385
  1170
       else if member (op =) finitizable_dataTs T then
blanchet@35385
  1171
         raise SAME ()
blanchet@33192
  1172
       else case T of
blanchet@35665
  1173
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
  1174
         let
blanchet@33192
  1175
           val k1 = aux avoid T1
blanchet@33192
  1176
           val k2 = aux avoid T2
blanchet@33192
  1177
         in
blanchet@33192
  1178
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1179
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1180
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1181
         end
blanchet@38190
  1182
       | Type (@{type_name prod}, [T1, T2]) =>
blanchet@33192
  1183
         let
blanchet@33192
  1184
           val k1 = aux avoid T1
blanchet@33192
  1185
           val k2 = aux avoid T2
blanchet@33192
  1186
         in
blanchet@33192
  1187
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1188
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1189
           else Int.min (max, k1 * k2)
blanchet@33192
  1190
         end
blanchet@33192
  1191
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1192
       | @{typ prop} => 2
blanchet@33192
  1193
       | @{typ bool} => 2
blanchet@33192
  1194
       | Type _ =>
blanchet@35070
  1195
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1196
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1197
                  else raise SAME ()
blanchet@33192
  1198
          | constrs =>
blanchet@33192
  1199
            let
blanchet@33192
  1200
              val constr_cards =
blanchet@35280
  1201
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1202
                    constrs
blanchet@33192
  1203
            in
blanchet@34121
  1204
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1205
              else Integer.sum constr_cards
blanchet@33192
  1206
            end)
blanchet@33192
  1207
       | _ => raise SAME ())
blanchet@34123
  1208
      handle SAME () =>
blanchet@34123
  1209
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1210
  in Int.min (max, aux [] T) end
blanchet@33192
  1211
blanchet@35665
  1212
val small_type_max_card = 5
blanchet@35665
  1213
blanchet@35384
  1214
fun is_finite_type hol_ctxt T =
blanchet@35665
  1215
  bounded_exact_card_of_type hol_ctxt [] 1 2 [] T > 0
blanchet@35665
  1216
fun is_small_finite_type hol_ctxt T =
blanchet@35665
  1217
  let val n = bounded_exact_card_of_type hol_ctxt [] 1 2 [] T in
blanchet@35665
  1218
    n > 0 andalso n <= small_type_max_card
blanchet@35665
  1219
  end
blanchet@33192
  1220
blanchet@33192
  1221
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1222
  | is_ground_term (Const _) = true
blanchet@33192
  1223
  | is_ground_term _ = false
blanchet@33192
  1224
blanchet@36062
  1225
fun hashw_term (t1 $ t2) = hashw (hashw_term t1, hashw_term t2)
blanchet@36062
  1226
  | hashw_term (Const (s, _)) = hashw_string (s, 0w0)
blanchet@33192
  1227
  | hashw_term _ = 0w0
blanchet@33192
  1228
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1229
blanchet@33192
  1230
fun special_bounds ts =
wenzelm@35408
  1231
  fold Term.add_vars ts [] |> sort (Term_Ord.fast_indexname_ord o pairself fst)
blanchet@33192
  1232
blanchet@38190
  1233
(* FIXME: detect "rep_datatype"? *)
blanchet@38240
  1234
fun is_funky_typedef_name ctxt s =
blanchet@38190
  1235
  member (op =) [@{type_name unit}, @{type_name prod},
blanchet@38190
  1236
                 @{type_name Sum_Type.sum}, @{type_name int}] s orelse
blanchet@38240
  1237
  is_frac_type ctxt (Type (s, []))
blanchet@38240
  1238
fun is_funky_typedef ctxt (Type (s, _)) = is_funky_typedef_name ctxt s
blanchet@33571
  1239
  | is_funky_typedef _ _ = false
blanchet@33192
  1240
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1241
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1242
  | is_arity_type_axiom _ = false
blanchet@37256
  1243
fun is_typedef_axiom ctxt boring (@{const "==>"} $ _ $ t2) =
blanchet@37256
  1244
    is_typedef_axiom ctxt boring t2
blanchet@37256
  1245
  | is_typedef_axiom ctxt boring
blanchet@33192
  1246
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@35665
  1247
         $ Const (_, Type (@{type_name fun}, [Type (s, _), _]))
blanchet@35665
  1248
         $ Const _ $ _)) =
blanchet@38240
  1249
    boring <> is_funky_typedef_name ctxt s andalso is_typedef ctxt s
blanchet@33192
  1250
  | is_typedef_axiom _ _ _ = false
blanchet@36126
  1251
val is_class_axiom =
blanchet@36126
  1252
  Logic.strip_horn #> swap #> op :: #> forall (can Logic.dest_of_class)
blanchet@33192
  1253
blanchet@33192
  1254
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1255
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1256
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1257
   using "typedef_info". *)
blanchet@37256
  1258
fun partition_axioms_by_definitionality ctxt axioms def_names =
blanchet@33192
  1259
  let
blanchet@33192
  1260
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1261
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1262
    val nondefs =
blanchet@33192
  1263
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@37256
  1264
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom ctxt true) o snd)
blanchet@33192
  1265
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1266
blanchet@33197
  1267
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1268
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1269
   commands. *)
blanchet@33192
  1270
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1271
blanchet@35283
  1272
val is_trivial_definition =
blanchet@35283
  1273
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1274
val is_plain_definition =
blanchet@33192
  1275
  let
blanchet@33192
  1276
    fun do_lhs t1 =
blanchet@33192
  1277
      case strip_comb t1 of
blanchet@34936
  1278
        (Const _, args) =>
blanchet@34936
  1279
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1280
      | _ => false
blanchet@33192
  1281
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
haftmann@38864
  1282
      | do_eq (@{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ t1 $ _)) =
blanchet@33192
  1283
        do_lhs t1
blanchet@33192
  1284
      | do_eq _ = false
blanchet@33192
  1285
  in do_eq end
blanchet@33192
  1286
blanchet@37256
  1287
fun all_axioms_of ctxt subst =
blanchet@33192
  1288
  let
blanchet@37256
  1289
    val thy = ProofContext.theory_of ctxt
blanchet@35335
  1290
    val axioms_of_thys =
blanchet@35893
  1291
      maps Thm.axioms_of
blanchet@35893
  1292
      #> map (apsnd (subst_atomic subst o prop_of))
blanchet@35893
  1293
      #> filter_out (is_class_axiom o snd)
blanchet@33192
  1294
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1295
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1296
                    |> OrdList.make fast_string_ord
blanchet@33192
  1297
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1298
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1299
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1300
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1301
    val (built_in_defs, built_in_nondefs) =
blanchet@37256
  1302
      partition_axioms_by_definitionality ctxt built_in_axioms def_names
blanchet@37256
  1303
      ||> filter (is_typedef_axiom ctxt false)
blanchet@33192
  1304
    val (user_defs, user_nondefs) =
blanchet@37256
  1305
      partition_axioms_by_definitionality ctxt user_axioms def_names
blanchet@33197
  1306
    val (built_in_nondefs, user_nondefs) =
blanchet@37256
  1307
      List.partition (is_typedef_axiom ctxt false) user_nondefs
blanchet@33197
  1308
      |>> append built_in_nondefs
blanchet@34121
  1309
    val defs =
blanchet@34121
  1310
      (thy |> PureThy.all_thms_of
blanchet@34121
  1311
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1312
           |> map (prop_of o snd)
blanchet@35283
  1313
           |> filter_out is_trivial_definition
blanchet@35283
  1314
           |> filter is_plain_definition) @
blanchet@34121
  1315
      user_defs @ built_in_defs
blanchet@33192
  1316
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1317
blanchet@35220
  1318
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1319
  if s = @{const_name If} then
blanchet@33192
  1320
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1321
  else
blanchet@35220
  1322
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1323
      case AList.lookup (op =)
blanchet@35220
  1324
                    (built_in_consts
blanchet@35220
  1325
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1326
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1327
        SOME n => SOME n
blanchet@35220
  1328
      | NONE =>
blanchet@35220
  1329
        case AList.lookup (op =)
blanchet@35220
  1330
                 (built_in_typed_consts
blanchet@35220
  1331
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1332
                 (s, unarize_type T) of
blanchet@35220
  1333
          SOME n => SOME n
blanchet@35220
  1334
        | NONE =>
blanchet@35280
  1335
          case s of
blanchet@35280
  1336
            @{const_name zero_class.zero} =>
blanchet@35280
  1337
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1338
          | @{const_name Suc} =>
blanchet@35280
  1339
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1340
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1341
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1342
                 else
blanchet@35280
  1343
                   NONE
blanchet@35220
  1344
    end
blanchet@35220
  1345
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1346
blanchet@33192
  1347
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1348
   simplification rules (equational specifications). *)
blanchet@33192
  1349
fun term_under_def t =
blanchet@33192
  1350
  case t of
blanchet@33192
  1351
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1352
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1353
  | @{const Trueprop} $ t1 => term_under_def t1
haftmann@38864
  1354
  | Const (@{const_name HOL.eq}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1355
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1356
  | t1 $ _ => term_under_def t1
blanchet@33192
  1357
  | _ => t
blanchet@33192
  1358
blanchet@36555
  1359
(* Here we crucially rely on "specialize_type" performing a preorder traversal
blanchet@36555
  1360
   of the term, without which the wrong occurrence of a constant could be
blanchet@36555
  1361
   matched in the face of overloading. *)
blanchet@35220
  1362
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1363
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1364
    []
blanchet@33192
  1365
  else
blanchet@33192
  1366
    these (Symtab.lookup table s)
blanchet@36555
  1367
    |> map_filter (try (specialize_type thy x))
blanchet@34121
  1368
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1369
blanchet@35280
  1370
fun normalized_rhs_of t =
blanchet@33192
  1371
  let
blanchet@33743
  1372
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1373
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1374
      | aux _ _ = NONE
blanchet@33192
  1375
    val (lhs, rhs) =
blanchet@33192
  1376
      case t of
blanchet@33192
  1377
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
haftmann@38864
  1378
      | @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ t1 $ t2) =>
blanchet@33192
  1379
        (t1, t2)
blanchet@33232
  1380
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1381
    val args = strip_comb lhs |> snd
blanchet@33743
  1382
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1383
blanchet@33192
  1384
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1385
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1386
     original_name s <> s then
blanchet@33192
  1387
    NONE
blanchet@33192
  1388
  else
blanchet@37476
  1389
    x |> def_props_for_const thy [(NONE, false)] false table
blanchet@37476
  1390
      |> List.last
blanchet@35280
  1391
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1392
    handle List.Empty => NONE
blanchet@33192
  1393
blanchet@33192
  1394
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1395
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1396
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1397
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1398
blanchet@33192
  1399
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1400
  let
blanchet@33192
  1401
    fun is_good_arg (Bound _) = true
blanchet@33192
  1402
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1403
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1404
        s = @{const_name undefined}
blanchet@33192
  1405
      | is_good_arg _ = false
blanchet@33192
  1406
  in
blanchet@33192
  1407
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1408
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1409
      (case def_of_const thy table x of
blanchet@38180
  1410
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso
blanchet@38180
  1411
                    forall is_good_arg ts
blanchet@33192
  1412
       | NONE => false)
blanchet@33192
  1413
    | _ => false
blanchet@33192
  1414
  end
blanchet@33192
  1415
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1416
  map_aterms (fn t as Const x =>
blanchet@33192
  1417
                 (case def_of_const thy table x of
blanchet@33192
  1418
                    SOME t' =>
blanchet@33192
  1419
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1420
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1421
                      else t
blanchet@33192
  1422
                    end
blanchet@33192
  1423
                 | NONE => t)
blanchet@33192
  1424
               | t => t)
blanchet@33192
  1425
blanchet@38240
  1426
fun case_const_names ctxt stds =
blanchet@38240
  1427
  let val thy = ProofContext.theory_of ctxt in
blanchet@38240
  1428
    Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@38240
  1429
                    if is_basic_datatype thy stds dtype_s then
blanchet@38240
  1430
                      I
blanchet@38240
  1431
                    else
blanchet@38240
  1432
                      cons (case_name, AList.lookup (op =) descr index
blanchet@38240
  1433
                                       |> the |> #3 |> length))
blanchet@38240
  1434
                (Datatype.get_all thy) [] @
blanchet@38240
  1435
    map (apsnd length o snd) (#codatatypes (Data.get (Context.Proof ctxt)))
blanchet@38240
  1436
  end
blanchet@33192
  1437
blanchet@35718
  1438
fun fixpoint_kind_of_const thy table x =
blanchet@35718
  1439
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@35718
  1440
    NoFp
blanchet@35718
  1441
  else
blanchet@35718
  1442
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@35718
  1443
    handle Option.Option => NoFp
blanchet@33192
  1444
blanchet@35718
  1445
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35718
  1446
                             ...} : hol_context) x =
blanchet@35718
  1447
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35718
  1448
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@38205
  1449
fun is_inductive_pred hol_ctxt (x as (s, _)) =
blanchet@38205
  1450
  is_real_inductive_pred hol_ctxt x orelse String.isPrefix ubfp_prefix s orelse
blanchet@38205
  1451
  String.isPrefix lbfp_prefix s
blanchet@33192
  1452
blanchet@35718
  1453
fun lhs_of_equation t =
blanchet@35718
  1454
  case t of
blanchet@35718
  1455
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1456
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1457
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1458
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@35718
  1459
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
haftmann@38864
  1460
  | Const (@{const_name HOL.eq}, _) $ t1 $ _ => SOME t1
haftmann@38786
  1461
  | @{const HOL.implies} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1462
  | _ => NONE
blanchet@35718
  1463
fun is_constr_pattern _ (Bound _) = true
blanchet@35718
  1464
  | is_constr_pattern _ (Var _) = true
blanchet@37256
  1465
  | is_constr_pattern ctxt t =
blanchet@35718
  1466
    case strip_comb t of
blanchet@35718
  1467
      (Const x, args) =>
blanchet@37256
  1468
      is_constr_like ctxt x andalso forall (is_constr_pattern ctxt) args
blanchet@35718
  1469
    | _ => false
blanchet@37256
  1470
fun is_constr_pattern_lhs ctxt t =
blanchet@37256
  1471
  forall (is_constr_pattern ctxt) (snd (strip_comb t))
blanchet@37256
  1472
fun is_constr_pattern_formula ctxt t =
blanchet@35718
  1473
  case lhs_of_equation t of
blanchet@37256
  1474
    SOME t' => is_constr_pattern_lhs ctxt t'
blanchet@35718
  1475
  | NONE => false
blanchet@35718
  1476
blanchet@36555
  1477
(* Similar to "specialize_type" but returns all matches rather than only the
blanchet@36555
  1478
   first (preorder) match. *)
blanchet@35807
  1479
fun multi_specialize_type thy slack (s, T) t =
blanchet@35807
  1480
  let
blanchet@35807
  1481
    fun aux (Const (s', T')) ys =
blanchet@35807
  1482
        if s = s' then
blanchet@35807
  1483
          ys |> (if AList.defined (op =) ys T' then
blanchet@35807
  1484
                   I
blanchet@35807
  1485
                 else
blanchet@36555
  1486
                   cons (T', monomorphic_term (Sign.typ_match thy (T', T)
blanchet@36555
  1487
                                                              Vartab.empty) t)
blanchet@35807
  1488
                   handle Type.TYPE_MATCH => I
blanchet@36575
  1489
                        | TERM _ =>
blanchet@35807
  1490
                          if slack then
blanchet@35807
  1491
                            I
blanchet@35807
  1492
                          else
blanchet@37253
  1493
                            raise NOT_SUPPORTED
blanchet@37253
  1494
                                      ("too much polymorphism in axiom \"" ^
blanchet@37253
  1495
                                       Syntax.string_of_term_global thy t ^
blanchet@37253
  1496
                                       "\" involving " ^ quote s))
blanchet@35807
  1497
        else
blanchet@35807
  1498
          ys
blanchet@35807
  1499
      | aux _ ys = ys
blanchet@35807
  1500
  in map snd (fold_aterms aux t []) end
blanchet@35807
  1501
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@35807
  1502
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@35807
  1503
blanchet@35807
  1504
fun unvarify_term (t1 $ t2) = unvarify_term t1 $ unvarify_term t2
blanchet@35807
  1505
  | unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@35807
  1506
  | unvarify_term (Abs (s, T, t')) = Abs (s, T, unvarify_term t')
blanchet@35807
  1507
  | unvarify_term t = t
blanchet@35807
  1508
fun axiom_for_choice_spec thy =
blanchet@35807
  1509
  unvarify_term
blanchet@35807
  1510
  #> Object_Logic.atomize_term thy
blanchet@35807
  1511
  #> Choice_Specification.close_form
blanchet@35807
  1512
  #> HOLogic.mk_Trueprop
blanchet@35807
  1513
fun is_choice_spec_fun ({thy, def_table, nondef_table, choice_spec_table, ...}
blanchet@35807
  1514
                        : hol_context) x =
blanchet@35807
  1515
  case nondef_props_for_const thy true choice_spec_table x of
blanchet@35807
  1516
    [] => false
blanchet@35807
  1517
  | ts => case def_of_const thy def_table x of
blanchet@35807
  1518
            SOME (Const (@{const_name Eps}, _) $ _) => true
blanchet@35807
  1519
          | SOME _ => false
blanchet@35807
  1520
          | NONE =>
blanchet@35807
  1521
            let val ts' = nondef_props_for_const thy true nondef_table x in
blanchet@35807
  1522
              length ts' = length ts andalso
blanchet@35807
  1523
              forall (fn t =>
blanchet@35807
  1524
                         exists (curry (op aconv) (axiom_for_choice_spec thy t))
blanchet@35807
  1525
                                ts') ts
blanchet@35807
  1526
            end
blanchet@35807
  1527
blanchet@35807
  1528
fun is_choice_spec_axiom thy choice_spec_table t =
blanchet@35807
  1529
  Symtab.exists (fn (_, ts) =>
blanchet@35807
  1530
                    exists (curry (op aconv) t o axiom_for_choice_spec thy) ts)
blanchet@35807
  1531
                choice_spec_table
blanchet@35807
  1532
blanchet@38205
  1533
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@38205
  1534
                             ...} : hol_context) x =
blanchet@38205
  1535
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@38205
  1536
                                                     x)))
blanchet@38205
  1537
         [!simp_table, psimp_table]
blanchet@38202
  1538
fun is_equational_fun_but_no_plain_def hol_ctxt =
blanchet@38205
  1539
  is_real_equational_fun hol_ctxt orf is_inductive_pred hol_ctxt
blanchet@38202
  1540
blanchet@35718
  1541
(** Constant unfolding **)
blanchet@33192
  1542
blanchet@37476
  1543
fun constr_case_body ctxt stds (func_t, (x as (_, T))) =
blanchet@33192
  1544
  let val arg_Ts = binder_types T in
blanchet@37476
  1545
    s_betapplys [] (func_t, map2 (select_nth_constr_arg ctxt stds x (Bound 0))
blanchet@37476
  1546
                                 (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1547
  end
blanchet@37476
  1548
fun add_constr_case res_T (body_t, guard_t) res_t =
blanchet@37476
  1549
  if res_T = bool_T then
blanchet@37476
  1550
    s_conj (HOLogic.mk_imp (guard_t, body_t), res_t)
blanchet@37476
  1551
  else
blanchet@37476
  1552
    Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@37476
  1553
    $ guard_t $ body_t $ res_t
blanchet@37476
  1554
fun optimized_case_def (hol_ctxt as {ctxt, stds, ...}) dataT res_T func_ts =
blanchet@33192
  1555
  let
blanchet@35070
  1556
    val xs = datatype_constrs hol_ctxt dataT
blanchet@37476
  1557
    val cases =
blanchet@37476
  1558
      func_ts ~~ xs
blanchet@37476
  1559
      |> map (fn (func_t, x) =>
blanchet@37476
  1560
                 (constr_case_body ctxt stds (incr_boundvars 1 func_t, x),
blanchet@37476
  1561
                  discriminate_value hol_ctxt x (Bound 0)))
blanchet@37476
  1562
      |> AList.group (op aconv)
blanchet@37476
  1563
      |> map (apsnd (List.foldl s_disj @{const False}))
blanchet@37482
  1564
      |> sort (int_ord o pairself (size_of_term o snd))
blanchet@37476
  1565
      |> rev
blanchet@33192
  1566
  in
blanchet@37476
  1567
    if res_T = bool_T then
blanchet@37476
  1568
      if forall (member (op =) [@{const False}, @{const True}] o fst) cases then
blanchet@37476
  1569
        case cases of
blanchet@37476
  1570
          [(body_t, _)] => body_t
blanchet@37476
  1571
        | [_, (@{const True}, head_t2)] => head_t2
blanchet@37476
  1572
        | [_, (@{const False}, head_t2)] => @{const Not} $ head_t2
blanchet@37476
  1573
        | _ => raise BAD ("Nitpick_HOL.optimized_case_def", "impossible cases")
blanchet@39315
  1574
      else
blanchet@37476
  1575
        @{const True} |> fold_rev (add_constr_case res_T) cases
blanchet@37476
  1576
    else
blanchet@37476
  1577
      fst (hd cases) |> fold_rev (add_constr_case res_T) (tl cases)
blanchet@33192
  1578
  end
blanchet@37476
  1579
  |> curry absdummy dataT
blanchet@37476
  1580
blanchet@37256
  1581
fun optimized_record_get (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T res_T t =
blanchet@35070
  1582
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1583
    case no_of_record_field thy s rec_T of
blanchet@33192
  1584
      ~1 => (case rec_T of
blanchet@33192
  1585
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1586
               let
blanchet@33192
  1587
                 val rec_T' = List.last Ts
blanchet@33192
  1588
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1589
               in
blanchet@37256
  1590
                 select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@35070
  1591
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1592
               end
blanchet@33232
  1593
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1594
                                []))
blanchet@37256
  1595
    | j => select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@33192
  1596
  end
blanchet@37256
  1597
fun optimized_record_update (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T fun_t
blanchet@37256
  1598
                            rec_t =
blanchet@33192
  1599
  let
blanchet@35070
  1600
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1601
    val Ts = binder_types constr_T
blanchet@33192
  1602
    val n = length Ts
blanchet@33192
  1603
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1604
    val ts =
blanchet@35220
  1605
      map2 (fn j => fn T =>
blanchet@37256
  1606
               let val t = select_nth_constr_arg ctxt stds constr_x rec_t j T in
blanchet@35220
  1607
                 if j = special_j then
blanchet@37476
  1608
                   s_betapply [] (fun_t, t)
blanchet@35220
  1609
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1610
                   optimized_record_update hol_ctxt s
blanchet@35220
  1611
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1612
                 else
blanchet@35220
  1613
                   t
blanchet@35220
  1614
               end) (index_seq 0 n) Ts
blanchet@33192
  1615
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1616
blanchet@35070
  1617
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1618
val unfold_max_depth = 255
blanchet@33192
  1619
blanchet@38206
  1620
(* Inline definitions or define as an equational constant? Booleans tend to
blanchet@38206
  1621
   benefit more from inlining, due to the polarity analysis. *)
blanchet@38206
  1622
val def_inline_threshold_for_booleans = 50
blanchet@38206
  1623
val def_inline_threshold_for_non_booleans = 20
blanchet@38202
  1624
blanchet@38209
  1625
fun unfold_defs_in_term
blanchet@38209
  1626
        (hol_ctxt as {thy, ctxt, stds, whacks, fast_descrs, case_names,
blanchet@38209
  1627
                      def_table, ground_thm_table, ersatz_table, ...}) =
blanchet@33192
  1628
  let
blanchet@33192
  1629
    fun do_term depth Ts t =
blanchet@33192
  1630
      case t of
blanchet@33192
  1631
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@35665
  1632
                      Type (@{type_name fun}, [_, ran_T]))) $ t1 =>
blanchet@38240
  1633
        ((if is_number_type ctxt ran_T then
blanchet@33192
  1634
            let
blanchet@33192
  1635
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1636
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1637
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1638
            in
blanchet@35220
  1639
              if is_integer_like_type ran_T then
blanchet@35220
  1640
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1641
                  Const (s, ran_T)
blanchet@35220
  1642
                else
blanchet@35220
  1643
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1644
              else
blanchet@33192
  1645
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1646
                                  $ Const (s, int_T))
blanchet@33192
  1647
            end
blanchet@33192
  1648
            handle TERM _ => raise SAME ()
blanchet@33192
  1649
          else
blanchet@33192
  1650
            raise SAME ())
blanchet@37476
  1651
         handle SAME () =>
blanchet@37476
  1652
                s_betapply [] (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1653
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1654
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1655
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@37476
  1656
        s_betapplys Ts (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@37476
  1657
                        map (do_term depth Ts) [t1, t2])
blanchet@33192
  1658
      | Const (x as (@{const_name distinct},
blanchet@35665
  1659
               Type (@{type_name fun}, [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1660
        $ (t1 as _ $ _) =>
blanchet@33192
  1661
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1662
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1663
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1664
        if is_ground_term t1 andalso
blanchet@34936
  1665
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1666
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1667
          do_term depth Ts t2
blanchet@33192
  1668
        else
blanchet@33192
  1669
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1670
      | Const x => do_const depth Ts t x []
blanchet@37476
  1671
      | t1 $ t2 =>
blanchet@37476
  1672
        (case strip_comb t of
blanchet@37476
  1673
           (Const x, ts) => do_const depth Ts t x ts
blanchet@37476
  1674
         | _ => s_betapply [] (do_term depth Ts t1, do_term depth Ts t2))
blanchet@33192
  1675
      | Bound _ => t
blanchet@33192
  1676
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@38209
  1677
      | _ => if member (term_match thy) whacks t then
blanchet@38209
  1678
               Const (@{const_name unknown}, fastype_of1 (Ts, t))
blanchet@38209
  1679
             else
blanchet@38209
  1680
               t
blanchet@33192
  1681
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1682
        (Abs (Name.uu, body_type T,
blanchet@37256
  1683
              select_nth_constr_arg ctxt stds x (Bound 0) n res_T), [])
blanchet@33192
  1684
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@37256
  1685
        (select_nth_constr_arg ctxt stds x (do_term depth Ts t) n res_T, ts)
blanchet@38207
  1686
    and quot_rep_of depth Ts abs_T rep_T ts =
blanchet@38207
  1687
      select_nth_constr_arg_with_args depth Ts
blanchet@38207
  1688
          (@{const_name Quot}, rep_T --> abs_T) ts 0 rep_T
blanchet@33192
  1689
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@38209
  1690
      if member (term_match thy) whacks (Const x) then
blanchet@38209
  1691
        Const (@{const_name unknown}, fastype_of1 (Ts, t))
blanchet@38209
  1692
      else case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1693
        SOME s' =>
blanchet@33192
  1694
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1695
      | NONE =>
blanchet@33192
  1696
        let
blanchet@38206
  1697
          fun def_inline_threshold () =
blanchet@38206
  1698
            if is_boolean_type (nth_range_type (length ts) T) then
blanchet@38206
  1699
              def_inline_threshold_for_booleans
blanchet@38206
  1700
            else
blanchet@38206
  1701
              def_inline_threshold_for_non_booleans
blanchet@33192
  1702
          val (const, ts) =
blanchet@35220
  1703
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1704
              (Const x, ts)
blanchet@33192
  1705
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1706
              SOME n =>
blanchet@37476
  1707
              if length ts < n then
blanchet@37476
  1708
                (do_term depth Ts (eta_expand Ts t (n - length ts)), [])
blanchet@37476
  1709
              else
blanchet@37476
  1710
                let
blanchet@37476
  1711
                  val (dataT, res_T) = nth_range_type n T
blanchet@37476
  1712
                                       |> pairf domain_type range_type
blanchet@37476
  1713
                in
blanchet@37476
  1714
                  (optimized_case_def hol_ctxt dataT res_T
blanchet@37476
  1715
                                      (map (do_term depth Ts) (take n ts)),
blanchet@37476
  1716
                   drop n ts)
blanchet@37476
  1717
                end
blanchet@33192
  1718
            | _ =>
blanchet@37256
  1719
              if is_constr ctxt stds x then
blanchet@33192
  1720
                (Const x, ts)
blanchet@37256
  1721
              else if is_stale_constr ctxt x then
blanchet@34936
  1722
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1723
                                     \(\"" ^ s ^ "\")")
blanchet@35284
  1724
              else if is_quot_abs_fun ctxt x then
blanchet@34936
  1725
                let
blanchet@34936
  1726
                  val rep_T = domain_type T
blanchet@34936
  1727
                  val abs_T = range_type T
blanchet@34936
  1728
                in
blanchet@34936
  1729
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1730
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@35311
  1731
                               $ (Const (quot_normal_name_for_type ctxt abs_T,
blanchet@34936
  1732
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1733
                end
blanchet@35284
  1734
              else if is_quot_rep_fun ctxt x then
blanchet@38207
  1735
                quot_rep_of depth Ts (domain_type T) (range_type T) ts
blanchet@33192
  1736
              else if is_record_get thy x then
blanchet@33192
  1737
                case length ts of
blanchet@33192
  1738
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1739
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1740
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1741
              else if is_record_update thy x then
blanchet@33192
  1742
                case length ts of
blanchet@35070
  1743
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1744
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1745
                            (do_term depth Ts (hd ts))
blanchet@33580
  1746
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1747
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@38207
  1748
              else if is_abs_fun ctxt x andalso
blanchet@38240
  1749
                      is_quot_type ctxt (range_type T) then
blanchet@38207
  1750
                let
blanchet@38207
  1751
                  val abs_T = range_type T
blanchet@38207
  1752
                  val rep_T = domain_type (domain_type T)
blanchet@38207
  1753
                  val eps_fun = Const (@{const_name Eps},
blanchet@38207
  1754
                                       (rep_T --> bool_T) --> rep_T)
blanchet@39315
  1755
                  val normal_fun =
blanchet@38207
  1756
                    Const (quot_normal_name_for_type ctxt abs_T,
blanchet@38207
  1757
                           rep_T --> rep_T)
blanchet@38207
  1758
                  val abs_fun = Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@38207
  1759
                in
blanchet@38207
  1760
                  (Abs (Name.uu, rep_T --> bool_T,
blanchet@38207
  1761
                        abs_fun $ (normal_fun $ (eps_fun $ Bound 0)))
blanchet@38207
  1762
                   |> do_term (depth + 1) Ts, ts)
blanchet@38207
  1763
                end
blanchet@37256
  1764
              else if is_rep_fun ctxt x then
blanchet@37256
  1765
                let val x' = mate_of_rep_fun ctxt x in
blanchet@37256
  1766
                  if is_constr ctxt stds x' then
blanchet@33192
  1767
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1768
                                                    (range_type T)
blanchet@38240
  1769
                  else if is_quot_type ctxt (domain_type T) then
blanchet@38207
  1770
                    let
blanchet@38207
  1771
                      val abs_T = domain_type T
blanchet@38207
  1772
                      val rep_T = domain_type (range_type T)
blanchet@38207
  1773
                      val (rep_fun, _) = quot_rep_of depth Ts abs_T rep_T []
blanchet@38243
  1774
                      val (equiv_rel, _) =
blanchet@38243
  1775
                        equiv_relation_for_quot_type thy abs_T
blanchet@38207
  1776
                    in
blanchet@38207
  1777
                      (Abs (Name.uu, abs_T, equiv_rel $ (rep_fun $ Bound 0)),
blanchet@38207
  1778
                       ts)
blanchet@38207
  1779
                    end
blanchet@33192
  1780
                  else
blanchet@38208
  1781
                    (Const x, ts)
blanchet@33192
  1782
                end
blanchet@38202
  1783
              else if is_equational_fun_but_no_plain_def hol_ctxt x orelse
blanchet@35807
  1784
                      is_choice_spec_fun hol_ctxt x then
blanchet@33192
  1785
                (Const x, ts)
blanchet@33192
  1786
              else case def_of_const thy def_table x of
blanchet@33192
  1787
                SOME def =>
blanchet@33192
  1788
                if depth > unfold_max_depth then
blanchet@34124
  1789
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1790
                                   "too many nested definitions (" ^
blanchet@34124
  1791
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1792
                                   quote s)
blanchet@33192
  1793
                else if s = @{const_name wfrec'} then
blanchet@37476
  1794
                  (do_term (depth + 1) Ts (s_betapplys Ts (def, ts)), [])
blanchet@38206
  1795
                else if size_of_term def > def_inline_threshold () then
blanchet@38202
  1796
                  (Const x, ts)
blanchet@33192
  1797
                else
blanchet@33192
  1798
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1799
              | NONE => (Const x, ts)
blanchet@37476
  1800
        in
blanchet@37476
  1801
          s_betapplys Ts (const, map (do_term depth Ts) ts)
blanchet@37476
  1802
          |> s_beta_norm Ts
blanchet@37476
  1803
        end
blanchet@33192
  1804
  in do_term 0 [] end
blanchet@33192
  1805
blanchet@35718
  1806
(** Axiom extraction/generation **)
blanchet@35718
  1807
blanchet@38206
  1808
fun extensional_equal j (Type (@{type_name fun}, [dom_T, ran_T])) t1 t2 =
blanchet@38206
  1809
    let val var_t = Var (("x", j), dom_T) in
blanchet@38206
  1810
      extensional_equal (j + 1) ran_T (betapply (t1, var_t))
blanchet@38206
  1811
                        (betapply (t2, var_t))
blanchet@38206
  1812
    end
blanchet@38206
  1813
  | extensional_equal _ T t1 t2 =
haftmann@38864
  1814
    Const (@{const_name HOL.eq}, T --> T --> bool_T) $ t1 $ t2
blanchet@38206
  1815
blanchet@38202
  1816
fun equationalize_term ctxt tag t =
blanchet@38206
  1817
  let
blanchet@38206
  1818
    val j = maxidx_of_term t + 1
blanchet@38206
  1819
    val (prems, concl) = Logic.strip_horn t
blanchet@38206
  1820
  in
blanchet@38174
  1821
    Logic.list_implies (prems,
blanchet@38200
  1822
        case concl of
haftmann@38864
  1823
          @{const Trueprop} $ (Const (@{const_name HOL.eq}, Type (_, [T, _]))
blanchet@38206
  1824
                               $ t1 $ t2) =>
blanchet@38206
  1825
          @{const Trueprop} $ extensional_equal j T t1 t2
blanchet@38200
  1826
        | @{const Trueprop} $ t' =>
blanchet@38200
  1827
          @{const Trueprop} $ HOLogic.mk_eq (t', @{const True})
blanchet@38201
  1828
        | Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>
blanchet@38206
  1829
          @{const Trueprop} $ extensional_equal j T t1 t2
blanchet@38201
  1830
        | _ => (warning ("Ignoring " ^ quote tag ^ " for non-equation" ^
blanchet@38201
  1831
                         quote (Syntax.string_of_term ctxt t) ^ ".");
blanchet@38201
  1832
                raise SAME ()))
blanchet@38201
  1833
    |> SOME
blanchet@38200
  1834
  end
blanchet@38201
  1835
  handle SAME () => NONE
blanchet@38172
  1836
blanchet@35807
  1837
fun pair_for_prop t =
blanchet@35807
  1838
  case term_under_def t of
blanchet@35807
  1839
    Const (s, _) => (s, t)
blanchet@35807
  1840
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@38172
  1841
blanchet@35807
  1842
fun def_table_for get ctxt subst =
blanchet@35807
  1843
  ctxt |> get |> map (pair_for_prop o subst_atomic subst)
blanchet@35807
  1844
       |> AList.group (op =) |> Symtab.make
blanchet@38172
  1845
blanchet@35718
  1846
fun const_def_table ctxt subst ts =
blanchet@35807
  1847
  def_table_for (map prop_of o Nitpick_Defs.get) ctxt subst
blanchet@35718
  1848
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@35718
  1849
          (map pair_for_prop ts)
blanchet@38172
  1850
blanchet@38172
  1851
fun paired_with_consts t = map (rpair t) (Term.add_const_names t [])
blanchet@35718
  1852
fun const_nondef_table ts =
blanchet@35807
  1853
  fold (append o paired_with_consts) ts [] |> AList.group (op =) |> Symtab.make
blanchet@38172
  1854
blanchet@38201
  1855
fun const_simp_table ctxt =
blanchet@38202
  1856
  def_table_for (map_filter (equationalize_term ctxt "nitpick_simp" o prop_of)
blanchet@38201
  1857
                 o Nitpick_Simps.get) ctxt
blanchet@38201
  1858
fun const_psimp_table ctxt =
blanchet@38202
  1859
  def_table_for (map_filter (equationalize_term ctxt "nitpick_psimp" o prop_of)
blanchet@38201
  1860
                 o Nitpick_Psimps.get) ctxt
blanchet@38172
  1861
blanchet@35807
  1862
fun const_choice_spec_table ctxt subst =
blanchet@35807
  1863
  map (subst_atomic subst o prop_of) (Nitpick_Choice_Specs.get ctxt)
blanchet@35807
  1864
  |> const_nondef_table
blanchet@38172
  1865
blanchet@35718
  1866
fun inductive_intro_table ctxt subst def_table =
blanchet@37264
  1867
  let val thy = ProofContext.theory_of ctxt in
blanchet@37264
  1868
    def_table_for
blanchet@37264
  1869
        (maps (map (unfold_mutually_inductive_preds thy def_table o prop_of)
blanchet@37264
  1870
               o snd o snd)
blanchet@37264
  1871
         o filter (fn (cat, _) => cat = Spec_Rules.Inductive orelse
blanchet@37264
  1872
                                  cat = Spec_Rules.Co_Inductive)
blanchet@37264
  1873
         o Spec_Rules.get) ctxt subst
blanchet@37264
  1874
  end
blanchet@38172
  1875
blanchet@35718
  1876
fun ground_theorem_table thy =
blanchet@35718
  1877
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@35718
  1878
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@35718
  1879
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@35718
  1880
blanchet@35807
  1881
(* TODO: Move to "Nitpick.thy" *)
blanchet@35718
  1882
val basic_ersatz_table =
blanchet@37213
  1883
  [(@{const_name card}, @{const_name card'}),
blanchet@35718
  1884
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@35718
  1885
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@35718
  1886
   (@{const_name wf}, @{const_name wf'}),
blanchet@35718
  1887
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@35718
  1888
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@35718
  1889
blanchet@38240
  1890
fun ersatz_table ctxt =
blanchet@38240
  1891
 basic_ersatz_table
blanchet@38240
  1892
 |> fold (append o snd) (#frac_types (Data.get (Context.Proof ctxt)))
blanchet@35718
  1893
blanchet@35718
  1894
fun add_simps simp_table s eqs =
blanchet@35718
  1895
  Unsynchronized.change simp_table
blanchet@35718
  1896
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@35718
  1897
blanchet@37256
  1898
fun inverse_axioms_for_rep_fun ctxt (x as (_, T)) =
blanchet@37256
  1899
  let
blanchet@37256
  1900
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1901
    val abs_T = domain_type T
blanchet@37256
  1902
  in
blanchet@37256
  1903
    typedef_info ctxt (fst (dest_Type abs_T)) |> the
blanchet@35718
  1904
    |> pairf #Abs_inverse #Rep_inverse
blanchet@36555
  1905
    |> pairself (specialize_type thy x o prop_of o the)
blanchet@35718
  1906
    ||> single |> op ::
blanchet@35718
  1907
  end
blanchet@37256
  1908
fun optimized_typedef_axioms ctxt (abs_z as (abs_s, _)) =
blanchet@37256
  1909
  let
blanchet@37256
  1910
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1911
    val abs_T = Type abs_z
blanchet@37256
  1912
  in
blanchet@37256
  1913
    if is_univ_typedef ctxt abs_T then
blanchet@35718
  1914
      []
blanchet@37256
  1915
    else case typedef_info ctxt abs_s of
blanchet@35718
  1916
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@35718
  1917
      let
blanchet@38240
  1918
        val rep_T = varify_and_instantiate_type ctxt abs_type abs_T rep_type
blanchet@35718
  1919
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@35718
  1920
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@35718
  1921
        val set_t' =
blanchet@35718
  1922
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@36555
  1923
                      |> specialize_type thy (dest_Const rep_t)
blanchet@35718
  1924
                      |> HOLogic.dest_mem |> snd
blanchet@35718
  1925
      in
blanchet@35718
  1926
        [HOLogic.all_const abs_T
blanchet@35718
  1927
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@35718
  1928
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@35718
  1929
        |> map HOLogic.mk_Trueprop
blanchet@35718
  1930
      end
blanchet@35718
  1931
    | NONE => []
blanchet@35718
  1932
  end
blanchet@35718
  1933
fun optimized_quot_type_axioms ctxt stds abs_z =
blanchet@35718
  1934
  let
blanchet@35718
  1935
    val thy = ProofContext.theory_of ctxt
blanchet@35718
  1936
    val abs_T = Type abs_z
blanchet@35718
  1937
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@38243
  1938
    val (equiv_rel, partial) = equiv_relation_for_quot_type thy abs_T
blanchet@35718
  1939
    val a_var = Var (("a", 0), abs_T)
blanchet@35718
  1940
    val x_var = Var (("x", 0), rep_T)
blanchet@35718
  1941
    val y_var = Var (("y", 0), rep_T)
blanchet@35718
  1942
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@37256
  1943
    val sel_a_t = select_nth_constr_arg ctxt stds x a_var 0 rep_T
blanchet@38207
  1944
    val normal_fun =
blanchet@38207
  1945
      Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T)
blanchet@38207
  1946
    val normal_x = normal_fun $ x_var
blanchet@38207
  1947
    val normal_y = normal_fun $ y_var
blanchet@35718
  1948
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@35718
  1949
  in
blanchet@38207
  1950
    [Logic.mk_equals (normal_fun $ sel_a_t, sel_a_t),
blanchet@35718
  1951
     Logic.list_implies
blanchet@35718
  1952
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@35718
  1953
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@35718
  1954
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@35718
  1955
           Logic.mk_equals (normal_x, normal_y)),
blanchet@35718
  1956
     Logic.list_implies
blanchet@35718
  1957
         ([HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)),
blanchet@35718
  1958
           HOLogic.mk_Trueprop (@{const Not} $ HOLogic.mk_eq (normal_x, x_var))],
blanchet@35718
  1959
          HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@38243
  1960
    |> partial ? cons (HOLogic.mk_Trueprop (equiv_rel $ sel_a_t $ sel_a_t))
blanchet@35718
  1961
  end
blanchet@35718
  1962
blanchet@38240
  1963
fun codatatype_bisim_axioms (hol_ctxt as {thy, ctxt, stds, ...}) T =
blanchet@33192
  1964
  let
blanchet@35070
  1965
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1966
    val set_T = T --> bool_T
blanchet@33192
  1967
    val iter_T = @{typ bisim_iterator}
blanchet@33192
  1968
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1969
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1970
    val n_var_minus_1 =
blanchet@35671
  1971
      Const (@{const_name safe_The}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1972
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1973
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1974
    val x_var = Var (("x", 0), T)
blanchet@33192
  1975
    val y_var = Var (("y", 0), T)
blanchet@38161
  1976
    fun bisim_const T =
blanchet@38161
  1977
      Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1978
    fun nth_sub_bisim x n nth_T =
blanchet@38240
  1979
      (if is_codatatype ctxt nth_T then bisim_const nth_T $ n_var_minus_1
blanchet@33192
  1980
       else HOLogic.eq_const nth_T)
blanchet@37256
  1981
      $ select_nth_constr_arg ctxt stds x x_var n nth_T
blanchet@37256
  1982
      $ select_nth_constr_arg ctxt stds x y_var n nth_T
blanchet@33192
  1983
    fun case_func (x as (_, T)) =
blanchet@33192
  1984
      let
blanchet@33192
  1985
        val arg_Ts = binder_types T
blanchet@33192
  1986
        val core_t =
blanchet@35070
  1987
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1988
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1989
          |> foldr1 s_conj
blanchet@33192
  1990
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1991
  in
blanchet@38163
  1992
    [HOLogic.mk_imp
blanchet@38163
  1993
       (HOLogic.mk_disj (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T,
blanchet@38163
  1994
            s_betapply [] (optimized_case_def hol_ctxt T bool_T
blanchet@38163
  1995
                                              (map case_func xs), x_var)),
blanchet@38163
  1996
        bisim_const T $ n_var $ x_var $ y_var),
blanchet@38161
  1997
     HOLogic.eq_const set_T $ (bisim_const T $ bisim_max $ x_var)
blanchet@34124
  1998
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  1999
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  2000
    |> map HOLogic.mk_Trueprop
blanchet@33192
  2001
  end
blanchet@33192
  2002
blanchet@33192
  2003
exception NO_TRIPLE of unit
blanchet@33192
  2004
blanchet@33192
  2005
fun triple_for_intro_rule thy x t =
blanchet@33192
  2006
  let
wenzelm@35625
  2007
    val prems = Logic.strip_imp_prems t |> map (Object_Logic.atomize_term thy)
wenzelm@35625
  2008
    val concl = Logic.strip_imp_concl t |> Object_Logic.atomize_term thy
blanchet@34121
  2009
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@36385
  2010
    val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  2011
  in
blanchet@33192
  2012
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  2013
  end
blanchet@33192
  2014
blanchet@33192
  2015
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  2016
fun wf_constraint_for rel side concl main =
blanchet@33192
  2017
  let
blanchet@37269
  2018
    val core = HOLogic.mk_mem (HOLogic.mk_prod
blanchet@37269
  2019
                               (pairself tuple_for_args (main, concl)), Var rel)
blanchet@33192
  2020
    val t = List.foldl HOLogic.mk_imp core side
blanchet@37269
  2021
    val vars = filter_out (curry (op =) rel) (Term.add_vars t [])
blanchet@33192
  2022
  in
blanchet@33192
  2023
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  2024
                      HOLogic.all_const T
blanchet@33192
  2025
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  2026
                  (t, vars)
blanchet@33192
  2027
  end
blanchet@33192
  2028
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  2029
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  2030
blanchet@33192
  2031
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  2032
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  2033
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  2034
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  2035
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  2036
blanchet@35181
  2037
val max_cached_wfs = 50
blanchet@35181
  2038
val cached_timeout =
blanchet@35181
  2039
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  2040
val cached_wf_props =
blanchet@35181
  2041
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  2042
krauss@33351
  2043
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  2044
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  2045
blanchet@33580
  2046
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  2047
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  2048
         : hol_context) (x as (_, T)) =
blanchet@35220
  2049
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  2050
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  2051
                      [Const x])
blanchet@33192
  2052
  | intro_ts =>
blanchet@33192
  2053
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  2054
          |> filter_out (null o #2) of
blanchet@33192
  2055
       [] => true
blanchet@33192
  2056
     | triples =>
blanchet@33192
  2057
       let
blanchet@33192
  2058
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  2059
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  2060
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  2061
         val rel = (("R", j), rel_T)
blanchet@33192
  2062
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  2063
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  2064
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  2065
         val _ = if debug then
blanchet@33192
  2066
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  2067
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  2068
                 else
blanchet@33192
  2069
                   ()
blanchet@33192
  2070
       in
blanchet@35181
  2071
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  2072
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  2073
           ()
blanchet@33557
  2074
         else
blanchet@35181
  2075
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  2076
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  2077
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  2078
           SOME wf => wf
blanchet@33192
  2079
         | NONE =>
blanchet@33192
  2080
           let
blanchet@33192
  2081
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  2082
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  2083
                             termination_tacs
blanchet@35181
  2084
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  2085
       end)
blanchet@35309
  2086
    handle List.Empty => false | NO_TRIPLE () => false
blanchet@33192
  2087
blanchet@35070
  2088
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  2089
blanchet@33192
  2090
fun is_well_founded_inductive_pred
blanchet@35070
  2091
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  2092
        (x as (s, _)) =
blanchet@33192
  2093
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  2094
    SOME (SOME b) => b
blanchet@34936
  2095
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  2096
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  2097
           SOME (_, wf) => wf
blanchet@35181
  2098
         | NONE =>
blanchet@35181
  2099
           let
blanchet@35181
  2100
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  2101
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  2102
           in
blanchet@35181
  2103
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  2104
           end
blanchet@33192
  2105
blanchet@35280
  2106
fun ap_curry [_] _ t = t
blanchet@35280
  2107
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  2108
    let val n = length arg_Ts in
blanchet@33192
  2109
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  2110
                incr_boundvars n t
blanchet@33192
  2111
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  2112
    end
blanchet@33192
  2113
blanchet@33192
  2114
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  2115
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  2116
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  2117
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  2118
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  2119
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  2120
blanchet@33192
  2121
val is_linear_inductive_pred_def =
blanchet@33192
  2122
  let
blanchet@33192
  2123
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  2124
        do_disjunct (j + 1) t2
blanchet@33192
  2125
      | do_disjunct j t =
blanchet@33192
  2126
        case num_occs_of_bound_in_term j t of
blanchet@33192
  2127
          0 => true
blanchet@35070
  2128
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  2129
        | _ => false
blanchet@33192
  2130
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2131
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  2132
          case length xs of
blanchet@33192
  2133
            1 => false
blanchet@35070
  2134
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  2135
        end
blanchet@33192
  2136
      | do_lfp_def _ = false
blanchet@33192
  2137
  in do_lfp_def o strip_abs_body end
blanchet@33192
  2138
blanchet@33851
  2139
fun n_ptuple_paths 0 = []
blanchet@33851
  2140
  | n_ptuple_paths 1 = []
blanchet@33851
  2141
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  2142
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  2143
blanchet@33192
  2144
val linear_pred_base_and_step_rhss =
blanchet@33192
  2145
  let
blanchet@33192
  2146
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2147
        let
blanchet@33192
  2148
          val (xs, body) = strip_abs t2
blanchet@33192
  2149
          val arg_Ts = map snd (tl xs)
blanchet@33192
  2150