src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Mon Jun 21 11:15:21 2010 +0200 (2010-06-21)
changeset 37476 0681e46b4022
parent 37269 49c45156c9e1
child 37482 6849464ab10e
permissions -rw-r--r--
optimized code generated for datatype cases + more;
more = lazy creation of debugging messages in mono code
+ use of "let" when performing some beta-applications (to avoid exponential blowup)
+ removal of some set constructs, to simplify the code and increase precision in some cases (and decrease it in others, but this can be regained)
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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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     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 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 : theory -> 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_quot_type : theory -> typ -> bool
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  val is_codatatype : theory -> typ -> bool
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  val is_pure_typedef : Proof.context -> typ -> bool
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  val is_univ_typedef : Proof.context -> typ -> bool
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  val is_datatype : Proof.context -> (typ option * bool) list -> typ -> bool
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  val is_record_constr : styp -> bool
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  val is_record_get : theory -> styp -> bool
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  val is_record_update : theory -> styp -> bool
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  val is_abs_fun : Proof.context -> styp -> bool
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  val is_rep_fun : Proof.context -> styp -> bool
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  val is_quot_abs_fun : Proof.context -> styp -> bool
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  val is_quot_rep_fun : Proof.context -> styp -> bool
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  val mate_of_rep_fun : Proof.context -> styp -> styp
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  val is_constr_like : Proof.context -> styp -> bool
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  val is_constr : Proof.context -> (typ option * bool) list -> styp -> bool
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  val is_sel : string -> bool
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  val is_sel_like_and_no_discr : string -> bool
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  val box_type : hol_context -> boxability -> typ -> typ
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  val binarize_nat_and_int_in_type : typ -> typ
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  val binarize_nat_and_int_in_term : term -> term
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  val discr_for_constr : styp -> styp
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  val num_sels_for_constr_type : typ -> int
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  val nth_sel_name_for_constr_name : string -> int -> string
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  val nth_sel_for_constr : styp -> int -> styp
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  val binarized_and_boxed_nth_sel_for_constr :
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    hol_context -> bool -> styp -> int -> styp
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  val sel_no_from_name : string -> int
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  val close_form : term -> term
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  val eta_expand : typ list -> term -> int -> term
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  val extensionalize : term -> term
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  val distinctness_formula : typ -> term list -> term
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  val register_frac_type : string -> (string * string) list -> theory -> theory
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  val unregister_frac_type : string -> theory -> theory
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  val register_codatatype : typ -> string -> styp list -> theory -> theory
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  val unregister_codatatype : 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 : theory -> 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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    theory -> (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 : theory -> (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_inductive_pred : hol_context -> styp -> bool
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  val is_equational_fun : 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 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 merge_type_vars_in_terms : term list -> term list
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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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   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 = Theory_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
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val base_prefix = nitpick_prefix ^ "base" ^ name_sep
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val step_prefix = nitpick_prefix ^ "step" ^ name_sep
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val ubfp_prefix = nitpick_prefix ^ "ubfp" ^ name_sep
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val lbfp_prefix = nitpick_prefix ^ "lbfp" ^ name_sep
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val quot_normal_prefix = nitpick_prefix ^ "qn" ^ name_sep
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val skolem_prefix = nitpick_prefix ^ "sk"
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val special_prefix = nitpick_prefix ^ "sp"
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val uncurry_prefix = nitpick_prefix ^ "unc"
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val eval_prefix = nitpick_prefix ^ "eval"
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val iter_var_prefix = "i"
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(** Constant/type information and term/type manipulation **)
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fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
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fun quot_normal_name_for_type ctxt T =
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  quot_normal_prefix ^ unyxml (Syntax.string_of_typ ctxt T)
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val strip_first_name_sep =
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   300
  Substring.full #> Substring.position name_sep ##> Substring.triml 1
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  #> pairself Substring.string
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   302
fun original_name s =
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  if String.isPrefix nitpick_prefix s then
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    case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
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   305
  else
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    s
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   308
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
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   309
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   310
fun let_var s = (nitpick_prefix ^ s, 999)
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   311
val let_inline_threshold = 20
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   312
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   313
fun s_let s n abs_T body_T f t =
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  if (n - 1) * (size_of_term t - 1) <= let_inline_threshold then
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    f t
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  else
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    let val z = (let_var s, abs_T) in
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      Const (@{const_name Let}, abs_T --> (abs_T --> body_T) --> body_T)
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      $ t $ abs_var z (incr_boundvars 1 (f (Var z)))
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   320
    end
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   321
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fun loose_bvar1_count (Bound i, k) = if i = k then 1 else 0
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  | loose_bvar1_count (t1 $ t2, k) =
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    loose_bvar1_count (t1, k) + loose_bvar1_count (t2, k)
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  | loose_bvar1_count (Abs (_, _, t), k) = loose_bvar1_count (t, k + 1)
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  | loose_bvar1_count _ = 0
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   327
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fun s_betapply _ (Const (@{const_name If}, _) $ @{const True} $ t1', _) = t1'
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   329
  | s_betapply _ (Const (@{const_name If}, _) $ @{const False} $ _, t2) = t2
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   330
  | s_betapply Ts (Const (@{const_name Let},
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   331
                          Type (_, [bound_T, Type (_, [_, body_T])]))
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                   $ t12 $ Abs (s, T, t13'), t2) =
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    let val body_T' = range_type body_T in
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      Const (@{const_name Let}, bound_T --> (bound_T --> body_T') --> body_T')
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   335
      $ t12 $ Abs (s, T, s_betapply (T :: Ts) (t13', incr_boundvars 1 t2))
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   336
    end
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   337
  | s_betapply Ts (t1 as Abs (s1, T1, t1'), t2) =
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   338
    (s_let s1 (loose_bvar1_count (t1', 0)) T1 (fastype_of1 (T1 :: Ts, t1'))
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              (curry betapply t1) t2
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     handle TERM _ => betapply (t1, t2)) (* FIXME: fix all uses *)
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  | s_betapply _ (t1, t2) = t1 $ t2
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   342
fun s_betapplys Ts = Library.foldl (s_betapply Ts)
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   343
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   344
fun s_beta_norm Ts t =
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  let
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    fun aux _ (Var _) = raise Same.SAME
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   347
      | aux Ts (Abs (s, T, t')) = Abs (s, T, aux (T :: Ts) t')
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   348
      | aux Ts ((t1 as Abs _) $ t2) =
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   349
        Same.commit (aux Ts) (s_betapply Ts (t1, t2))
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   350
      | aux Ts (t1 $ t2) =
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   351
        ((case aux Ts t1 of
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   352
           t1 as Abs _ => Same.commit (aux Ts) (s_betapply Ts (t1, t2))
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   353
         | t1 => t1 $ Same.commit (aux Ts) t2)
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   354
        handle Same.SAME => t1 $ aux Ts t2)
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   355
      | aux _ _ = raise Same.SAME
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   356
  in aux Ts t handle Same.SAME => t end
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   357
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   358
fun s_conj (t1, @{const True}) = t1
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   359
  | s_conj (@{const True}, t2) = t2
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  | s_conj (t1, t2) =
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    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
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   362
    else HOLogic.mk_conj (t1, t2)
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   363
fun s_disj (t1, @{const False}) = t1
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   364
  | s_disj (@{const False}, t2) = t2
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   365
  | s_disj (t1, t2) =
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    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
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   367
    else HOLogic.mk_disj (t1, t2)
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   368
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   369
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
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   370
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
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   371
  | strip_connective _ t = [t]
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   372
fun strip_any_connective (t as (t0 $ _ $ _)) =
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   373
    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
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   374
      (strip_connective t0 t, t0)
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   375
    else
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   376
      ([t], @{const Not})
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   377
  | strip_any_connective t = ([t], @{const Not})
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   378
val conjuncts_of = strip_connective @{const "op &"}
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   379
val disjuncts_of = strip_connective @{const "op |"}
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   380
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   381
(* When you add constants to these lists, make sure to handle them in
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   382
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
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   383
   well. *)
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   384
val built_in_consts =
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   385
  [(@{const_name all}, 1),
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   386
   (@{const_name "=="}, 2),
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   387
   (@{const_name "==>"}, 2),
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   388
   (@{const_name Pure.conjunction}, 2),
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   389
   (@{const_name Trueprop}, 1),
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   390
   (@{const_name Not}, 1),
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   391
   (@{const_name False}, 0),
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   392
   (@{const_name True}, 0),
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   393
   (@{const_name All}, 1),
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   394
   (@{const_name Ex}, 1),
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   395
   (@{const_name "op ="}, 1),
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   396
   (@{const_name "op &"}, 2),
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   397
   (@{const_name "op |"}, 2),
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   398
   (@{const_name "op -->"}, 2),
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   399
   (@{const_name If}, 3),
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   400
   (@{const_name Let}, 2),
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   401
   (@{const_name Unity}, 0),
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   402
   (@{const_name Pair}, 2),
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   403
   (@{const_name fst}, 1),
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   404
   (@{const_name snd}, 1),
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   405
   (@{const_name Id}, 0),
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   406
   (@{const_name converse}, 1),
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   407
   (@{const_name trancl}, 1),
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   408
   (@{const_name rel_comp}, 2),
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   409
   (@{const_name image}, 2),
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   410
   (@{const_name finite}, 1),
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   411
   (@{const_name unknown}, 0),
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   412
   (@{const_name is_unknown}, 1),
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   413
   (@{const_name safe_The}, 1),
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   414
   (@{const_name safe_Eps}, 1),
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   415
   (@{const_name Frac}, 0),
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   416
   (@{const_name norm_frac}, 0)]
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   417
val built_in_nat_consts =
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   418
  [(@{const_name Suc}, 0),
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   419
   (@{const_name nat}, 0),
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   420
   (@{const_name nat_gcd}, 0),
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   421
   (@{const_name nat_lcm}, 0)]
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   422
val built_in_descr_consts =
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   423
  [(@{const_name The}, 1),
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   424
   (@{const_name Eps}, 1)]
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   425
val built_in_typed_consts =
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   426
  [((@{const_name zero_class.zero}, int_T), 0),
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   427
   ((@{const_name one_class.one}, int_T), 0),
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   428
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
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   429
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
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   430
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
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   431
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
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   432
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
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   433
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
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   434
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
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   435
val built_in_typed_nat_consts =
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   436
  [((@{const_name zero_class.zero}, nat_T), 0),
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   437
   ((@{const_name one_class.one}, nat_T), 0),
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   438
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
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   439
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
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   440
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
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   441
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
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   442
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
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   443
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
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   444
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
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   445
val built_in_set_consts =
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   446
  [(@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   447
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   448
fun unarize_type @{typ "unsigned_bit word"} = nat_T
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   449
  | unarize_type @{typ "signed_bit word"} = int_T
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   450
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
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   451
  | unarize_type T = T
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   452
fun unarize_unbox_etc_type (Type (@{type_name fin_fun}, Ts)) =
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   453
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
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   454
  | unarize_unbox_etc_type (Type (@{type_name fun_box}, Ts)) =
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   455
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
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   456
  | unarize_unbox_etc_type (Type (@{type_name pair_box}, Ts)) =
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   457
    Type (@{type_name "*"}, map unarize_unbox_etc_type Ts)
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   458
  | unarize_unbox_etc_type @{typ "unsigned_bit word"} = nat_T
blanchet@35665
   459
  | unarize_unbox_etc_type @{typ "signed_bit word"} = int_T
blanchet@35665
   460
  | unarize_unbox_etc_type (Type (s, Ts as _ :: _)) =
blanchet@35665
   461
    Type (s, map unarize_unbox_etc_type Ts)
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   462
  | unarize_unbox_etc_type T = T
blanchet@35280
   463
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   464
  | uniterize_type @{typ bisim_iterator} = nat_T
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   465
  | uniterize_type T = T
blanchet@35665
   466
val uniterize_unarize_unbox_etc_type = uniterize_type o unarize_unbox_etc_type
blanchet@35280
   467
blanchet@35665
   468
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_unbox_etc_type
blanchet@33192
   469
blanchet@33192
   470
val prefix_name = Long_Name.qualify o Long_Name.base_name
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   471
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   472
val prefix_abs_vars = Term.map_abs_vars o prefix_name
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   473
fun short_name s =
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   474
  case space_explode name_sep s of
blanchet@33192
   475
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   476
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   477
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   478
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   479
  | shorten_names_in_type T = T
blanchet@34121
   480
val shorten_names_in_term =
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   481
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   482
  #> map_types shorten_names_in_type
blanchet@33192
   483
blanchet@35665
   484
fun strict_type_match thy (T1, T2) =
blanchet@33192
   485
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   486
  handle Type.TYPE_MATCH => false
blanchet@35665
   487
fun type_match thy = strict_type_match thy o pairself unarize_unbox_etc_type
blanchet@33192
   488
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   489
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   490
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   491
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   492
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   493
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   494
blanchet@35711
   495
fun frac_from_term_pair T t1 t2 =
blanchet@35711
   496
  case snd (HOLogic.dest_number t1) of
blanchet@35711
   497
    0 => HOLogic.mk_number T 0
blanchet@35711
   498
  | n1 => case snd (HOLogic.dest_number t2) of
blanchet@35711
   499
            1 => HOLogic.mk_number T n1
blanchet@35711
   500
          | n2 => Const (@{const_name divide}, T --> T --> T)
blanchet@35711
   501
                  $ HOLogic.mk_number T n1 $ HOLogic.mk_number T n2
blanchet@35711
   502
blanchet@33192
   503
fun is_TFree (TFree _) = true
blanchet@33192
   504
  | is_TFree _ = false
blanchet@35665
   505
fun is_higher_order_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   506
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   507
  | is_higher_order_type _ = false
blanchet@35665
   508
fun is_fun_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   509
  | is_fun_type _ = false
blanchet@35665
   510
fun is_set_type (Type (@{type_name fun}, [_, @{typ bool}])) = true
blanchet@33192
   511
  | is_set_type _ = false
blanchet@35665
   512
fun is_pair_type (Type (@{type_name "*"}, _)) = true
blanchet@33192
   513
  | is_pair_type _ = false
blanchet@33192
   514
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   515
  | is_lfp_iterator_type _ = false
blanchet@33192
   516
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   517
  | is_gfp_iterator_type _ = false
blanchet@33192
   518
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   519
fun is_iterator_type T =
blanchet@35280
   520
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   521
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   522
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   523
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   524
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   525
  | is_word_type _ = false
blanchet@35280
   526
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   527
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   528
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   529
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   530
  | is_frac_type _ _ = false
blanchet@35220
   531
fun is_number_type thy = is_integer_like_type orf is_frac_type thy
blanchet@33192
   532
blanchet@33192
   533
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   534
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   535
        binder_types T)
blanchet@35718
   536
fun const_for_iterator_type (Type (s, Ts)) =
blanchet@35718
   537
    (strip_first_name_sep s |> snd, Ts ---> bool_T)
blanchet@33192
   538
  | const_for_iterator_type T =
blanchet@33232
   539
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   540
blanchet@33192
   541
fun strip_n_binders 0 T = ([], T)
blanchet@35665
   542
  | strip_n_binders n (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
   543
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   544
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   545
    strip_n_binders n (Type (@{type_name fun}, Ts))
blanchet@33232
   546
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   547
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   548
blanchet@35665
   549
fun num_factors_in_type (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
   550
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   551
  | num_factors_in_type _ = 1
blanchet@35665
   552
fun num_binder_types (Type (@{type_name fun}, [_, T2])) =
blanchet@35665
   553
    1 + num_binder_types T2
blanchet@33192
   554
  | num_binder_types _ = 0
blanchet@33192
   555
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   556
fun maybe_curried_binder_types T =
blanchet@33192
   557
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   558
blanchet@33192
   559
fun mk_flat_tuple _ [t] = t
blanchet@35665
   560
  | mk_flat_tuple (Type (@{type_name "*"}, [T1, T2])) (t :: ts) =
blanchet@33192
   561
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   562
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   563
fun dest_n_tuple 1 t = [t]
blanchet@33192
   564
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   565
blanchet@35220
   566
type typedef_info =
blanchet@35220
   567
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   568
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   569
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   570
blanchet@37256
   571
fun typedef_info ctxt s =
blanchet@37256
   572
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   573
    if is_frac_type thy (Type (s, [])) then
blanchet@37256
   574
      SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@37256
   575
            Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@37256
   576
            set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@37256
   577
                            |> Logic.varify_global,
blanchet@37256
   578
            set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@37256
   579
    else case Typedef.get_info ctxt s of
blanchet@37258
   580
      (* When several entries are returned, it shouldn't matter much which one
blanchet@37258
   581
         we take (according to Florian Haftmann). *)
blanchet@37258
   582
      ({abs_type, rep_type, Abs_name, Rep_name, ...},
blanchet@37258
   583
       {set_def, Rep, Abs_inverse, Rep_inverse, ...}) :: _ =>
blanchet@37256
   584
      SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@37256
   585
            Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@37256
   586
            set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@37256
   587
            Rep_inverse = SOME Rep_inverse}
blanchet@37256
   588
    | _ => NONE
blanchet@37256
   589
  end
blanchet@35220
   590
blanchet@35220
   591
val is_typedef = is_some oo typedef_info
blanchet@35220
   592
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   593
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   594
blanchet@34121
   595
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   596
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   597
fun is_basic_datatype thy stds s =
blanchet@35220
   598
  member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@35220
   599
                 @{type_name int}, "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   600
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   601
blanchet@33192
   602
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   603
  Same.commit (Envir.subst_type_same
blanchet@35311
   604
                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
blanchet@33192
   605
  handle Type.TYPE_MATCH =>
blanchet@33232
   606
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@35311
   607
fun varify_and_instantiate_type thy T1 T1' T2 =
wenzelm@35845
   608
  instantiate_type thy (Logic.varifyT_global T1) T1' (Logic.varifyT_global T2)
blanchet@33192
   609
blanchet@33192
   610
fun repair_constr_type thy body_T' T =
blanchet@35311
   611
  varify_and_instantiate_type thy (body_type T) body_T' T
blanchet@33192
   612
blanchet@33192
   613
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   614
  let
blanchet@33583
   615
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   616
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   617
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   618
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   619
blanchet@33192
   620
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   621
  let
blanchet@33583
   622
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   623
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   624
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   625
    val _ =
blanchet@34936
   626
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35665
   627
         co_s <> @{type_name fun} andalso
blanchet@35220
   628
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   629
        ()
blanchet@34121
   630
      else
blanchet@34121
   631
        raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   632
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   633
                                   codatatypes
blanchet@33583
   634
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   635
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   636
blanchet@35284
   637
fun is_quot_type thy (Type (s, _)) =
blanchet@35284
   638
    is_some (Quotient_Info.quotdata_lookup_raw thy s)
blanchet@34936
   639
  | is_quot_type _ _ = false
blanchet@35280
   640
fun is_codatatype thy (Type (s, _)) =
blanchet@33583
   641
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   642
               |> Option.map snd |> these))
blanchet@33192
   643
  | is_codatatype _ _ = false
blanchet@37256
   644
fun is_pure_typedef ctxt (T as Type (s, _)) =
blanchet@37256
   645
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   646
      is_typedef ctxt s andalso
blanchet@37256
   647
      not (is_real_datatype thy s orelse is_quot_type thy T orelse
blanchet@37256
   648
           is_codatatype thy T orelse is_record_type T orelse
blanchet@37256
   649
           is_integer_like_type T)
blanchet@37256
   650
    end
blanchet@33192
   651
  | is_pure_typedef _ _ = false
blanchet@37256
   652
fun is_univ_typedef ctxt (Type (s, _)) =
blanchet@37256
   653
    (case typedef_info ctxt s of
blanchet@33192
   654
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@35332
   655
       let
blanchet@35332
   656
         val t_opt =
blanchet@35332
   657
           case set_def of
blanchet@35332
   658
             SOME thm => try (snd o Logic.dest_equals o prop_of) thm
blanchet@35332
   659
           | NONE => try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop)
blanchet@35332
   660
                         prop_of_Rep
blanchet@35332
   661
       in
blanchet@35332
   662
         case t_opt of
blanchet@35332
   663
           SOME (Const (@{const_name top}, _)) => true
blanchet@35386
   664
           (* "Multiset.multiset" *)
blanchet@35332
   665
         | SOME (Const (@{const_name Collect}, _)
blanchet@35332
   666
                 $ Abs (_, _, Const (@{const_name finite}, _) $ _)) => true
blanchet@35386
   667
           (* "FinFun.finfun" *)
blanchet@35386
   668
         | SOME (Const (@{const_name Collect}, _) $ Abs (_, _,
blanchet@35386
   669
                     Const (@{const_name Ex}, _) $ Abs (_, _,
blanchet@35386
   670
                         Const (@{const_name finite}, _) $ _))) => true
blanchet@35332
   671
         | _ => false
blanchet@35332
   672
       end
blanchet@33192
   673
     | NONE => false)
blanchet@33192
   674
  | is_univ_typedef _ _ = false
blanchet@37256
   675
fun is_datatype ctxt stds (T as Type (s, _)) =
blanchet@37256
   676
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   677
      (is_typedef ctxt s orelse is_codatatype thy T orelse T = @{typ ind} orelse
blanchet@37256
   678
       is_quot_type thy T) andalso not (is_basic_datatype thy stds s)
blanchet@37256
   679
    end
blanchet@35220
   680
  | is_datatype _ _ _ = false
blanchet@33192
   681
blanchet@33192
   682
fun all_record_fields thy T =
blanchet@33192
   683
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   684
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   685
  end
blanchet@33192
   686
  handle TYPE _ => []
blanchet@35280
   687
fun is_record_constr (s, T) =
blanchet@33192
   688
  String.isSuffix Record.extN s andalso
blanchet@33192
   689
  let val dataT = body_type T in
blanchet@33192
   690
    is_record_type dataT andalso
blanchet@33192
   691
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   692
  end
blanchet@33192
   693
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   694
fun no_of_record_field thy s T1 =
blanchet@34121
   695
  find_index (curry (op =) s o fst)
blanchet@34121
   696
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@35665
   697
fun is_record_get thy (s, Type (@{type_name fun}, [T1, _])) =
blanchet@34121
   698
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   699
  | is_record_get _ _ = false
blanchet@33192
   700
fun is_record_update thy (s, T) =
blanchet@33192
   701
  String.isSuffix Record.updateN s andalso
blanchet@34121
   702
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   703
         (all_record_fields thy (body_type T))
blanchet@33192
   704
  handle TYPE _ => false
blanchet@37256
   705
fun is_abs_fun ctxt (s, Type (@{type_name fun}, [_, Type (s', _)])) =
blanchet@37256
   706
    (case typedef_info ctxt s' of
blanchet@33192
   707
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   708
     | NONE => false)
blanchet@33192
   709
  | is_abs_fun _ _ = false
blanchet@37256
   710
fun is_rep_fun ctxt (s, Type (@{type_name fun}, [Type (s', _), _])) =
blanchet@37256
   711
    (case typedef_info ctxt s' of
blanchet@33192
   712
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   713
     | NONE => false)
blanchet@33192
   714
  | is_rep_fun _ _ = false
blanchet@35665
   715
fun is_quot_abs_fun ctxt
blanchet@35665
   716
                    (x as (_, Type (@{type_name fun}, [_, Type (s', _)]))) =
blanchet@35284
   717
    (try (Quotient_Term.absrep_const_chk Quotient_Term.AbsF ctxt) s'
blanchet@35284
   718
     = SOME (Const x))
blanchet@34936
   719
  | is_quot_abs_fun _ _ = false
blanchet@35665
   720
fun is_quot_rep_fun ctxt
blanchet@35665
   721
                    (x as (_, Type (@{type_name fun}, [Type (s', _), _]))) =
blanchet@35284
   722
    (try (Quotient_Term.absrep_const_chk Quotient_Term.RepF ctxt) s'
blanchet@35284
   723
     = SOME (Const x))
blanchet@34936
   724
  | is_quot_rep_fun _ _ = false
blanchet@33192
   725
blanchet@37256
   726
fun mate_of_rep_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@37256
   727
                                         [T1 as Type (s', _), T2]))) =
blanchet@37256
   728
    (case typedef_info ctxt s' of
blanchet@35665
   729
       SOME {Abs_name, ...} => (Abs_name, Type (@{type_name fun}, [T2, T1]))
blanchet@33232
   730
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   731
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@35284
   732
fun rep_type_for_quot_type thy (T as Type (s, _)) =
blanchet@35284
   733
  let val {qtyp, rtyp, ...} = Quotient_Info.quotdata_lookup thy s in
blanchet@35284
   734
    instantiate_type thy qtyp T rtyp
blanchet@35284
   735
  end
blanchet@35284
   736
fun equiv_relation_for_quot_type thy (Type (s, Ts)) =
blanchet@35284
   737
    let
blanchet@35284
   738
      val {qtyp, equiv_rel, ...} = Quotient_Info.quotdata_lookup thy s
blanchet@35284
   739
      val Ts' = qtyp |> dest_Type |> snd
blanchet@35284
   740
    in subst_atomic_types (Ts' ~~ Ts) equiv_rel end
blanchet@34936
   741
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   742
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   743
blanchet@33192
   744
fun is_coconstr thy (s, T) =
blanchet@33192
   745
  let
blanchet@33583
   746
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   747
    val co_T = body_type T
blanchet@33192
   748
    val co_s = dest_Type co_T |> fst
blanchet@33192
   749
  in
blanchet@33192
   750
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   751
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   752
  end
blanchet@33192
   753
  handle TYPE ("dest_Type", _, _) => false
blanchet@37256
   754
fun is_constr_like ctxt (s, T) =
blanchet@35665
   755
  member (op =) [@{const_name FinFun}, @{const_name FunBox},
blanchet@35665
   756
                 @{const_name PairBox}, @{const_name Quot},
blanchet@35665
   757
                 @{const_name Zero_Rep}, @{const_name Suc_Rep}] s orelse
blanchet@37256
   758
  let
blanchet@37256
   759
    val thy = ProofContext.theory_of ctxt
blanchet@37256
   760
    val (x as (_, T)) = (s, unarize_unbox_etc_type T)
blanchet@37256
   761
  in
blanchet@37260
   762
    is_real_constr thy x orelse is_record_constr x orelse
blanchet@37256
   763
    (is_abs_fun ctxt x andalso is_pure_typedef ctxt (range_type T)) orelse
blanchet@34936
   764
    is_coconstr thy x
blanchet@33192
   765
  end
blanchet@37256
   766
fun is_stale_constr ctxt (x as (_, T)) =
blanchet@37256
   767
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   768
    is_codatatype thy (body_type T) andalso is_constr_like ctxt x andalso
blanchet@37256
   769
    not (is_coconstr thy x)
blanchet@37256
   770
  end
blanchet@37256
   771
fun is_constr ctxt stds (x as (_, T)) =
blanchet@37256
   772
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   773
    is_constr_like ctxt x andalso
blanchet@37256
   774
    not (is_basic_datatype thy stds
blanchet@35220
   775
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@37256
   776
    not (is_stale_constr ctxt x)
blanchet@37256
   777
  end
blanchet@33192
   778
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   779
val is_sel_like_and_no_discr =
blanchet@35665
   780
  String.isPrefix sel_prefix orf
blanchet@35665
   781
  (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   782
blanchet@33192
   783
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   784
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   785
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   786
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   787
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   788
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   789
blanchet@35070
   790
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   791
  case T of
blanchet@35665
   792
    Type (@{type_name fun}, _) =>
blanchet@34936
   793
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   794
    not (is_boolean_type (body_type T))
blanchet@35665
   795
  | Type (@{type_name "*"}, Ts) =>
blanchet@34936
   796
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   797
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   798
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   799
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   800
  | _ => false
blanchet@35280
   801
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   802
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   803
    SOME (SOME box_me) => box_me
blanchet@35070
   804
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   805
and box_type hol_ctxt boxy T =
blanchet@33192
   806
  case T of
blanchet@35665
   807
    Type (z as (@{type_name fun}, [T1, T2])) =>
blanchet@34936
   808
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   809
       should_box_type hol_ctxt boxy z then
blanchet@33192
   810
      Type (@{type_name fun_box},
blanchet@35070
   811
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   812
    else
blanchet@35070
   813
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   814
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@35665
   815
  | Type (z as (@{type_name "*"}, Ts)) =>
blanchet@34982
   816
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   817
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   818
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   819
    else
blanchet@35665
   820
      Type (@{type_name "*"},
blanchet@35665
   821
            map (box_type hol_ctxt
blanchet@34121
   822
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   823
                           else InPair)) Ts)
blanchet@33192
   824
  | _ => T
blanchet@33192
   825
blanchet@35190
   826
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   827
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   828
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   829
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   830
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   831
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   832
blanchet@33192
   833
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   834
blanchet@33192
   835
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   836
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   837
  if s = @{const_name Pair} then
blanchet@33192
   838
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   839
  else
blanchet@33192
   840
    sel_prefix_for n ^ s
blanchet@33192
   841
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   842
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   843
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   844
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   845
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   846
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   847
  oo nth_sel_for_constr
blanchet@33192
   848
blanchet@33192
   849
fun sel_no_from_name s =
blanchet@33192
   850
  if String.isPrefix discr_prefix s then
blanchet@33192
   851
    ~1
blanchet@33192
   852
  else if String.isPrefix sel_prefix s then
blanchet@33192
   853
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   854
  else if s = @{const_name snd} then
blanchet@33192
   855
    1
blanchet@33192
   856
  else
blanchet@33192
   857
    0
blanchet@33192
   858
blanchet@35078
   859
val close_form =
blanchet@35078
   860
  let
blanchet@35078
   861
    fun close_up zs zs' =
blanchet@35078
   862
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   863
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   864
           (take (length zs' - length zs) zs')
blanchet@35078
   865
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   866
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   867
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   868
        end
blanchet@35078
   869
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   870
  in aux [] end
blanchet@35078
   871
blanchet@33192
   872
fun eta_expand _ t 0 = t
blanchet@33192
   873
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   874
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   875
  | eta_expand Ts t n =
blanchet@37261
   876
    fold_rev (curry3 Abs ("x" ^ nat_subscript n))
blanchet@33192
   877
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   878
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   879
blanchet@33192
   880
fun extensionalize t =
blanchet@33192
   881
  case t of
blanchet@33192
   882
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   883
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   884
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   885
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   886
    end
blanchet@33192
   887
  | _ => t
blanchet@33192
   888
blanchet@33192
   889
fun distinctness_formula T =
blanchet@33192
   890
  all_distinct_unordered_pairs_of
blanchet@33192
   891
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   892
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   893
blanchet@35220
   894
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   895
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   896
blanchet@37256
   897
fun uncached_datatype_constrs ({thy, ctxt, stds, ...} : hol_context)
blanchet@35220
   898
                              (T as Type (s, Ts)) =
blanchet@33583
   899
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@34982
   900
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   901
     | _ =>
blanchet@37256
   902
       if is_datatype ctxt stds T then
blanchet@33581
   903
         case Datatype.get_info thy s of
blanchet@33581
   904
           SOME {index, descr, ...} =>
blanchet@33581
   905
           let
blanchet@33581
   906
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   907
           in
blanchet@37260
   908
             map (apsnd (fn Us =>
blanchet@37260
   909
                            map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@37260
   910
                 constrs
blanchet@33581
   911
           end
blanchet@33581
   912
         | NONE =>
blanchet@33581
   913
           if is_record_type T then
blanchet@33581
   914
             let
blanchet@33581
   915
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   916
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   917
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   918
             in [(s', T')] end
blanchet@34936
   919
           else if is_quot_type thy T then
blanchet@34936
   920
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@37256
   921
           else case typedef_info ctxt s of
blanchet@33581
   922
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@35311
   923
             [(Abs_name,
blanchet@35311
   924
               varify_and_instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   925
           | NONE =>
blanchet@33581
   926
             if T = @{typ ind} then
blanchet@33581
   927
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   928
             else
blanchet@33581
   929
               []
blanchet@33581
   930
       else
blanchet@33581
   931
         [])
blanchet@33580
   932
  | uncached_datatype_constrs _ _ = []
blanchet@35220
   933
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   934
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   935
    SOME xs => xs
blanchet@33580
   936
  | NONE =>
blanchet@35220
   937
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   938
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   939
    end
blanchet@35190
   940
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   941
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   942
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@33192
   943
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   944
blanchet@33192
   945
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   946
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   947
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   948
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   949
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   950
    AList.lookup (op =)
blanchet@35190
   951
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   952
        s
blanchet@33192
   953
    |> the |> pair s
blanchet@33192
   954
  end
blanchet@34982
   955
blanchet@35070
   956
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   957
  let val dataT = body_type T in
blanchet@33192
   958
    if s = @{const_name Suc} then
blanchet@33192
   959
      Abs (Name.uu, dataT,
blanchet@33192
   960
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
   961
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
   962
      Const (discr_for_constr x)
blanchet@33192
   963
    else
blanchet@33192
   964
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   965
  end
blanchet@37256
   966
fun discriminate_value (hol_ctxt as {ctxt, ...}) x t =
blanchet@35280
   967
  case head_of t of
blanchet@35280
   968
    Const x' =>
blanchet@33192
   969
    if x = x' then @{const True}
blanchet@37256
   970
    else if is_constr_like ctxt x' then @{const False}
blanchet@37476
   971
    else s_betapply [] (discr_term_for_constr hol_ctxt x, t)
blanchet@37476
   972
  | _ => s_betapply [] (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
   973
blanchet@35220
   974
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
   975
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
   976
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
   977
      @{term "%n::nat. n - 1"}
blanchet@33192
   978
    else if is_pair_type dataT then
blanchet@33192
   979
      Const (nth_sel_for_constr x n)
blanchet@33192
   980
    else
blanchet@33192
   981
      let
blanchet@35665
   982
        fun aux m (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
   983
            let
blanchet@33192
   984
              val (m, t1) = aux m T1
blanchet@33192
   985
              val (m, t2) = aux m T2
blanchet@33192
   986
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   987
          | aux m T =
blanchet@33192
   988
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
   989
                    $ Bound 0)
blanchet@33192
   990
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
   991
                     (List.take (arg_Ts, n)) 0
blanchet@33192
   992
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
   993
  end
blanchet@37256
   994
fun select_nth_constr_arg ctxt stds x t n res_T =
blanchet@37256
   995
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   996
    (case strip_comb t of
blanchet@37256
   997
       (Const x', args) =>
blanchet@37256
   998
       if x = x' then nth args n
blanchet@37256
   999
       else if is_constr_like ctxt x' then Const (@{const_name unknown}, res_T)
blanchet@37256
  1000
       else raise SAME ()
blanchet@37256
  1001
     | _ => raise SAME())
blanchet@37476
  1002
    handle SAME () =>
blanchet@37476
  1003
           s_betapply [] (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@37256
  1004
  end
blanchet@33192
  1005
blanchet@35220
  1006
fun construct_value _ _ x [] = Const x
blanchet@37256
  1007
  | construct_value ctxt stds (x as (s, _)) args =
blanchet@33192
  1008
    let val args = map Envir.eta_contract args in
blanchet@33192
  1009
      case hd args of
blanchet@35280
  1010
        Const (s', _) $ t =>
blanchet@34936
  1011
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
  1012
           constr_name_for_sel_like s' = s andalso
blanchet@35220
  1013
           forall (fn (n, t') =>
blanchet@37256
  1014
                      select_nth_constr_arg ctxt stds x t n dummyT = t')
blanchet@34936
  1015
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  1016
          t
blanchet@33192
  1017
        else
blanchet@33192
  1018
          list_comb (Const x, args)
blanchet@33192
  1019
      | _ => list_comb (Const x, args)
blanchet@33192
  1020
    end
blanchet@33192
  1021
blanchet@37256
  1022
fun constr_expand (hol_ctxt as {ctxt, stds, ...}) T t =
blanchet@35665
  1023
  (case head_of t of
blanchet@37256
  1024
     Const x => if is_constr_like ctxt x then t else raise SAME ()
blanchet@35665
  1025
   | _ => raise SAME ())
blanchet@35665
  1026
  handle SAME () =>
blanchet@35665
  1027
         let
blanchet@35665
  1028
           val x' as (_, T') =
blanchet@35665
  1029
             if is_pair_type T then
blanchet@35665
  1030
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@35665
  1031
                 (@{const_name Pair}, T1 --> T2 --> T)
blanchet@35665
  1032
               end
blanchet@35665
  1033
             else
blanchet@35665
  1034
               datatype_constrs hol_ctxt T |> hd
blanchet@35665
  1035
           val arg_Ts = binder_types T'
blanchet@35665
  1036
         in
blanchet@37256
  1037
           list_comb (Const x', map2 (select_nth_constr_arg ctxt stds x' t)
blanchet@35665
  1038
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@35665
  1039
         end
blanchet@35665
  1040
blanchet@35665
  1041
fun coerce_bound_no f j t =
blanchet@35665
  1042
  case t of
blanchet@35665
  1043
    t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
blanchet@35665
  1044
  | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
blanchet@35665
  1045
  | Bound j' => if j' = j then f t else t
blanchet@35665
  1046
  | _ => t
blanchet@35665
  1047
fun coerce_bound_0_in_term hol_ctxt new_T old_T =
blanchet@35665
  1048
  old_T <> new_T ? coerce_bound_no (coerce_term hol_ctxt [new_T] old_T new_T) 0
blanchet@37256
  1049
and coerce_term (hol_ctxt as {ctxt, stds, fast_descrs, ...}) Ts new_T old_T t =
blanchet@35665
  1050
  if old_T = new_T then
blanchet@35665
  1051
    t
blanchet@35665
  1052
  else
blanchet@35665
  1053
    case (new_T, old_T) of
blanchet@35665
  1054
      (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1055
       Type (@{type_name fun}, [old_T1, old_T2])) =>
blanchet@35665
  1056
      (case eta_expand Ts t 1 of
blanchet@35665
  1057
         Abs (s, _, t') =>
blanchet@35665
  1058
         Abs (s, new_T1,
blanchet@35665
  1059
              t' |> coerce_bound_0_in_term hol_ctxt new_T1 old_T1
blanchet@35665
  1060
                 |> coerce_term hol_ctxt (new_T1 :: Ts) new_T2 old_T2)
blanchet@35665
  1061
         |> Envir.eta_contract
blanchet@35665
  1062
         |> new_s <> @{type_name fun}
blanchet@37256
  1063
            ? construct_value ctxt stds
blanchet@35665
  1064
                  (if new_s = @{type_name fin_fun} then @{const_name FinFun}
blanchet@35665
  1065
                   else @{const_name FunBox},
blanchet@35665
  1066
                   Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1067
              o single
blanchet@35665
  1068
       | t' => raise TERM ("Nitpick_HOL.coerce_term", [t']))
blanchet@35665
  1069
    | (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1070
       Type (old_s, old_Ts as [old_T1, old_T2])) =>
blanchet@35665
  1071
      if old_s = @{type_name fin_fun} orelse old_s = @{type_name fun_box} orelse
blanchet@35665
  1072
         old_s = @{type_name pair_box} orelse old_s = @{type_name "*"} then
blanchet@35665
  1073
        case constr_expand hol_ctxt old_T t of
blanchet@35665
  1074
          Const (old_s, _) $ t1 =>
blanchet@35665
  1075
          if new_s = @{type_name fun} then
blanchet@35665
  1076
            coerce_term hol_ctxt Ts new_T (Type (@{type_name fun}, old_Ts)) t1
blanchet@35665
  1077
          else
blanchet@37256
  1078
            construct_value ctxt stds
blanchet@35665
  1079
                (old_s, Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1080
                [coerce_term hol_ctxt Ts (Type (@{type_name fun}, new_Ts))
blanchet@35665
  1081
                             (Type (@{type_name fun}, old_Ts)) t1]
blanchet@35665
  1082
        | Const _ $ t1 $ t2 =>
blanchet@37256
  1083
          construct_value ctxt stds
blanchet@35665
  1084
              (if new_s = @{type_name "*"} then @{const_name Pair}
blanchet@35665
  1085
               else @{const_name PairBox}, new_Ts ---> new_T)
blanchet@35665
  1086
              (map3 (coerce_term hol_ctxt Ts) [new_T1, new_T2] [old_T1, old_T2]
blanchet@35665
  1087
                    [t1, t2])
blanchet@35665
  1088
        | t' => raise TERM ("Nitpick_HOL.coerce_term", [t'])
blanchet@35665
  1089
      else
blanchet@35665
  1090
        raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1091
    | _ => raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1092
blanchet@35665
  1093
fun card_of_type assigns (Type (@{type_name fun}, [T1, T2])) =
blanchet@34123
  1094
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@35665
  1095
  | card_of_type assigns (Type (@{type_name "*"}, [T1, T2])) =
blanchet@34123
  1096
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1097
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1098
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1099
  | card_of_type _ @{typ bool} = 2
blanchet@33192
  1100
  | card_of_type _ @{typ unit} = 1
blanchet@34123
  1101
  | card_of_type assigns T =
blanchet@34123
  1102
    case AList.lookup (op =) assigns T of
blanchet@33192
  1103
      SOME k => k
blanchet@33192
  1104
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1105
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@35665
  1106
fun bounded_card_of_type max default_card assigns
blanchet@35665
  1107
                         (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
  1108
    let
blanchet@34123
  1109
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1110
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1111
    in
blanchet@33192
  1112
      if k1 = max orelse k2 = max then max
blanchet@33192
  1113
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1114
    end
blanchet@35665
  1115
  | bounded_card_of_type max default_card assigns
blanchet@35665
  1116
                         (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
  1117
    let
blanchet@34123
  1118
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1119
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1120
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1121
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1122
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1123
                    card_of_type assigns T
blanchet@33192
  1124
                  else
blanchet@34123
  1125
                    card_of_type assigns T
blanchet@33232
  1126
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1127
                           default_card)
blanchet@35385
  1128
fun bounded_exact_card_of_type hol_ctxt finitizable_dataTs max default_card
blanchet@35385
  1129
                               assigns T =
blanchet@33192
  1130
  let
blanchet@33192
  1131
    fun aux avoid T =
blanchet@34121
  1132
      (if member (op =) avoid T then
blanchet@33192
  1133
         0
blanchet@35385
  1134
       else if member (op =) finitizable_dataTs T then
blanchet@35385
  1135
         raise SAME ()
blanchet@33192
  1136
       else case T of
blanchet@35665
  1137
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
  1138
         let
blanchet@33192
  1139
           val k1 = aux avoid T1
blanchet@33192
  1140
           val k2 = aux avoid T2
blanchet@33192
  1141
         in
blanchet@33192
  1142
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1143
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1144
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1145
         end
blanchet@35665
  1146
       | Type (@{type_name "*"}, [T1, T2]) =>
blanchet@33192
  1147
         let
blanchet@33192
  1148
           val k1 = aux avoid T1
blanchet@33192
  1149
           val k2 = aux avoid T2
blanchet@33192
  1150
         in
blanchet@33192
  1151
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1152
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1153
           else Int.min (max, k1 * k2)
blanchet@33192
  1154
         end
blanchet@33192
  1155
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1156
       | @{typ prop} => 2
blanchet@33192
  1157
       | @{typ bool} => 2
blanchet@33192
  1158
       | @{typ unit} => 1
blanchet@33192
  1159
       | Type _ =>
blanchet@35070
  1160
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1161
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1162
                  else raise SAME ()
blanchet@33192
  1163
          | constrs =>
blanchet@33192
  1164
            let
blanchet@33192
  1165
              val constr_cards =
blanchet@35280
  1166
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1167
                    constrs
blanchet@33192
  1168
            in
blanchet@34121
  1169
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1170
              else Integer.sum constr_cards
blanchet@33192
  1171
            end)
blanchet@33192
  1172
       | _ => raise SAME ())
blanchet@34123
  1173
      handle SAME () =>
blanchet@34123
  1174
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1175
  in Int.min (max, aux [] T) end
blanchet@33192
  1176
blanchet@35665
  1177
val small_type_max_card = 5
blanchet@35665
  1178
blanchet@35384
  1179
fun is_finite_type hol_ctxt T =
blanchet@35665
  1180
  bounded_exact_card_of_type hol_ctxt [] 1 2 [] T > 0
blanchet@35665
  1181
fun is_small_finite_type hol_ctxt T =
blanchet@35665
  1182
  let val n = bounded_exact_card_of_type hol_ctxt [] 1 2 [] T in
blanchet@35665
  1183
    n > 0 andalso n <= small_type_max_card
blanchet@35665
  1184
  end
blanchet@33192
  1185
blanchet@33192
  1186
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1187
  | is_ground_term (Const _) = true
blanchet@33192
  1188
  | is_ground_term _ = false
blanchet@33192
  1189
blanchet@36062
  1190
fun hashw_term (t1 $ t2) = hashw (hashw_term t1, hashw_term t2)
blanchet@36062
  1191
  | hashw_term (Const (s, _)) = hashw_string (s, 0w0)
blanchet@33192
  1192
  | hashw_term _ = 0w0
blanchet@33192
  1193
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1194
blanchet@33192
  1195
fun special_bounds ts =
wenzelm@35408
  1196
  fold Term.add_vars ts [] |> sort (Term_Ord.fast_indexname_ord o pairself fst)
blanchet@33192
  1197
blanchet@33571
  1198
fun is_funky_typedef_name thy s =
blanchet@34121
  1199
  member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@34936
  1200
                 @{type_name int}] s orelse
blanchet@34936
  1201
  is_frac_type thy (Type (s, []))
blanchet@33571
  1202
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
  1203
  | is_funky_typedef _ _ = false
blanchet@33192
  1204
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1205
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1206
  | is_arity_type_axiom _ = false
blanchet@37256
  1207
fun is_typedef_axiom ctxt boring (@{const "==>"} $ _ $ t2) =
blanchet@37256
  1208
    is_typedef_axiom ctxt boring t2
blanchet@37256
  1209
  | is_typedef_axiom ctxt boring
blanchet@33192
  1210
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@35665
  1211
         $ Const (_, Type (@{type_name fun}, [Type (s, _), _]))
blanchet@35665
  1212
         $ Const _ $ _)) =
blanchet@37256
  1213
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
  1214
      boring <> is_funky_typedef_name thy s andalso is_typedef ctxt s
blanchet@37256
  1215
    end
blanchet@33192
  1216
  | is_typedef_axiom _ _ _ = false
blanchet@36126
  1217
val is_class_axiom =
blanchet@36126
  1218
  Logic.strip_horn #> swap #> op :: #> forall (can Logic.dest_of_class)
blanchet@33192
  1219
blanchet@33192
  1220
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1221
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1222
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1223
   using "typedef_info". *)
blanchet@37256
  1224
fun partition_axioms_by_definitionality ctxt axioms def_names =
blanchet@33192
  1225
  let
blanchet@33192
  1226
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1227
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1228
    val nondefs =
blanchet@33192
  1229
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@37256
  1230
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom ctxt true) o snd)
blanchet@33192
  1231
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1232
blanchet@33197
  1233
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1234
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1235
   commands. *)
blanchet@33192
  1236
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1237
blanchet@35283
  1238
val is_trivial_definition =
blanchet@35283
  1239
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1240
val is_plain_definition =
blanchet@33192
  1241
  let
blanchet@33192
  1242
    fun do_lhs t1 =
blanchet@33192
  1243
      case strip_comb t1 of
blanchet@34936
  1244
        (Const _, args) =>
blanchet@34936
  1245
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1246
      | _ => false
blanchet@33192
  1247
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1248
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1249
        do_lhs t1
blanchet@33192
  1250
      | do_eq _ = false
blanchet@33192
  1251
  in do_eq end
blanchet@33192
  1252
blanchet@37256
  1253
fun all_axioms_of ctxt subst =
blanchet@33192
  1254
  let
blanchet@37256
  1255
    val thy = ProofContext.theory_of ctxt
blanchet@35335
  1256
    val axioms_of_thys =
blanchet@35893
  1257
      maps Thm.axioms_of
blanchet@35893
  1258
      #> map (apsnd (subst_atomic subst o prop_of))
blanchet@35893
  1259
      #> filter_out (is_class_axiom o snd)
blanchet@33192
  1260
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1261
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1262
                    |> OrdList.make fast_string_ord
blanchet@33192
  1263
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1264
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1265
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1266
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1267
    val (built_in_defs, built_in_nondefs) =
blanchet@37256
  1268
      partition_axioms_by_definitionality ctxt built_in_axioms def_names
blanchet@37256
  1269
      ||> filter (is_typedef_axiom ctxt false)
blanchet@33192
  1270
    val (user_defs, user_nondefs) =
blanchet@37256
  1271
      partition_axioms_by_definitionality ctxt user_axioms def_names
blanchet@33197
  1272
    val (built_in_nondefs, user_nondefs) =
blanchet@37256
  1273
      List.partition (is_typedef_axiom ctxt false) user_nondefs
blanchet@33197
  1274
      |>> append built_in_nondefs
blanchet@34121
  1275
    val defs =
blanchet@34121
  1276
      (thy |> PureThy.all_thms_of
blanchet@34121
  1277
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1278
           |> map (prop_of o snd)
blanchet@35283
  1279
           |> filter_out is_trivial_definition
blanchet@35283
  1280
           |> filter is_plain_definition) @
blanchet@34121
  1281
      user_defs @ built_in_defs
blanchet@33192
  1282
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1283
blanchet@35220
  1284
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1285
  if s = @{const_name If} then
blanchet@33192
  1286
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1287
  else
blanchet@35220
  1288
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1289
      case AList.lookup (op =)
blanchet@35220
  1290
                    (built_in_consts
blanchet@35220
  1291
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1292
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1293
        SOME n => SOME n
blanchet@35220
  1294
      | NONE =>
blanchet@35220
  1295
        case AList.lookup (op =)
blanchet@35220
  1296
                 (built_in_typed_consts
blanchet@35220
  1297
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1298
                 (s, unarize_type T) of
blanchet@35220
  1299
          SOME n => SOME n
blanchet@35220
  1300
        | NONE =>
blanchet@35280
  1301
          case s of
blanchet@35280
  1302
            @{const_name zero_class.zero} =>
blanchet@35280
  1303
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1304
          | @{const_name Suc} =>
blanchet@35280
  1305
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1306
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1307
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1308
                 else
blanchet@35280
  1309
                   NONE
blanchet@35220
  1310
    end
blanchet@35220
  1311
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1312
blanchet@33192
  1313
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1314
   simplification rules (equational specifications). *)
blanchet@33192
  1315
fun term_under_def t =
blanchet@33192
  1316
  case t of
blanchet@33192
  1317
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1318
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1319
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1320
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1321
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1322
  | t1 $ _ => term_under_def t1
blanchet@33192
  1323
  | _ => t
blanchet@33192
  1324
blanchet@36555
  1325
(* Here we crucially rely on "specialize_type" performing a preorder traversal
blanchet@36555
  1326
   of the term, without which the wrong occurrence of a constant could be
blanchet@36555
  1327
   matched in the face of overloading. *)
blanchet@35220
  1328
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1329
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1330
    []
blanchet@33192
  1331
  else
blanchet@33192
  1332
    these (Symtab.lookup table s)
blanchet@36555
  1333
    |> map_filter (try (specialize_type thy x))
blanchet@34121
  1334
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1335
blanchet@35280
  1336
fun normalized_rhs_of t =
blanchet@33192
  1337
  let
blanchet@33743
  1338
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1339
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1340
      | aux _ _ = NONE
blanchet@33192
  1341
    val (lhs, rhs) =
blanchet@33192
  1342
      case t of
blanchet@33192
  1343
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1344
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1345
        (t1, t2)
blanchet@33232
  1346
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1347
    val args = strip_comb lhs |> snd
blanchet@33743
  1348
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1349
blanchet@33192
  1350
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1351
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1352
     original_name s <> s then
blanchet@33192
  1353
    NONE
blanchet@33192
  1354
  else
blanchet@37476
  1355
    x |> def_props_for_const thy [(NONE, false)] false table
blanchet@37476
  1356
      |> List.last
blanchet@35280
  1357
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1358
    handle List.Empty => NONE
blanchet@33192
  1359
blanchet@33192
  1360
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1361
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1362
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1363
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1364
blanchet@33192
  1365
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1366
  let
blanchet@33192
  1367
    fun is_good_arg (Bound _) = true
blanchet@33192
  1368
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1369
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1370
        s = @{const_name undefined}
blanchet@33192
  1371
      | is_good_arg _ = false
blanchet@33192
  1372
  in
blanchet@33192
  1373
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1374
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1375
      (case def_of_const thy table x of
blanchet@33192
  1376
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1377
       | NONE => false)
blanchet@33192
  1378
    | _ => false
blanchet@33192
  1379
  end
blanchet@33192
  1380
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1381
  map_aterms (fn t as Const x =>
blanchet@33192
  1382
                 (case def_of_const thy table x of
blanchet@33192
  1383
                    SOME t' =>
blanchet@33192
  1384
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1385
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1386
                      else t
blanchet@33192
  1387
                    end
blanchet@33192
  1388
                 | NONE => t)
blanchet@33192
  1389
               | t => t)
blanchet@33192
  1390
blanchet@35220
  1391
fun case_const_names thy stds =
blanchet@33192
  1392
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@35220
  1393
                  if is_basic_datatype thy stds dtype_s then
blanchet@33192
  1394
                    I
blanchet@33192
  1395
                  else
blanchet@33192
  1396
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1397
                                     |> the |> #3 |> length))
blanchet@33192
  1398
              (Datatype.get_all thy) [] @
blanchet@33583
  1399
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1400
blanchet@35718
  1401
fun fixpoint_kind_of_const thy table x =
blanchet@35718
  1402
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@35718
  1403
    NoFp
blanchet@35718
  1404
  else
blanchet@35718
  1405
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@35718
  1406
    handle Option.Option => NoFp
blanchet@33192
  1407
blanchet@35718
  1408
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35718
  1409
                             ...} : hol_context) x =
blanchet@35718
  1410
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35718
  1411
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@35718
  1412
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@35718
  1413
                             ...} : hol_context) x =
blanchet@35718
  1414
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@35718
  1415
                                                     x)))
blanchet@35718
  1416
         [!simp_table, psimp_table]
blanchet@35718
  1417
fun is_inductive_pred hol_ctxt =
blanchet@35718
  1418
  is_real_inductive_pred hol_ctxt andf (not o is_real_equational_fun hol_ctxt)
blanchet@35718
  1419
fun is_equational_fun hol_ctxt =
blanchet@35718
  1420
  (is_real_equational_fun hol_ctxt orf is_real_inductive_pred hol_ctxt orf
blanchet@35718
  1421
   (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1422
blanchet@35718
  1423
fun lhs_of_equation t =
blanchet@35718
  1424
  case t of
blanchet@35718
  1425
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1426
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1427
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1428
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@35718
  1429
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1430
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1431
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1432
  | _ => NONE
blanchet@35718
  1433
fun is_constr_pattern _ (Bound _) = true
blanchet@35718
  1434
  | is_constr_pattern _ (Var _) = true
blanchet@37256
  1435
  | is_constr_pattern ctxt t =
blanchet@35718
  1436
    case strip_comb t of
blanchet@35718
  1437
      (Const x, args) =>
blanchet@37256
  1438
      is_constr_like ctxt x andalso forall (is_constr_pattern ctxt) args
blanchet@35718
  1439
    | _ => false
blanchet@37256
  1440
fun is_constr_pattern_lhs ctxt t =
blanchet@37256
  1441
  forall (is_constr_pattern ctxt) (snd (strip_comb t))
blanchet@37256
  1442
fun is_constr_pattern_formula ctxt t =
blanchet@35718
  1443
  case lhs_of_equation t of
blanchet@37256
  1444
    SOME t' => is_constr_pattern_lhs ctxt t'
blanchet@35718
  1445
  | NONE => false
blanchet@35718
  1446
blanchet@36555
  1447
(* Similar to "specialize_type" but returns all matches rather than only the
blanchet@36555
  1448
   first (preorder) match. *)
blanchet@35807
  1449
fun multi_specialize_type thy slack (s, T) t =
blanchet@35807
  1450
  let
blanchet@35807
  1451
    fun aux (Const (s', T')) ys =
blanchet@35807
  1452
        if s = s' then
blanchet@35807
  1453
          ys |> (if AList.defined (op =) ys T' then
blanchet@35807
  1454
                   I
blanchet@35807
  1455
                 else
blanchet@36555
  1456
                   cons (T', monomorphic_term (Sign.typ_match thy (T', T)
blanchet@36555
  1457
                                                              Vartab.empty) t)
blanchet@35807
  1458
                   handle Type.TYPE_MATCH => I
blanchet@36575
  1459
                        | TERM _ =>
blanchet@35807
  1460
                          if slack then
blanchet@35807
  1461
                            I
blanchet@35807
  1462
                          else
blanchet@37253
  1463
                            raise NOT_SUPPORTED
blanchet@37253
  1464
                                      ("too much polymorphism in axiom \"" ^
blanchet@37253
  1465
                                       Syntax.string_of_term_global thy t ^
blanchet@37253
  1466
                                       "\" involving " ^ quote s))
blanchet@35807
  1467
        else
blanchet@35807
  1468
          ys
blanchet@35807
  1469
      | aux _ ys = ys
blanchet@35807
  1470
  in map snd (fold_aterms aux t []) end
blanchet@35807
  1471
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@35807
  1472
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@35807
  1473
blanchet@35807
  1474
fun unvarify_term (t1 $ t2) = unvarify_term t1 $ unvarify_term t2
blanchet@35807
  1475
  | unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@35807
  1476
  | unvarify_term (Abs (s, T, t')) = Abs (s, T, unvarify_term t')
blanchet@35807
  1477
  | unvarify_term t = t
blanchet@35807
  1478
fun axiom_for_choice_spec thy =
blanchet@35807
  1479
  unvarify_term
blanchet@35807
  1480
  #> Object_Logic.atomize_term thy
blanchet@35807
  1481
  #> Choice_Specification.close_form
blanchet@35807
  1482
  #> HOLogic.mk_Trueprop
blanchet@35807
  1483
fun is_choice_spec_fun ({thy, def_table, nondef_table, choice_spec_table, ...}
blanchet@35807
  1484
                        : hol_context) x =
blanchet@35807
  1485
  case nondef_props_for_const thy true choice_spec_table x of
blanchet@35807
  1486
    [] => false
blanchet@35807
  1487
  | ts => case def_of_const thy def_table x of
blanchet@35807
  1488
            SOME (Const (@{const_name Eps}, _) $ _) => true
blanchet@35807
  1489
          | SOME _ => false
blanchet@35807
  1490
          | NONE =>
blanchet@35807
  1491
            let val ts' = nondef_props_for_const thy true nondef_table x in
blanchet@35807
  1492
              length ts' = length ts andalso
blanchet@35807
  1493
              forall (fn t =>
blanchet@35807
  1494
                         exists (curry (op aconv) (axiom_for_choice_spec thy t))
blanchet@35807
  1495
                                ts') ts
blanchet@35807
  1496
            end
blanchet@35807
  1497
blanchet@35807
  1498
fun is_choice_spec_axiom thy choice_spec_table t =
blanchet@35807
  1499
  Symtab.exists (fn (_, ts) =>
blanchet@35807
  1500
                    exists (curry (op aconv) t o axiom_for_choice_spec thy) ts)
blanchet@35807
  1501
                choice_spec_table
blanchet@35807
  1502
blanchet@35718
  1503
(** Constant unfolding **)
blanchet@33192
  1504
blanchet@37476
  1505
fun constr_case_body ctxt stds (func_t, (x as (_, T))) =
blanchet@33192
  1506
  let val arg_Ts = binder_types T in
blanchet@37476
  1507
    s_betapplys [] (func_t, map2 (select_nth_constr_arg ctxt stds x (Bound 0))
blanchet@37476
  1508
                                 (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1509
  end
blanchet@37476
  1510
fun add_constr_case res_T (body_t, guard_t) res_t =
blanchet@37476
  1511
  if res_T = bool_T then
blanchet@37476
  1512
    s_conj (HOLogic.mk_imp (guard_t, body_t), res_t)
blanchet@37476
  1513
  else
blanchet@37476
  1514
    Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@37476
  1515
    $ guard_t $ body_t $ res_t
blanchet@37476
  1516
fun optimized_case_def (hol_ctxt as {ctxt, stds, ...}) dataT res_T func_ts =
blanchet@33192
  1517
  let
blanchet@35070
  1518
    val xs = datatype_constrs hol_ctxt dataT
blanchet@37476
  1519
    val cases =
blanchet@37476
  1520
      func_ts ~~ xs
blanchet@37476
  1521
      |> map (fn (func_t, x) =>
blanchet@37476
  1522
                 (constr_case_body ctxt stds (incr_boundvars 1 func_t, x),
blanchet@37476
  1523
                  discriminate_value hol_ctxt x (Bound 0)))
blanchet@37476
  1524
      |> AList.group (op aconv)
blanchet@37476
  1525
      |> map (apsnd (List.foldl s_disj @{const False}))
blanchet@37476
  1526
      |> sort (int_ord o pairself (size_of_term o fst))
blanchet@37476
  1527
      |> rev
blanchet@33192
  1528
  in
blanchet@37476
  1529
    if res_T = bool_T then
blanchet@37476
  1530
      if forall (member (op =) [@{const False}, @{const True}] o fst) cases then
blanchet@37476
  1531
        case cases of
blanchet@37476
  1532
          [(body_t, _)] => body_t
blanchet@37476
  1533
        | [_, (@{const True}, head_t2)] => head_t2
blanchet@37476
  1534
        | [_, (@{const False}, head_t2)] => @{const Not} $ head_t2
blanchet@37476
  1535
        | _ => raise BAD ("Nitpick_HOL.optimized_case_def", "impossible cases")
blanchet@37476
  1536
      else 
blanchet@37476
  1537
        @{const True} |> fold_rev (add_constr_case res_T) cases
blanchet@37476
  1538
    else
blanchet@37476
  1539
      fst (hd cases) |> fold_rev (add_constr_case res_T) (tl cases)
blanchet@33192
  1540
  end
blanchet@37476
  1541
  |> curry absdummy dataT
blanchet@37476
  1542
blanchet@37256
  1543
fun optimized_record_get (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T res_T t =
blanchet@35070
  1544
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1545
    case no_of_record_field thy s rec_T of
blanchet@33192
  1546
      ~1 => (case rec_T of
blanchet@33192
  1547
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1548
               let
blanchet@33192
  1549
                 val rec_T' = List.last Ts
blanchet@33192
  1550
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1551
               in
blanchet@37256
  1552
                 select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@35070
  1553
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1554
               end
blanchet@33232
  1555
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1556
                                []))
blanchet@37256
  1557
    | j => select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@33192
  1558
  end
blanchet@37256
  1559
fun optimized_record_update (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T fun_t
blanchet@37256
  1560
                            rec_t =
blanchet@33192
  1561
  let
blanchet@35070
  1562
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1563
    val Ts = binder_types constr_T
blanchet@33192
  1564
    val n = length Ts
blanchet@33192
  1565
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1566
    val ts =
blanchet@35220
  1567
      map2 (fn j => fn T =>
blanchet@37256
  1568
               let val t = select_nth_constr_arg ctxt stds constr_x rec_t j T in
blanchet@35220
  1569
                 if j = special_j then
blanchet@37476
  1570
                   s_betapply [] (fun_t, t)
blanchet@35220
  1571
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1572
                   optimized_record_update hol_ctxt s
blanchet@35220
  1573
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1574
                 else
blanchet@35220
  1575
                   t
blanchet@35220
  1576
               end) (index_seq 0 n) Ts
blanchet@33192
  1577
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1578
blanchet@35070
  1579
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1580
val unfold_max_depth = 255
blanchet@33192
  1581
blanchet@35284
  1582
fun unfold_defs_in_term (hol_ctxt as {thy, ctxt, stds, fast_descrs, case_names,
blanchet@35280
  1583
                                      def_table, ground_thm_table, ersatz_table,
blanchet@35280
  1584
                                      ...}) =
blanchet@33192
  1585
  let
blanchet@33192
  1586
    fun do_term depth Ts t =
blanchet@33192
  1587
      case t of
blanchet@33192
  1588
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@35665
  1589
                      Type (@{type_name fun}, [_, ran_T]))) $ t1 =>
blanchet@33192
  1590
        ((if is_number_type thy ran_T then
blanchet@33192
  1591
            let
blanchet@33192
  1592
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1593
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1594
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1595
            in
blanchet@35220
  1596
              if is_integer_like_type ran_T then
blanchet@35220
  1597
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1598
                  Const (s, ran_T)
blanchet@35220
  1599
                else
blanchet@35220
  1600
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1601
              else
blanchet@33192
  1602
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1603
                                  $ Const (s, int_T))
blanchet@33192
  1604
            end
blanchet@33192
  1605
            handle TERM _ => raise SAME ()
blanchet@33192
  1606
          else
blanchet@33192
  1607
            raise SAME ())
blanchet@37476
  1608
         handle SAME () =>
blanchet@37476
  1609
                s_betapply [] (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1610
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1611
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1612
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@37476
  1613
        s_betapplys Ts (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@37476
  1614
                        map (do_term depth Ts) [t1, t2])
blanchet@33192
  1615
      | Const (x as (@{const_name distinct},
blanchet@35665
  1616
               Type (@{type_name fun}, [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1617
        $ (t1 as _ $ _) =>
blanchet@33192
  1618
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1619
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1620
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1621
        if is_ground_term t1 andalso
blanchet@34936
  1622
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1623
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1624
          do_term depth Ts t2
blanchet@33192
  1625
        else
blanchet@33192
  1626
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1627
      | Const x => do_const depth Ts t x []
blanchet@37476
  1628
      | t1 $ t2 =>
blanchet@37476
  1629
        (case strip_comb t of
blanchet@37476
  1630
           (Const x, ts) => do_const depth Ts t x ts
blanchet@37476
  1631
         | _ => s_betapply [] (do_term depth Ts t1, do_term depth Ts t2))
blanchet@33192
  1632
      | Free _ => t
blanchet@33192
  1633
      | Var _ => t
blanchet@33192
  1634
      | Bound _ => t
blanchet@33192
  1635
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1636
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1637
        (Abs (Name.uu, body_type T,
blanchet@37256
  1638
              select_nth_constr_arg ctxt stds x (Bound 0) n res_T), [])
blanchet@33192
  1639
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@37256
  1640
        (select_nth_constr_arg ctxt stds x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1641
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1642
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1643
        SOME s' =>
blanchet@33192
  1644
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1645
      | NONE =>
blanchet@33192
  1646
        let
blanchet@33192
  1647
          val (const, ts) =
blanchet@35220
  1648
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1649
              (Const x, ts)
blanchet@33192
  1650
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1651
              SOME n =>
blanchet@37476
  1652
              if length ts < n then
blanchet@37476
  1653
                (do_term depth Ts (eta_expand Ts t (n - length ts)), [])
blanchet@37476
  1654
              else
blanchet@37476
  1655
                let
blanchet@37476
  1656
                  val (dataT, res_T) = nth_range_type n T
blanchet@37476
  1657
                                       |> pairf domain_type range_type
blanchet@37476
  1658
                in
blanchet@37476
  1659
                  (optimized_case_def hol_ctxt dataT res_T
blanchet@37476
  1660
                                      (map (do_term depth Ts) (take n ts)),
blanchet@37476
  1661
                   drop n ts)
blanchet@37476
  1662
                end
blanchet@33192
  1663
            | _ =>
blanchet@37256
  1664
              if is_constr ctxt stds x then
blanchet@33192
  1665
                (Const x, ts)
blanchet@37256
  1666
              else if is_stale_constr ctxt x then
blanchet@34936
  1667
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1668
                                     \(\"" ^ s ^ "\")")
blanchet@35284
  1669
              else if is_quot_abs_fun ctxt x then
blanchet@34936
  1670
                let
blanchet@34936
  1671
                  val rep_T = domain_type T
blanchet@34936
  1672
                  val abs_T = range_type T
blanchet@34936
  1673
                in
blanchet@34936
  1674
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1675
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@35311
  1676
                               $ (Const (quot_normal_name_for_type ctxt abs_T,
blanchet@34936
  1677
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1678
                end
blanchet@35284
  1679
              else if is_quot_rep_fun ctxt x then
blanchet@34936
  1680
                let
blanchet@34936
  1681
                  val abs_T = domain_type T
blanchet@34936
  1682
                  val rep_T = range_type T
blanchet@34936
  1683
                  val x' = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1684
                in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
blanchet@33192
  1685
              else if is_record_get thy x then
blanchet@33192
  1686
                case length ts of
blanchet@33192
  1687
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1688
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1689
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1690
              else if is_record_update thy x then
blanchet@33192
  1691
                case length ts of
blanchet@35070
  1692
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1693
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1694
                            (do_term depth Ts (hd ts))
blanchet@33580
  1695
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1696
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@37256
  1697
              else if is_rep_fun ctxt x then
blanchet@37256
  1698
                let val x' = mate_of_rep_fun ctxt x in
blanchet@37256
  1699
                  if is_constr ctxt stds x' then
blanchet@33192
  1700
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1701
                                                    (range_type T)
blanchet@33192
  1702
                  else
blanchet@33192
  1703
                    (Const x, ts)
blanchet@33192
  1704
                end
blanchet@35807
  1705
              else if is_equational_fun hol_ctxt x orelse
blanchet@35807
  1706
                      is_choice_spec_fun hol_ctxt x then
blanchet@33192
  1707
                (Const x, ts)
blanchet@33192
  1708
              else case def_of_const thy def_table x of
blanchet@33192
  1709
                SOME def =>
blanchet@33192
  1710
                if depth > unfold_max_depth then
blanchet@34124
  1711
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1712
                                   "too many nested definitions (" ^
blanchet@34124
  1713
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1714
                                   quote s)
blanchet@33192
  1715
                else if s = @{const_name wfrec'} then
blanchet@37476
  1716
                  (do_term (depth + 1) Ts (s_betapplys Ts (def, ts)), [])
blanchet@33192
  1717
                else
blanchet@33192
  1718
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1719
              | NONE => (Const x, ts)
blanchet@37476
  1720
        in
blanchet@37476
  1721
          s_betapplys Ts (const, map (do_term depth Ts) ts)
blanchet@37476
  1722
          |> s_beta_norm Ts
blanchet@37476
  1723
        end
blanchet@33192
  1724
  in do_term 0 [] end
blanchet@33192
  1725
blanchet@35718
  1726
(** Axiom extraction/generation **)
blanchet@35718
  1727
blanchet@35807
  1728
fun pair_for_prop t =
blanchet@35807
  1729
  case term_under_def t of
blanchet@35807
  1730
    Const (s, _) => (s, t)
blanchet@35807
  1731
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@35807
  1732
fun def_table_for get ctxt subst =
blanchet@35807
  1733
  ctxt |> get |> map (pair_for_prop o subst_atomic subst)
blanchet@35807
  1734
       |> AList.group (op =) |> Symtab.make
blanchet@35807
  1735
fun paired_with_consts t = map (rpair t) (Term.add_const_names t [])
blanchet@35718
  1736
fun const_def_table ctxt subst ts =
blanchet@35807
  1737
  def_table_for (map prop_of o Nitpick_Defs.get) ctxt subst
blanchet@35718
  1738
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@35718
  1739
          (map pair_for_prop ts)
blanchet@35718
  1740
fun const_nondef_table ts =
blanchet@35807
  1741
  fold (append o paired_with_consts) ts [] |> AList.group (op =) |> Symtab.make
blanchet@35807
  1742
val const_simp_table = def_table_for (map prop_of o Nitpick_Simps.get)
blanchet@35807
  1743
val const_psimp_table = def_table_for (map prop_of o Nitpick_Psimps.get)
blanchet@35807
  1744
fun const_choice_spec_table ctxt subst =
blanchet@35807
  1745
  map (subst_atomic subst o prop_of) (Nitpick_Choice_Specs.get ctxt)
blanchet@35807
  1746
  |> const_nondef_table
blanchet@35718
  1747
fun inductive_intro_table ctxt subst def_table =
blanchet@37264
  1748
  let val thy = ProofContext.theory_of ctxt in
blanchet@37264
  1749
    def_table_for
blanchet@37264
  1750
        (maps (map (unfold_mutually_inductive_preds thy def_table o prop_of)
blanchet@37264
  1751
               o snd o snd)
blanchet@37264
  1752
         o filter (fn (cat, _) => cat = Spec_Rules.Inductive orelse
blanchet@37264
  1753
                                  cat = Spec_Rules.Co_Inductive)
blanchet@37264
  1754
         o Spec_Rules.get) ctxt subst
blanchet@37264
  1755
  end
blanchet@35718
  1756
fun ground_theorem_table thy =
blanchet@35718
  1757
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@35718
  1758
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@35718
  1759
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@35718
  1760
blanchet@35807
  1761
(* TODO: Move to "Nitpick.thy" *)
blanchet@35718
  1762
val basic_ersatz_table =
blanchet@37213
  1763
  [(@{const_name card}, @{const_name card'}),
blanchet@35718
  1764
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@35718
  1765
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@35718
  1766
   (@{const_name wf}, @{const_name wf'}),
blanchet@35718
  1767
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@35718
  1768
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@35718
  1769
blanchet@35718
  1770
fun ersatz_table thy =
blanchet@35718
  1771
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@35718
  1772
blanchet@35718
  1773
fun add_simps simp_table s eqs =
blanchet@35718
  1774
  Unsynchronized.change simp_table
blanchet@35718
  1775
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@35718
  1776
blanchet@37256
  1777
fun inverse_axioms_for_rep_fun ctxt (x as (_, T)) =
blanchet@37256
  1778
  let
blanchet@37256
  1779
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1780
    val abs_T = domain_type T
blanchet@37256
  1781
  in
blanchet@37256
  1782
    typedef_info ctxt (fst (dest_Type abs_T)) |> the
blanchet@35718
  1783
    |> pairf #Abs_inverse #Rep_inverse
blanchet@36555
  1784
    |> pairself (specialize_type thy x o prop_of o the)
blanchet@35718
  1785
    ||> single |> op ::
blanchet@35718
  1786
  end
blanchet@37256
  1787
fun optimized_typedef_axioms ctxt (abs_z as (abs_s, _)) =
blanchet@37256
  1788
  let
blanchet@37256
  1789
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1790
    val abs_T = Type abs_z
blanchet@37256
  1791
  in
blanchet@37256
  1792
    if is_univ_typedef ctxt abs_T then
blanchet@35718
  1793
      []
blanchet@37256
  1794
    else case typedef_info ctxt abs_s of
blanchet@35718
  1795
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@35718
  1796
      let
blanchet@35718
  1797
        val rep_T = varify_and_instantiate_type thy abs_type abs_T rep_type
blanchet@35718
  1798
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@35718
  1799
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@35718
  1800
        val set_t' =
blanchet@35718
  1801
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@36555
  1802
                      |> specialize_type thy (dest_Const rep_t)
blanchet@35718
  1803
                      |> HOLogic.dest_mem |> snd
blanchet@35718
  1804
      in
blanchet@35718
  1805
        [HOLogic.all_const abs_T
blanchet@35718
  1806
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@35718
  1807
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@35718
  1808
        |> map HOLogic.mk_Trueprop
blanchet@35718
  1809
      end
blanchet@35718
  1810
    | NONE => []
blanchet@35718
  1811
  end
blanchet@35718
  1812
fun optimized_quot_type_axioms ctxt stds abs_z =
blanchet@35718
  1813
  let
blanchet@35718
  1814
    val thy = ProofContext.theory_of ctxt
blanchet@35718
  1815
    val abs_T = Type abs_z
blanchet@35718
  1816
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@35718
  1817
    val equiv_rel = equiv_relation_for_quot_type thy abs_T
blanchet@35718
  1818
    val a_var = Var (("a", 0), abs_T)
blanchet@35718
  1819
    val x_var = Var (("x", 0), rep_T)
blanchet@35718
  1820
    val y_var = Var (("y", 0), rep_T)
blanchet@35718
  1821
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@37256
  1822
    val sel_a_t = select_nth_constr_arg ctxt stds x a_var 0 rep_T
blanchet@35718
  1823
    val normal_t = Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T)
blanchet@35718
  1824
    val normal_x = normal_t $ x_var
blanchet@35718
  1825
    val normal_y = normal_t $ y_var
blanchet@35718
  1826
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@35718
  1827
  in
blanchet@35718
  1828
    [Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
blanchet@35718
  1829
     Logic.list_implies
blanchet@35718
  1830
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@35718
  1831
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@35718
  1832
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@35718
  1833
           Logic.mk_equals (normal_x, normal_y)),
blanchet@35718
  1834
     Logic.list_implies
blanchet@35718
  1835
         ([HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)),
blanchet@35718
  1836
           HOLogic.mk_Trueprop (@{const Not} $ HOLogic.mk_eq (normal_x, x_var))],
blanchet@35718
  1837
          HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@35718
  1838
  end
blanchet@35718
  1839
blanchet@37256
  1840
fun codatatype_bisim_axioms (hol_ctxt as {ctxt, thy, stds, ...}) T =
blanchet@33192
  1841
  let
blanchet@35070
  1842
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1843
    val set_T = T --> bool_T
blanchet@33192
  1844
    val iter_T = @{typ bisim_iterator}
blanchet@34124
  1845
    val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1846
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1847
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1848
    val n_var_minus_1 =
blanchet@35671
  1849
      Const (@{const_name safe_The}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1850
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1851
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1852
    val x_var = Var (("x", 0), T)
blanchet@33192
  1853
    val y_var = Var (("y", 0), T)
blanchet@33192
  1854
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1855
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1856
       else HOLogic.eq_const nth_T)
blanchet@37256
  1857
      $ select_nth_constr_arg ctxt stds x x_var n nth_T
blanchet@37256
  1858
      $ select_nth_constr_arg ctxt stds x y_var n nth_T
blanchet@33192
  1859
    fun case_func (x as (_, T)) =
blanchet@33192
  1860
      let
blanchet@33192
  1861
        val arg_Ts = binder_types T
blanchet@33192
  1862
        val core_t =
blanchet@35070
  1863
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1864
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1865
          |> foldr1 s_conj
blanchet@33192
  1866
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1867
  in
blanchet@33192
  1868
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1869
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@37476
  1870
        $ (s_betapply []
blanchet@37476
  1871
                      (optimized_case_def hol_ctxt T bool_T (map case_func xs),
blanchet@37476
  1872
                       x_var))),
blanchet@33192
  1873
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@34124
  1874
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  1875
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  1876
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1877
  end
blanchet@33192
  1878
blanchet@33192
  1879
exception NO_TRIPLE of unit
blanchet@33192
  1880
blanchet@33192
  1881
fun triple_for_intro_rule thy x t =
blanchet@33192
  1882
  let
wenzelm@35625
  1883
    val prems = Logic.strip_imp_prems t |> map (Object_Logic.atomize_term thy)
wenzelm@35625
  1884
    val concl = Logic.strip_imp_concl t |> Object_Logic.atomize_term thy
blanchet@34121
  1885
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@36385
  1886
    val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  1887
  in
blanchet@33192
  1888
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1889
  end
blanchet@33192
  1890
blanchet@33192
  1891
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1892
fun wf_constraint_for rel side concl main =
blanchet@33192
  1893
  let
blanchet@37269
  1894
    val core = HOLogic.mk_mem (HOLogic.mk_prod
blanchet@37269
  1895
                               (pairself tuple_for_args (main, concl)), Var rel)
blanchet@33192
  1896
    val t = List.foldl HOLogic.mk_imp core side
blanchet@37269
  1897
    val vars = filter_out (curry (op =) rel) (Term.add_vars t [])
blanchet@33192
  1898
  in
blanchet@33192
  1899
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1900
                      HOLogic.all_const T
blanchet@33192
  1901
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1902
                  (t, vars)
blanchet@33192
  1903
  end
blanchet@33192
  1904
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1905
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1906
blanchet@33192
  1907
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1908
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1909
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1910
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1911
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1912
blanchet@35181
  1913
val max_cached_wfs = 50
blanchet@35181
  1914
val cached_timeout =
blanchet@35181
  1915
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  1916
val cached_wf_props =
blanchet@35181
  1917
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  1918
krauss@33351
  1919
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1920
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1921
blanchet@33580
  1922
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  1923
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  1924
         : hol_context) (x as (_, T)) =
blanchet@35220
  1925
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  1926
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  1927
                      [Const x])
blanchet@33192
  1928
  | intro_ts =>
blanchet@33192
  1929
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1930
          |> filter_out (null o #2) of
blanchet@33192
  1931
       [] => true
blanchet@33192
  1932
     | triples =>
blanchet@33192
  1933
       let
blanchet@33192
  1934
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1935
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  1936
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  1937
         val rel = (("R", j), rel_T)
blanchet@33192
  1938
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1939
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1940
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1941
         val _ = if debug then
blanchet@33192
  1942
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1943
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1944
                 else
blanchet@33192
  1945
                   ()
blanchet@33192
  1946
       in
blanchet@35181
  1947
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  1948
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  1949
           ()
blanchet@33557
  1950
         else
blanchet@35181
  1951
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  1952
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  1953
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  1954
           SOME wf => wf
blanchet@33192
  1955
         | NONE =>
blanchet@33192
  1956
           let
blanchet@33192
  1957
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  1958
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  1959
                             termination_tacs
blanchet@35181
  1960
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1961
       end)
blanchet@35309
  1962
    handle List.Empty => false | NO_TRIPLE () => false
blanchet@33192
  1963
blanchet@35070
  1964
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  1965
blanchet@33192
  1966
fun is_well_founded_inductive_pred
blanchet@35070
  1967
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  1968
        (x as (s, _)) =
blanchet@33192
  1969
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1970
    SOME (SOME b) => b
blanchet@34936
  1971
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  1972
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  1973
           SOME (_, wf) => wf
blanchet@35181
  1974
         | NONE =>
blanchet@35181
  1975
           let
blanchet@35181
  1976
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  1977
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  1978
           in
blanchet@35181
  1979
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  1980
           end
blanchet@33192
  1981
blanchet@35280
  1982
fun ap_curry [_] _ t = t
blanchet@35280
  1983
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  1984
    let val n = length arg_Ts in
blanchet@33192
  1985
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1986
                incr_boundvars n t
blanchet@33192
  1987
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1988
    end
blanchet@33192
  1989
blanchet@33192
  1990
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1991
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  1992
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  1993
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1994
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1995
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1996
blanchet@33192
  1997
val is_linear_inductive_pred_def =
blanchet@33192
  1998
  let
blanchet@33192
  1999
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  2000
        do_disjunct (j + 1) t2
blanchet@33192
  2001
      | do_disjunct j t =
blanchet@33192
  2002
        case num_occs_of_bound_in_term j t of
blanchet@33192
  2003
          0 => true
blanchet@35070
  2004
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  2005
        | _ => false
blanchet@33192
  2006
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2007
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  2008
          case length xs of
blanchet@33192
  2009
            1 => false
blanchet@35070
  2010
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  2011
        end
blanchet@33192
  2012
      | do_lfp_def _ = false
blanchet@33192
  2013
  in do_lfp_def o strip_abs_body end
blanchet@33192
  2014
blanchet@33851
  2015
fun n_ptuple_paths 0 = []
blanchet@33851
  2016
  | n_ptuple_paths 1 = []
blanchet@33851
  2017
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  2018
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  2019
blanchet@33192
  2020
val linear_pred_base_and_step_rhss =
blanchet@33192
  2021
  let
blanchet@33192
  2022
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2023
        let
blanchet@33192
  2024
          val (xs, body) = strip_abs t2
blanchet@33192
  2025
          val arg_Ts = map snd (tl xs)
blanchet@33192
  2026
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  2027
          val j = length arg_Ts
blanchet@33192
  2028
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  2029
              Const (@{const_name Ex}, T1)
blanchet@33192
  2030
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  2031
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  2032
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  2033
            | repair_rec j t =
blanchet@33192
  2034
              let val (head, args) = strip_comb t in
blanchet@33192
  2035
                if head = Bound j then
blanchet@33192
  2036
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  2037
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  2038
                else
blanchet@33192
  2039
                  t
blanchet@33192
  2040
              end
blanchet@33192
  2041
          val (nonrecs, recs) =
blanchet@34121
  2042
            List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
blanchet@35070
  2043
                           (disjuncts_of body)
blanchet@33192
  2044
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  2045
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  2046
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  2047
        in
blanchet@33192
  2048
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  2049
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  2050
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  2051
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  2052
        end
blanchet@33192
  2053
      | aux t =
blanchet@33232
  2054
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  2055
  in aux end
blanchet@33192
  2056
blanchet@35280
  2057
fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (s, T) def =
blanchet@33192
  2058
  let
blanchet@33192
  2059
    val j = maxidx_of_term def + 1
blanchet@33192
  2060
    val (outer, fp_app) = strip_abs def
blanchet@33192
  2061
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2062
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  2063
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  2064
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  2065
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  2066
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  2067
    val set_T = tuple_T --> bool_T
blanchet@33192
  2068
    val curried_T = tuple_T --> set_T
blanchet@35665
  2069
    val uncurried_T = Type (@{type_name "*"}, [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  2070
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  2071
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  2072
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  2073
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2074
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  2075
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  2076
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  2077
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2078
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  2079
  in
blanchet@33192
  2080
    list_abs (outer,
blanchet@33192
  2081
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  2082
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  2083
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  2084
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  2085
              $ list_comb (Const base_x, outer_bounds)
blanchet@35280
  2086
              |> ap_curry tuple_arg_Ts tuple_T)
blanchet@35070
  2087
    |> unfold_defs_in_term hol_ctxt
blanchet@33192
  2088
  end
blanchet@33192
  2089
blanchet@35070
  2090
fun unrolled_inductive_pred_const (hol_ctxt as {thy, star_linear_preds,
blanchet@33192
  2091
                                                def_table, simp_table, ...})
blanchet@33192
  2092
                                  gfp (x as (s, T)) =
blanchet@33192
  2093
  let
blanchet@33192
  2094
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  2095
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  2096
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  2097
    val def = the (def_of_const thy def_table x)
blanchet@33192
  2098
  in
blanchet@35070
  2099
    if is_equational_fun hol_ctxt x' then
blanchet@33192
  2100
      unrolled_const (* already done *)
blanchet@34936
  2101
    else if not gfp andalso is_linear_inductive_pred_def def andalso
blanchet@34936
  2102
         star_linear_preds then
blanchet@35070
  2103
      starred_linear_pred_const hol_ctxt x def
blanchet@33192
  2104
    else
blanchet@33192
  2105
      let
blanchet@33192
  2106
        val j = maxidx_of_term def + 1
blanchet@33192
  2107
        val (outer, fp_app) = strip_abs def
blanchet@33192
  2108
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2109
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  2110
        val next = suc_const iter_T $ cur
blanchet@37476
  2111
        val rhs =
blanchet@37476
  2112
          case fp_app of
blanchet@37476
  2113
            Const _ $ t =>
blanchet@37476
  2114
            s_betapply [] (t, list_comb (Const x', next :: outer_bounds))
blanchet@37476
  2115
          | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_const",
blanchet@37476
  2116
                             [fp_app])
blanchet@33192
  2117
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  2118
        val all = outer @ inner
blanchet@33192
  2119
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  2120
        val vars = map (fn (s, T) => Var ((s, j), T)) all