src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Tue Jun 01 15:38:47 2010 +0200 (2010-06-01)
changeset 37264 8b931fb51cc6
parent 37261 8a89fd40ed0b
child 37269 49c45156c9e1
permissions -rw-r--r--
removed "nitpick_intro" attribute -- Nitpick noew uses Spec_Rules instead
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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 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 abs_var : indexname * typ -> term -> term
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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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   297
  Substring.full #> Substring.position name_sep ##> Substring.triml 1
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  #> pairself Substring.string
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   299
fun original_name s =
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   300
  if String.isPrefix nitpick_prefix s then
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   301
    case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
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   302
  else
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   303
    s
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   304
blanchet@35718
   305
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
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   306
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
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   307
  | s_betapply p = betapply p
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   308
val s_betapplys = Library.foldl s_betapply
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   309
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   310
fun s_conj (t1, @{const True}) = t1
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   311
  | s_conj (@{const True}, t2) = t2
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   312
  | s_conj (t1, t2) =
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   313
    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
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   314
    else HOLogic.mk_conj (t1, t2)
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   315
fun s_disj (t1, @{const False}) = t1
blanchet@34998
   316
  | s_disj (@{const False}, t2) = t2
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   317
  | s_disj (t1, t2) =
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   318
    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
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   319
    else HOLogic.mk_disj (t1, t2)
blanchet@34998
   320
blanchet@34998
   321
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
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   322
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
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   323
  | strip_connective _ t = [t]
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   324
fun strip_any_connective (t as (t0 $ _ $ _)) =
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   325
    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
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   326
      (strip_connective t0 t, t0)
blanchet@34998
   327
    else
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   328
      ([t], @{const Not})
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   329
  | strip_any_connective t = ([t], @{const Not})
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   330
val conjuncts_of = strip_connective @{const "op &"}
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   331
val disjuncts_of = strip_connective @{const "op |"}
blanchet@34998
   332
blanchet@33192
   333
(* When you add constants to these lists, make sure to handle them in
blanchet@33232
   334
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
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   335
   well. *)
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   336
val built_in_consts =
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   337
  [(@{const_name all}, 1),
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   338
   (@{const_name "=="}, 2),
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   339
   (@{const_name "==>"}, 2),
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   340
   (@{const_name Pure.conjunction}, 2),
blanchet@33192
   341
   (@{const_name Trueprop}, 1),
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   342
   (@{const_name Not}, 1),
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   343
   (@{const_name False}, 0),
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   344
   (@{const_name True}, 0),
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   345
   (@{const_name All}, 1),
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   346
   (@{const_name Ex}, 1),
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   347
   (@{const_name "op ="}, 2),
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   348
   (@{const_name "op &"}, 2),
blanchet@33192
   349
   (@{const_name "op |"}, 2),
blanchet@33192
   350
   (@{const_name "op -->"}, 2),
blanchet@33192
   351
   (@{const_name If}, 3),
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   352
   (@{const_name Let}, 2),
blanchet@33192
   353
   (@{const_name Unity}, 0),
blanchet@33192
   354
   (@{const_name Pair}, 2),
blanchet@33192
   355
   (@{const_name fst}, 1),
blanchet@33192
   356
   (@{const_name snd}, 1),
blanchet@33192
   357
   (@{const_name Id}, 0),
blanchet@33192
   358
   (@{const_name insert}, 2),
blanchet@33192
   359
   (@{const_name converse}, 1),
blanchet@33192
   360
   (@{const_name trancl}, 1),
blanchet@33192
   361
   (@{const_name rel_comp}, 2),
blanchet@33192
   362
   (@{const_name image}, 2),
blanchet@33192
   363
   (@{const_name finite}, 1),
blanchet@34936
   364
   (@{const_name unknown}, 0),
blanchet@34936
   365
   (@{const_name is_unknown}, 1),
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   366
   (@{const_name safe_The}, 1),
blanchet@35671
   367
   (@{const_name safe_Eps}, 1),
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   368
   (@{const_name Frac}, 0),
blanchet@33192
   369
   (@{const_name norm_frac}, 0)]
blanchet@35220
   370
val built_in_nat_consts =
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   371
  [(@{const_name Suc}, 0),
blanchet@35220
   372
   (@{const_name nat}, 0),
blanchet@35220
   373
   (@{const_name nat_gcd}, 0),
blanchet@35220
   374
   (@{const_name nat_lcm}, 0)]
blanchet@33192
   375
val built_in_descr_consts =
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   376
  [(@{const_name The}, 1),
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   377
   (@{const_name Eps}, 1)]
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   378
val built_in_typed_consts =
blanchet@35220
   379
  [((@{const_name zero_class.zero}, int_T), 0),
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   380
   ((@{const_name one_class.one}, int_T), 0),
blanchet@35220
   381
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   382
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   383
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
blanchet@35220
   384
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
blanchet@35220
   385
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
blanchet@35220
   386
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
blanchet@35220
   387
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
blanchet@35220
   388
val built_in_typed_nat_consts =
blanchet@35220
   389
  [((@{const_name zero_class.zero}, nat_T), 0),
blanchet@35220
   390
   ((@{const_name one_class.one}, nat_T), 0),
blanchet@35220
   391
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   392
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   393
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   394
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   395
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   396
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   397
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   398
val built_in_set_consts =
blanchet@35220
   399
  [(@{const_name semilattice_inf_class.inf}, 2),
blanchet@35220
   400
   (@{const_name semilattice_sup_class.sup}, 2),
blanchet@35220
   401
   (@{const_name minus_class.minus}, 2),
blanchet@35220
   402
   (@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   403
blanchet@35190
   404
fun unarize_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   405
  | unarize_type @{typ "signed_bit word"} = int_T
blanchet@35190
   406
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
blanchet@35190
   407
  | unarize_type T = T
blanchet@35665
   408
fun unarize_unbox_etc_type (Type (@{type_name fin_fun}, Ts)) =
blanchet@35665
   409
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   410
  | unarize_unbox_etc_type (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   411
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   412
  | unarize_unbox_etc_type (Type (@{type_name pair_box}, Ts)) =
blanchet@35665
   413
    Type (@{type_name "*"}, map unarize_unbox_etc_type Ts)
blanchet@35665
   414
  | unarize_unbox_etc_type @{typ "unsigned_bit word"} = nat_T
blanchet@35665
   415
  | unarize_unbox_etc_type @{typ "signed_bit word"} = int_T
blanchet@35665
   416
  | unarize_unbox_etc_type (Type (s, Ts as _ :: _)) =
blanchet@35665
   417
    Type (s, map unarize_unbox_etc_type Ts)
blanchet@35665
   418
  | unarize_unbox_etc_type T = T
blanchet@35280
   419
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   420
  | uniterize_type @{typ bisim_iterator} = nat_T
blanchet@35280
   421
  | uniterize_type T = T
blanchet@35665
   422
val uniterize_unarize_unbox_etc_type = uniterize_type o unarize_unbox_etc_type
blanchet@35280
   423
blanchet@35665
   424
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_unbox_etc_type
blanchet@33192
   425
blanchet@33192
   426
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@34121
   427
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   428
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@34121
   429
fun short_name s =
blanchet@33192
   430
  case space_explode name_sep s of
blanchet@33192
   431
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   432
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   433
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   434
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   435
  | shorten_names_in_type T = T
blanchet@34121
   436
val shorten_names_in_term =
blanchet@34121
   437
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   438
  #> map_types shorten_names_in_type
blanchet@33192
   439
blanchet@35665
   440
fun strict_type_match thy (T1, T2) =
blanchet@33192
   441
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   442
  handle Type.TYPE_MATCH => false
blanchet@35665
   443
fun type_match thy = strict_type_match thy o pairself unarize_unbox_etc_type
blanchet@33192
   444
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   445
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   446
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   447
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   448
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   449
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   450
blanchet@35711
   451
fun frac_from_term_pair T t1 t2 =
blanchet@35711
   452
  case snd (HOLogic.dest_number t1) of
blanchet@35711
   453
    0 => HOLogic.mk_number T 0
blanchet@35711
   454
  | n1 => case snd (HOLogic.dest_number t2) of
blanchet@35711
   455
            1 => HOLogic.mk_number T n1
blanchet@35711
   456
          | n2 => Const (@{const_name divide}, T --> T --> T)
blanchet@35711
   457
                  $ HOLogic.mk_number T n1 $ HOLogic.mk_number T n2
blanchet@35711
   458
blanchet@33192
   459
fun is_TFree (TFree _) = true
blanchet@33192
   460
  | is_TFree _ = false
blanchet@35665
   461
fun is_higher_order_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   462
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   463
  | is_higher_order_type _ = false
blanchet@35665
   464
fun is_fun_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   465
  | is_fun_type _ = false
blanchet@35665
   466
fun is_set_type (Type (@{type_name fun}, [_, @{typ bool}])) = true
blanchet@33192
   467
  | is_set_type _ = false
blanchet@35665
   468
fun is_pair_type (Type (@{type_name "*"}, _)) = true
blanchet@33192
   469
  | is_pair_type _ = false
blanchet@33192
   470
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   471
  | is_lfp_iterator_type _ = false
blanchet@33192
   472
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   473
  | is_gfp_iterator_type _ = false
blanchet@33192
   474
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   475
fun is_iterator_type T =
blanchet@35280
   476
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   477
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   478
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   479
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   480
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   481
  | is_word_type _ = false
blanchet@35280
   482
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   483
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   484
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   485
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   486
  | is_frac_type _ _ = false
blanchet@35220
   487
fun is_number_type thy = is_integer_like_type orf is_frac_type thy
blanchet@33192
   488
blanchet@33192
   489
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   490
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   491
        binder_types T)
blanchet@35718
   492
fun const_for_iterator_type (Type (s, Ts)) =
blanchet@35718
   493
    (strip_first_name_sep s |> snd, Ts ---> bool_T)
blanchet@33192
   494
  | const_for_iterator_type T =
blanchet@33232
   495
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   496
blanchet@33192
   497
fun strip_n_binders 0 T = ([], T)
blanchet@35665
   498
  | strip_n_binders n (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
   499
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   500
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   501
    strip_n_binders n (Type (@{type_name fun}, Ts))
blanchet@33232
   502
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   503
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   504
blanchet@35665
   505
fun num_factors_in_type (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
   506
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   507
  | num_factors_in_type _ = 1
blanchet@35665
   508
fun num_binder_types (Type (@{type_name fun}, [_, T2])) =
blanchet@35665
   509
    1 + num_binder_types T2
blanchet@33192
   510
  | num_binder_types _ = 0
blanchet@33192
   511
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   512
fun maybe_curried_binder_types T =
blanchet@33192
   513
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   514
blanchet@33192
   515
fun mk_flat_tuple _ [t] = t
blanchet@35665
   516
  | mk_flat_tuple (Type (@{type_name "*"}, [T1, T2])) (t :: ts) =
blanchet@33192
   517
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   518
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   519
fun dest_n_tuple 1 t = [t]
blanchet@33192
   520
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   521
blanchet@35220
   522
type typedef_info =
blanchet@35220
   523
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   524
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   525
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   526
blanchet@37256
   527
fun typedef_info ctxt s =
blanchet@37256
   528
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   529
    if is_frac_type thy (Type (s, [])) then
blanchet@37256
   530
      SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@37256
   531
            Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@37256
   532
            set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@37256
   533
                            |> Logic.varify_global,
blanchet@37256
   534
            set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@37256
   535
    else case Typedef.get_info ctxt s of
blanchet@37258
   536
      (* When several entries are returned, it shouldn't matter much which one
blanchet@37258
   537
         we take (according to Florian Haftmann). *)
blanchet@37258
   538
      ({abs_type, rep_type, Abs_name, Rep_name, ...},
blanchet@37258
   539
       {set_def, Rep, Abs_inverse, Rep_inverse, ...}) :: _ =>
blanchet@37256
   540
      SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@37256
   541
            Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@37256
   542
            set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@37256
   543
            Rep_inverse = SOME Rep_inverse}
blanchet@37256
   544
    | _ => NONE
blanchet@37256
   545
  end
blanchet@35220
   546
blanchet@35220
   547
val is_typedef = is_some oo typedef_info
blanchet@35220
   548
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   549
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   550
blanchet@34121
   551
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   552
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   553
fun is_basic_datatype thy stds s =
blanchet@35220
   554
  member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@35220
   555
                 @{type_name int}, "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   556
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   557
blanchet@33192
   558
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   559
  Same.commit (Envir.subst_type_same
blanchet@35311
   560
                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
blanchet@33192
   561
  handle Type.TYPE_MATCH =>
blanchet@33232
   562
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@35311
   563
fun varify_and_instantiate_type thy T1 T1' T2 =
wenzelm@35845
   564
  instantiate_type thy (Logic.varifyT_global T1) T1' (Logic.varifyT_global T2)
blanchet@33192
   565
blanchet@33192
   566
fun repair_constr_type thy body_T' T =
blanchet@35311
   567
  varify_and_instantiate_type thy (body_type T) body_T' T
blanchet@33192
   568
blanchet@33192
   569
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   570
  let
blanchet@33583
   571
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   572
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   573
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   574
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   575
blanchet@33192
   576
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   577
  let
blanchet@33583
   578
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   579
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   580
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   581
    val _ =
blanchet@34936
   582
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35665
   583
         co_s <> @{type_name fun} andalso
blanchet@35220
   584
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   585
        ()
blanchet@34121
   586
      else
blanchet@34121
   587
        raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   588
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   589
                                   codatatypes
blanchet@33583
   590
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   591
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   592
blanchet@35284
   593
fun is_quot_type thy (Type (s, _)) =
blanchet@35284
   594
    is_some (Quotient_Info.quotdata_lookup_raw thy s)
blanchet@34936
   595
  | is_quot_type _ _ = false
blanchet@35280
   596
fun is_codatatype thy (Type (s, _)) =
blanchet@33583
   597
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   598
               |> Option.map snd |> these))
blanchet@33192
   599
  | is_codatatype _ _ = false
blanchet@37256
   600
fun is_pure_typedef ctxt (T as Type (s, _)) =
blanchet@37256
   601
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   602
      is_typedef ctxt s andalso
blanchet@37256
   603
      not (is_real_datatype thy s orelse is_quot_type thy T orelse
blanchet@37256
   604
           is_codatatype thy T orelse is_record_type T orelse
blanchet@37256
   605
           is_integer_like_type T)
blanchet@37256
   606
    end
blanchet@33192
   607
  | is_pure_typedef _ _ = false
blanchet@37256
   608
fun is_univ_typedef ctxt (Type (s, _)) =
blanchet@37256
   609
    (case typedef_info ctxt s of
blanchet@33192
   610
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@35332
   611
       let
blanchet@35332
   612
         val t_opt =
blanchet@35332
   613
           case set_def of
blanchet@35332
   614
             SOME thm => try (snd o Logic.dest_equals o prop_of) thm
blanchet@35332
   615
           | NONE => try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop)
blanchet@35332
   616
                         prop_of_Rep
blanchet@35332
   617
       in
blanchet@35332
   618
         case t_opt of
blanchet@35332
   619
           SOME (Const (@{const_name top}, _)) => true
blanchet@35386
   620
           (* "Multiset.multiset" *)
blanchet@35332
   621
         | SOME (Const (@{const_name Collect}, _)
blanchet@35332
   622
                 $ Abs (_, _, Const (@{const_name finite}, _) $ _)) => true
blanchet@35386
   623
           (* "FinFun.finfun" *)
blanchet@35386
   624
         | SOME (Const (@{const_name Collect}, _) $ Abs (_, _,
blanchet@35386
   625
                     Const (@{const_name Ex}, _) $ Abs (_, _,
blanchet@35386
   626
                         Const (@{const_name finite}, _) $ _))) => true
blanchet@35332
   627
         | _ => false
blanchet@35332
   628
       end
blanchet@33192
   629
     | NONE => false)
blanchet@33192
   630
  | is_univ_typedef _ _ = false
blanchet@37256
   631
fun is_datatype ctxt stds (T as Type (s, _)) =
blanchet@37256
   632
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   633
      (is_typedef ctxt s orelse is_codatatype thy T orelse T = @{typ ind} orelse
blanchet@37256
   634
       is_quot_type thy T) andalso not (is_basic_datatype thy stds s)
blanchet@37256
   635
    end
blanchet@35220
   636
  | is_datatype _ _ _ = false
blanchet@33192
   637
blanchet@33192
   638
fun all_record_fields thy T =
blanchet@33192
   639
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   640
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   641
  end
blanchet@33192
   642
  handle TYPE _ => []
blanchet@35280
   643
fun is_record_constr (s, T) =
blanchet@33192
   644
  String.isSuffix Record.extN s andalso
blanchet@33192
   645
  let val dataT = body_type T in
blanchet@33192
   646
    is_record_type dataT andalso
blanchet@33192
   647
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   648
  end
blanchet@33192
   649
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   650
fun no_of_record_field thy s T1 =
blanchet@34121
   651
  find_index (curry (op =) s o fst)
blanchet@34121
   652
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@35665
   653
fun is_record_get thy (s, Type (@{type_name fun}, [T1, _])) =
blanchet@34121
   654
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   655
  | is_record_get _ _ = false
blanchet@33192
   656
fun is_record_update thy (s, T) =
blanchet@33192
   657
  String.isSuffix Record.updateN s andalso
blanchet@34121
   658
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   659
         (all_record_fields thy (body_type T))
blanchet@33192
   660
  handle TYPE _ => false
blanchet@37256
   661
fun is_abs_fun ctxt (s, Type (@{type_name fun}, [_, Type (s', _)])) =
blanchet@37256
   662
    (case typedef_info ctxt s' of
blanchet@33192
   663
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   664
     | NONE => false)
blanchet@33192
   665
  | is_abs_fun _ _ = false
blanchet@37256
   666
fun is_rep_fun ctxt (s, Type (@{type_name fun}, [Type (s', _), _])) =
blanchet@37256
   667
    (case typedef_info ctxt s' of
blanchet@33192
   668
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   669
     | NONE => false)
blanchet@33192
   670
  | is_rep_fun _ _ = false
blanchet@35665
   671
fun is_quot_abs_fun ctxt
blanchet@35665
   672
                    (x as (_, Type (@{type_name fun}, [_, Type (s', _)]))) =
blanchet@35284
   673
    (try (Quotient_Term.absrep_const_chk Quotient_Term.AbsF ctxt) s'
blanchet@35284
   674
     = SOME (Const x))
blanchet@34936
   675
  | is_quot_abs_fun _ _ = false
blanchet@35665
   676
fun is_quot_rep_fun ctxt
blanchet@35665
   677
                    (x as (_, Type (@{type_name fun}, [Type (s', _), _]))) =
blanchet@35284
   678
    (try (Quotient_Term.absrep_const_chk Quotient_Term.RepF ctxt) s'
blanchet@35284
   679
     = SOME (Const x))
blanchet@34936
   680
  | is_quot_rep_fun _ _ = false
blanchet@33192
   681
blanchet@37256
   682
fun mate_of_rep_fun ctxt (x as (_, Type (@{type_name fun},
blanchet@37256
   683
                                         [T1 as Type (s', _), T2]))) =
blanchet@37256
   684
    (case typedef_info ctxt s' of
blanchet@35665
   685
       SOME {Abs_name, ...} => (Abs_name, Type (@{type_name fun}, [T2, T1]))
blanchet@33232
   686
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   687
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@35284
   688
fun rep_type_for_quot_type thy (T as Type (s, _)) =
blanchet@35284
   689
  let val {qtyp, rtyp, ...} = Quotient_Info.quotdata_lookup thy s in
blanchet@35284
   690
    instantiate_type thy qtyp T rtyp
blanchet@35284
   691
  end
blanchet@35284
   692
fun equiv_relation_for_quot_type thy (Type (s, Ts)) =
blanchet@35284
   693
    let
blanchet@35284
   694
      val {qtyp, equiv_rel, ...} = Quotient_Info.quotdata_lookup thy s
blanchet@35284
   695
      val Ts' = qtyp |> dest_Type |> snd
blanchet@35284
   696
    in subst_atomic_types (Ts' ~~ Ts) equiv_rel end
blanchet@34936
   697
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   698
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   699
blanchet@33192
   700
fun is_coconstr thy (s, T) =
blanchet@33192
   701
  let
blanchet@33583
   702
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   703
    val co_T = body_type T
blanchet@33192
   704
    val co_s = dest_Type co_T |> fst
blanchet@33192
   705
  in
blanchet@33192
   706
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   707
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   708
  end
blanchet@33192
   709
  handle TYPE ("dest_Type", _, _) => false
blanchet@37256
   710
fun is_constr_like ctxt (s, T) =
blanchet@35665
   711
  member (op =) [@{const_name FinFun}, @{const_name FunBox},
blanchet@35665
   712
                 @{const_name PairBox}, @{const_name Quot},
blanchet@35665
   713
                 @{const_name Zero_Rep}, @{const_name Suc_Rep}] s orelse
blanchet@37256
   714
  let
blanchet@37256
   715
    val thy = ProofContext.theory_of ctxt
blanchet@37256
   716
    val (x as (_, T)) = (s, unarize_unbox_etc_type T)
blanchet@37256
   717
  in
blanchet@37260
   718
    is_real_constr thy x orelse is_record_constr x orelse
blanchet@37256
   719
    (is_abs_fun ctxt x andalso is_pure_typedef ctxt (range_type T)) orelse
blanchet@34936
   720
    is_coconstr thy x
blanchet@33192
   721
  end
blanchet@37256
   722
fun is_stale_constr ctxt (x as (_, T)) =
blanchet@37256
   723
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   724
    is_codatatype thy (body_type T) andalso is_constr_like ctxt x andalso
blanchet@37256
   725
    not (is_coconstr thy x)
blanchet@37256
   726
  end
blanchet@37256
   727
fun is_constr ctxt stds (x as (_, T)) =
blanchet@37256
   728
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   729
    is_constr_like ctxt x andalso
blanchet@37256
   730
    not (is_basic_datatype thy stds
blanchet@35220
   731
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@37256
   732
    not (is_stale_constr ctxt x)
blanchet@37256
   733
  end
blanchet@33192
   734
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   735
val is_sel_like_and_no_discr =
blanchet@35665
   736
  String.isPrefix sel_prefix orf
blanchet@35665
   737
  (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   738
blanchet@33192
   739
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   740
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   741
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   742
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   743
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   744
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   745
blanchet@35070
   746
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   747
  case T of
blanchet@35665
   748
    Type (@{type_name fun}, _) =>
blanchet@34936
   749
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   750
    not (is_boolean_type (body_type T))
blanchet@35665
   751
  | Type (@{type_name "*"}, Ts) =>
blanchet@34936
   752
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   753
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   754
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   755
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   756
  | _ => false
blanchet@35280
   757
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   758
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   759
    SOME (SOME box_me) => box_me
blanchet@35070
   760
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   761
and box_type hol_ctxt boxy T =
blanchet@33192
   762
  case T of
blanchet@35665
   763
    Type (z as (@{type_name fun}, [T1, T2])) =>
blanchet@34936
   764
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   765
       should_box_type hol_ctxt boxy z then
blanchet@33192
   766
      Type (@{type_name fun_box},
blanchet@35070
   767
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   768
    else
blanchet@35070
   769
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   770
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@35665
   771
  | Type (z as (@{type_name "*"}, Ts)) =>
blanchet@34982
   772
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   773
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   774
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   775
    else
blanchet@35665
   776
      Type (@{type_name "*"},
blanchet@35665
   777
            map (box_type hol_ctxt
blanchet@34121
   778
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   779
                           else InPair)) Ts)
blanchet@33192
   780
  | _ => T
blanchet@33192
   781
blanchet@35190
   782
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   783
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   784
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   785
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   786
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   787
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   788
blanchet@33192
   789
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   790
blanchet@33192
   791
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   792
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   793
  if s = @{const_name Pair} then
blanchet@33192
   794
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   795
  else
blanchet@33192
   796
    sel_prefix_for n ^ s
blanchet@33192
   797
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   798
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   799
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   800
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   801
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   802
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   803
  oo nth_sel_for_constr
blanchet@33192
   804
blanchet@33192
   805
fun sel_no_from_name s =
blanchet@33192
   806
  if String.isPrefix discr_prefix s then
blanchet@33192
   807
    ~1
blanchet@33192
   808
  else if String.isPrefix sel_prefix s then
blanchet@33192
   809
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   810
  else if s = @{const_name snd} then
blanchet@33192
   811
    1
blanchet@33192
   812
  else
blanchet@33192
   813
    0
blanchet@33192
   814
blanchet@35078
   815
val close_form =
blanchet@35078
   816
  let
blanchet@35078
   817
    fun close_up zs zs' =
blanchet@35078
   818
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   819
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   820
           (take (length zs' - length zs) zs')
blanchet@35078
   821
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   822
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   823
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   824
        end
blanchet@35078
   825
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   826
  in aux [] end
blanchet@35078
   827
blanchet@33192
   828
fun eta_expand _ t 0 = t
blanchet@33192
   829
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   830
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   831
  | eta_expand Ts t n =
blanchet@37261
   832
    fold_rev (curry3 Abs ("x" ^ nat_subscript n))
blanchet@33192
   833
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   834
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   835
blanchet@33192
   836
fun extensionalize t =
blanchet@33192
   837
  case t of
blanchet@33192
   838
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   839
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   840
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   841
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   842
    end
blanchet@33192
   843
  | _ => t
blanchet@33192
   844
blanchet@33192
   845
fun distinctness_formula T =
blanchet@33192
   846
  all_distinct_unordered_pairs_of
blanchet@33192
   847
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   848
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   849
blanchet@35220
   850
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   851
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   852
blanchet@37256
   853
fun uncached_datatype_constrs ({thy, ctxt, stds, ...} : hol_context)
blanchet@35220
   854
                              (T as Type (s, Ts)) =
blanchet@33583
   855
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@34982
   856
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   857
     | _ =>
blanchet@37256
   858
       if is_datatype ctxt stds T then
blanchet@33581
   859
         case Datatype.get_info thy s of
blanchet@33581
   860
           SOME {index, descr, ...} =>
blanchet@33581
   861
           let
blanchet@33581
   862
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   863
           in
blanchet@37260
   864
             map (apsnd (fn Us =>
blanchet@37260
   865
                            map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@37260
   866
                 constrs
blanchet@33581
   867
           end
blanchet@33581
   868
         | NONE =>
blanchet@33581
   869
           if is_record_type T then
blanchet@33581
   870
             let
blanchet@33581
   871
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   872
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   873
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   874
             in [(s', T')] end
blanchet@34936
   875
           else if is_quot_type thy T then
blanchet@34936
   876
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@37256
   877
           else case typedef_info ctxt s of
blanchet@33581
   878
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@35311
   879
             [(Abs_name,
blanchet@35311
   880
               varify_and_instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   881
           | NONE =>
blanchet@33581
   882
             if T = @{typ ind} then
blanchet@33581
   883
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   884
             else
blanchet@33581
   885
               []
blanchet@33581
   886
       else
blanchet@33581
   887
         [])
blanchet@33580
   888
  | uncached_datatype_constrs _ _ = []
blanchet@35220
   889
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   890
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   891
    SOME xs => xs
blanchet@33580
   892
  | NONE =>
blanchet@35220
   893
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   894
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   895
    end
blanchet@35190
   896
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   897
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   898
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@33192
   899
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   900
blanchet@33192
   901
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   902
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   903
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   904
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   905
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   906
    AList.lookup (op =)
blanchet@35190
   907
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   908
        s
blanchet@33192
   909
    |> the |> pair s
blanchet@33192
   910
  end
blanchet@34982
   911
blanchet@35070
   912
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   913
  let val dataT = body_type T in
blanchet@33192
   914
    if s = @{const_name Suc} then
blanchet@33192
   915
      Abs (Name.uu, dataT,
blanchet@33192
   916
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
   917
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
   918
      Const (discr_for_constr x)
blanchet@33192
   919
    else
blanchet@33192
   920
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   921
  end
blanchet@37256
   922
fun discriminate_value (hol_ctxt as {ctxt, ...}) x t =
blanchet@35280
   923
  case head_of t of
blanchet@35280
   924
    Const x' =>
blanchet@33192
   925
    if x = x' then @{const True}
blanchet@37256
   926
    else if is_constr_like ctxt x' then @{const False}
blanchet@35070
   927
    else betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@35070
   928
  | _ => betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
   929
blanchet@35220
   930
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
   931
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
   932
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
   933
      @{term "%n::nat. n - 1"}
blanchet@33192
   934
    else if is_pair_type dataT then
blanchet@33192
   935
      Const (nth_sel_for_constr x n)
blanchet@33192
   936
    else
blanchet@33192
   937
      let
blanchet@35665
   938
        fun aux m (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
   939
            let
blanchet@33192
   940
              val (m, t1) = aux m T1
blanchet@33192
   941
              val (m, t2) = aux m T2
blanchet@33192
   942
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   943
          | aux m T =
blanchet@33192
   944
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
   945
                    $ Bound 0)
blanchet@33192
   946
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
   947
                     (List.take (arg_Ts, n)) 0
blanchet@33192
   948
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
   949
  end
blanchet@37256
   950
fun select_nth_constr_arg ctxt stds x t n res_T =
blanchet@37256
   951
  let val thy = ProofContext.theory_of ctxt in
blanchet@37256
   952
    (case strip_comb t of
blanchet@37256
   953
       (Const x', args) =>
blanchet@37256
   954
       if x = x' then nth args n
blanchet@37256
   955
       else if is_constr_like ctxt x' then Const (@{const_name unknown}, res_T)
blanchet@37256
   956
       else raise SAME ()
blanchet@37256
   957
     | _ => raise SAME())
blanchet@37256
   958
    handle SAME () => betapply (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@37256
   959
  end
blanchet@33192
   960
blanchet@35220
   961
fun construct_value _ _ x [] = Const x
blanchet@37256
   962
  | construct_value ctxt stds (x as (s, _)) args =
blanchet@33192
   963
    let val args = map Envir.eta_contract args in
blanchet@33192
   964
      case hd args of
blanchet@35280
   965
        Const (s', _) $ t =>
blanchet@34936
   966
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
   967
           constr_name_for_sel_like s' = s andalso
blanchet@35220
   968
           forall (fn (n, t') =>
blanchet@37256
   969
                      select_nth_constr_arg ctxt stds x t n dummyT = t')
blanchet@34936
   970
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
   971
          t
blanchet@33192
   972
        else
blanchet@33192
   973
          list_comb (Const x, args)
blanchet@33192
   974
      | _ => list_comb (Const x, args)
blanchet@33192
   975
    end
blanchet@33192
   976
blanchet@37256
   977
fun constr_expand (hol_ctxt as {ctxt, stds, ...}) T t =
blanchet@35665
   978
  (case head_of t of
blanchet@37256
   979
     Const x => if is_constr_like ctxt x then t else raise SAME ()
blanchet@35665
   980
   | _ => raise SAME ())
blanchet@35665
   981
  handle SAME () =>
blanchet@35665
   982
         let
blanchet@35665
   983
           val x' as (_, T') =
blanchet@35665
   984
             if is_pair_type T then
blanchet@35665
   985
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@35665
   986
                 (@{const_name Pair}, T1 --> T2 --> T)
blanchet@35665
   987
               end
blanchet@35665
   988
             else
blanchet@35665
   989
               datatype_constrs hol_ctxt T |> hd
blanchet@35665
   990
           val arg_Ts = binder_types T'
blanchet@35665
   991
         in
blanchet@37256
   992
           list_comb (Const x', map2 (select_nth_constr_arg ctxt stds x' t)
blanchet@35665
   993
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@35665
   994
         end
blanchet@35665
   995
blanchet@35665
   996
fun coerce_bound_no f j t =
blanchet@35665
   997
  case t of
blanchet@35665
   998
    t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
blanchet@35665
   999
  | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
blanchet@35665
  1000
  | Bound j' => if j' = j then f t else t
blanchet@35665
  1001
  | _ => t
blanchet@35665
  1002
fun coerce_bound_0_in_term hol_ctxt new_T old_T =
blanchet@35665
  1003
  old_T <> new_T ? coerce_bound_no (coerce_term hol_ctxt [new_T] old_T new_T) 0
blanchet@37256
  1004
and coerce_term (hol_ctxt as {ctxt, stds, fast_descrs, ...}) Ts new_T old_T t =
blanchet@35665
  1005
  if old_T = new_T then
blanchet@35665
  1006
    t
blanchet@35665
  1007
  else
blanchet@35665
  1008
    case (new_T, old_T) of
blanchet@35665
  1009
      (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1010
       Type (@{type_name fun}, [old_T1, old_T2])) =>
blanchet@35665
  1011
      (case eta_expand Ts t 1 of
blanchet@35665
  1012
         Abs (s, _, t') =>
blanchet@35665
  1013
         Abs (s, new_T1,
blanchet@35665
  1014
              t' |> coerce_bound_0_in_term hol_ctxt new_T1 old_T1
blanchet@35665
  1015
                 |> coerce_term hol_ctxt (new_T1 :: Ts) new_T2 old_T2)
blanchet@35665
  1016
         |> Envir.eta_contract
blanchet@35665
  1017
         |> new_s <> @{type_name fun}
blanchet@37256
  1018
            ? construct_value ctxt stds
blanchet@35665
  1019
                  (if new_s = @{type_name fin_fun} then @{const_name FinFun}
blanchet@35665
  1020
                   else @{const_name FunBox},
blanchet@35665
  1021
                   Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1022
              o single
blanchet@35665
  1023
       | t' => raise TERM ("Nitpick_HOL.coerce_term", [t']))
blanchet@35665
  1024
    | (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1025
       Type (old_s, old_Ts as [old_T1, old_T2])) =>
blanchet@35665
  1026
      if old_s = @{type_name fin_fun} orelse old_s = @{type_name fun_box} orelse
blanchet@35665
  1027
         old_s = @{type_name pair_box} orelse old_s = @{type_name "*"} then
blanchet@35665
  1028
        case constr_expand hol_ctxt old_T t of
blanchet@35665
  1029
          Const (old_s, _) $ t1 =>
blanchet@35665
  1030
          if new_s = @{type_name fun} then
blanchet@35665
  1031
            coerce_term hol_ctxt Ts new_T (Type (@{type_name fun}, old_Ts)) t1
blanchet@35665
  1032
          else
blanchet@37256
  1033
            construct_value ctxt stds
blanchet@35665
  1034
                (old_s, Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1035
                [coerce_term hol_ctxt Ts (Type (@{type_name fun}, new_Ts))
blanchet@35665
  1036
                             (Type (@{type_name fun}, old_Ts)) t1]
blanchet@35665
  1037
        | Const _ $ t1 $ t2 =>
blanchet@37256
  1038
          construct_value ctxt stds
blanchet@35665
  1039
              (if new_s = @{type_name "*"} then @{const_name Pair}
blanchet@35665
  1040
               else @{const_name PairBox}, new_Ts ---> new_T)
blanchet@35665
  1041
              (map3 (coerce_term hol_ctxt Ts) [new_T1, new_T2] [old_T1, old_T2]
blanchet@35665
  1042
                    [t1, t2])
blanchet@35665
  1043
        | t' => raise TERM ("Nitpick_HOL.coerce_term", [t'])
blanchet@35665
  1044
      else
blanchet@35665
  1045
        raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1046
    | _ => raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1047
blanchet@35665
  1048
fun card_of_type assigns (Type (@{type_name fun}, [T1, T2])) =
blanchet@34123
  1049
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@35665
  1050
  | card_of_type assigns (Type (@{type_name "*"}, [T1, T2])) =
blanchet@34123
  1051
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1052
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1053
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1054
  | card_of_type _ @{typ bool} = 2
blanchet@33192
  1055
  | card_of_type _ @{typ unit} = 1
blanchet@34123
  1056
  | card_of_type assigns T =
blanchet@34123
  1057
    case AList.lookup (op =) assigns T of
blanchet@33192
  1058
      SOME k => k
blanchet@33192
  1059
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1060
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@35665
  1061
fun bounded_card_of_type max default_card assigns
blanchet@35665
  1062
                         (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
  1063
    let
blanchet@34123
  1064
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1065
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1066
    in
blanchet@33192
  1067
      if k1 = max orelse k2 = max then max
blanchet@33192
  1068
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1069
    end
blanchet@35665
  1070
  | bounded_card_of_type max default_card assigns
blanchet@35665
  1071
                         (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
  1072
    let
blanchet@34123
  1073
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1074
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1075
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1076
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1077
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1078
                    card_of_type assigns T
blanchet@33192
  1079
                  else
blanchet@34123
  1080
                    card_of_type assigns T
blanchet@33232
  1081
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1082
                           default_card)
blanchet@35385
  1083
fun bounded_exact_card_of_type hol_ctxt finitizable_dataTs max default_card
blanchet@35385
  1084
                               assigns T =
blanchet@33192
  1085
  let
blanchet@33192
  1086
    fun aux avoid T =
blanchet@34121
  1087
      (if member (op =) avoid T then
blanchet@33192
  1088
         0
blanchet@35385
  1089
       else if member (op =) finitizable_dataTs T then
blanchet@35385
  1090
         raise SAME ()
blanchet@33192
  1091
       else case T of
blanchet@35665
  1092
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
  1093
         let
blanchet@33192
  1094
           val k1 = aux avoid T1
blanchet@33192
  1095
           val k2 = aux avoid T2
blanchet@33192
  1096
         in
blanchet@33192
  1097
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1098
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1099
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1100
         end
blanchet@35665
  1101
       | Type (@{type_name "*"}, [T1, T2]) =>
blanchet@33192
  1102
         let
blanchet@33192
  1103
           val k1 = aux avoid T1
blanchet@33192
  1104
           val k2 = aux avoid T2
blanchet@33192
  1105
         in
blanchet@33192
  1106
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1107
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1108
           else Int.min (max, k1 * k2)
blanchet@33192
  1109
         end
blanchet@33192
  1110
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1111
       | @{typ prop} => 2
blanchet@33192
  1112
       | @{typ bool} => 2
blanchet@33192
  1113
       | @{typ unit} => 1
blanchet@33192
  1114
       | Type _ =>
blanchet@35070
  1115
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1116
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1117
                  else raise SAME ()
blanchet@33192
  1118
          | constrs =>
blanchet@33192
  1119
            let
blanchet@33192
  1120
              val constr_cards =
blanchet@35280
  1121
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1122
                    constrs
blanchet@33192
  1123
            in
blanchet@34121
  1124
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1125
              else Integer.sum constr_cards
blanchet@33192
  1126
            end)
blanchet@33192
  1127
       | _ => raise SAME ())
blanchet@34123
  1128
      handle SAME () =>
blanchet@34123
  1129
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1130
  in Int.min (max, aux [] T) end
blanchet@33192
  1131
blanchet@35665
  1132
val small_type_max_card = 5
blanchet@35665
  1133
blanchet@35384
  1134
fun is_finite_type hol_ctxt T =
blanchet@35665
  1135
  bounded_exact_card_of_type hol_ctxt [] 1 2 [] T > 0
blanchet@35665
  1136
fun is_small_finite_type hol_ctxt T =
blanchet@35665
  1137
  let val n = bounded_exact_card_of_type hol_ctxt [] 1 2 [] T in
blanchet@35665
  1138
    n > 0 andalso n <= small_type_max_card
blanchet@35665
  1139
  end
blanchet@33192
  1140
blanchet@33192
  1141
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1142
  | is_ground_term (Const _) = true
blanchet@33192
  1143
  | is_ground_term _ = false
blanchet@33192
  1144
blanchet@36062
  1145
fun hashw_term (t1 $ t2) = hashw (hashw_term t1, hashw_term t2)
blanchet@36062
  1146
  | hashw_term (Const (s, _)) = hashw_string (s, 0w0)
blanchet@33192
  1147
  | hashw_term _ = 0w0
blanchet@33192
  1148
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1149
blanchet@33192
  1150
fun special_bounds ts =
wenzelm@35408
  1151
  fold Term.add_vars ts [] |> sort (Term_Ord.fast_indexname_ord o pairself fst)
blanchet@33192
  1152
blanchet@33192
  1153
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
  1154
blanchet@33571
  1155
fun is_funky_typedef_name thy s =
blanchet@34121
  1156
  member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@34936
  1157
                 @{type_name int}] s orelse
blanchet@34936
  1158
  is_frac_type thy (Type (s, []))
blanchet@33571
  1159
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
  1160
  | is_funky_typedef _ _ = false
blanchet@33192
  1161
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1162
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1163
  | is_arity_type_axiom _ = false
blanchet@37256
  1164
fun is_typedef_axiom ctxt boring (@{const "==>"} $ _ $ t2) =
blanchet@37256
  1165
    is_typedef_axiom ctxt boring t2
blanchet@37256
  1166
  | is_typedef_axiom ctxt boring
blanchet@33192
  1167
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@35665
  1168
         $ Const (_, Type (@{type_name fun}, [Type (s, _), _]))
blanchet@35665
  1169
         $ Const _ $ _)) =
blanchet@37256
  1170
    let val thy = ProofContext.theory_of ctxt in
blanchet@37256
  1171
      boring <> is_funky_typedef_name thy s andalso is_typedef ctxt s
blanchet@37256
  1172
    end
blanchet@33192
  1173
  | is_typedef_axiom _ _ _ = false
blanchet@36126
  1174
val is_class_axiom =
blanchet@36126
  1175
  Logic.strip_horn #> swap #> op :: #> forall (can Logic.dest_of_class)
blanchet@33192
  1176
blanchet@33192
  1177
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1178
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1179
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1180
   using "typedef_info". *)
blanchet@37256
  1181
fun partition_axioms_by_definitionality ctxt axioms def_names =
blanchet@33192
  1182
  let
blanchet@33192
  1183
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1184
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1185
    val nondefs =
blanchet@33192
  1186
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@37256
  1187
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom ctxt true) o snd)
blanchet@33192
  1188
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1189
blanchet@33197
  1190
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1191
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1192
   commands. *)
blanchet@33192
  1193
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1194
blanchet@35283
  1195
val is_trivial_definition =
blanchet@35283
  1196
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1197
val is_plain_definition =
blanchet@33192
  1198
  let
blanchet@33192
  1199
    fun do_lhs t1 =
blanchet@33192
  1200
      case strip_comb t1 of
blanchet@34936
  1201
        (Const _, args) =>
blanchet@34936
  1202
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1203
      | _ => false
blanchet@33192
  1204
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1205
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1206
        do_lhs t1
blanchet@33192
  1207
      | do_eq _ = false
blanchet@33192
  1208
  in do_eq end
blanchet@33192
  1209
blanchet@37256
  1210
fun all_axioms_of ctxt subst =
blanchet@33192
  1211
  let
blanchet@37256
  1212
    val thy = ProofContext.theory_of ctxt
blanchet@35335
  1213
    val axioms_of_thys =
blanchet@35893
  1214
      maps Thm.axioms_of
blanchet@35893
  1215
      #> map (apsnd (subst_atomic subst o prop_of))
blanchet@35893
  1216
      #> filter_out (is_class_axiom o snd)
blanchet@33192
  1217
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1218
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1219
                    |> OrdList.make fast_string_ord
blanchet@33192
  1220
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1221
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1222
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1223
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1224
    val (built_in_defs, built_in_nondefs) =
blanchet@37256
  1225
      partition_axioms_by_definitionality ctxt built_in_axioms def_names
blanchet@37256
  1226
      ||> filter (is_typedef_axiom ctxt false)
blanchet@33192
  1227
    val (user_defs, user_nondefs) =
blanchet@37256
  1228
      partition_axioms_by_definitionality ctxt user_axioms def_names
blanchet@33197
  1229
    val (built_in_nondefs, user_nondefs) =
blanchet@37256
  1230
      List.partition (is_typedef_axiom ctxt false) user_nondefs
blanchet@33197
  1231
      |>> append built_in_nondefs
blanchet@34121
  1232
    val defs =
blanchet@34121
  1233
      (thy |> PureThy.all_thms_of
blanchet@34121
  1234
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1235
           |> map (prop_of o snd)
blanchet@35283
  1236
           |> filter_out is_trivial_definition
blanchet@35283
  1237
           |> filter is_plain_definition) @
blanchet@34121
  1238
      user_defs @ built_in_defs
blanchet@33192
  1239
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1240
blanchet@35220
  1241
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1242
  if s = @{const_name If} then
blanchet@33192
  1243
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1244
  else
blanchet@35220
  1245
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1246
      case AList.lookup (op =)
blanchet@35220
  1247
                    (built_in_consts
blanchet@35220
  1248
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1249
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1250
        SOME n => SOME n
blanchet@35220
  1251
      | NONE =>
blanchet@35220
  1252
        case AList.lookup (op =)
blanchet@35220
  1253
                 (built_in_typed_consts
blanchet@35220
  1254
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1255
                 (s, unarize_type T) of
blanchet@35220
  1256
          SOME n => SOME n
blanchet@35220
  1257
        | NONE =>
blanchet@35280
  1258
          case s of
blanchet@35280
  1259
            @{const_name zero_class.zero} =>
blanchet@35280
  1260
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1261
          | @{const_name Suc} =>
blanchet@35280
  1262
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1263
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1264
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1265
                 else
blanchet@35280
  1266
                   NONE
blanchet@35220
  1267
    end
blanchet@35220
  1268
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1269
blanchet@33192
  1270
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1271
   simplification rules (equational specifications). *)
blanchet@33192
  1272
fun term_under_def t =
blanchet@33192
  1273
  case t of
blanchet@33192
  1274
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1275
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1276
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1277
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1278
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1279
  | t1 $ _ => term_under_def t1
blanchet@33192
  1280
  | _ => t
blanchet@33192
  1281
blanchet@36555
  1282
(* Here we crucially rely on "specialize_type" performing a preorder traversal
blanchet@36555
  1283
   of the term, without which the wrong occurrence of a constant could be
blanchet@36555
  1284
   matched in the face of overloading. *)
blanchet@35220
  1285
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1286
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1287
    []
blanchet@33192
  1288
  else
blanchet@33192
  1289
    these (Symtab.lookup table s)
blanchet@36555
  1290
    |> map_filter (try (specialize_type thy x))
blanchet@34121
  1291
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1292
blanchet@35280
  1293
fun normalized_rhs_of t =
blanchet@33192
  1294
  let
blanchet@33743
  1295
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1296
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1297
      | aux _ _ = NONE
blanchet@33192
  1298
    val (lhs, rhs) =
blanchet@33192
  1299
      case t of
blanchet@33192
  1300
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1301
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1302
        (t1, t2)
blanchet@33232
  1303
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1304
    val args = strip_comb lhs |> snd
blanchet@33743
  1305
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1306
blanchet@33192
  1307
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1308
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1309
     original_name s <> s then
blanchet@33192
  1310
    NONE
blanchet@33192
  1311
  else
blanchet@35220
  1312
    x |> def_props_for_const thy [(NONE, false)] false table |> List.last
blanchet@35280
  1313
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1314
    handle List.Empty => NONE
blanchet@33192
  1315
blanchet@33192
  1316
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1317
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1318
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1319
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1320
blanchet@33192
  1321
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1322
  let
blanchet@33192
  1323
    fun is_good_arg (Bound _) = true
blanchet@33192
  1324
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1325
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1326
        s = @{const_name undefined}
blanchet@33192
  1327
      | is_good_arg _ = false
blanchet@33192
  1328
  in
blanchet@33192
  1329
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1330
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1331
      (case def_of_const thy table x of
blanchet@33192
  1332
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1333
       | NONE => false)
blanchet@33192
  1334
    | _ => false
blanchet@33192
  1335
  end
blanchet@33192
  1336
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1337
  map_aterms (fn t as Const x =>
blanchet@33192
  1338
                 (case def_of_const thy table x of
blanchet@33192
  1339
                    SOME t' =>
blanchet@33192
  1340
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1341
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1342
                      else t
blanchet@33192
  1343
                    end
blanchet@33192
  1344
                 | NONE => t)
blanchet@33192
  1345
               | t => t)
blanchet@33192
  1346
blanchet@35220
  1347
fun case_const_names thy stds =
blanchet@33192
  1348
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@35220
  1349
                  if is_basic_datatype thy stds dtype_s then
blanchet@33192
  1350
                    I
blanchet@33192
  1351
                  else
blanchet@33192
  1352
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1353
                                     |> the |> #3 |> length))
blanchet@33192
  1354
              (Datatype.get_all thy) [] @
blanchet@33583
  1355
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1356
blanchet@35718
  1357
fun fixpoint_kind_of_const thy table x =
blanchet@35718
  1358
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@35718
  1359
    NoFp
blanchet@35718
  1360
  else
blanchet@35718
  1361
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@35718
  1362
    handle Option.Option => NoFp
blanchet@33192
  1363
blanchet@35718
  1364
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35718
  1365
                             ...} : hol_context) x =
blanchet@35718
  1366
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35718
  1367
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@35718
  1368
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@35718
  1369
                             ...} : hol_context) x =
blanchet@35718
  1370
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@35718
  1371
                                                     x)))
blanchet@35718
  1372
         [!simp_table, psimp_table]
blanchet@35718
  1373
fun is_inductive_pred hol_ctxt =
blanchet@35718
  1374
  is_real_inductive_pred hol_ctxt andf (not o is_real_equational_fun hol_ctxt)
blanchet@35718
  1375
fun is_equational_fun hol_ctxt =
blanchet@35718
  1376
  (is_real_equational_fun hol_ctxt orf is_real_inductive_pred hol_ctxt orf
blanchet@35718
  1377
   (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1378
blanchet@35718
  1379
fun lhs_of_equation t =
blanchet@35718
  1380
  case t of
blanchet@35718
  1381
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1382
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1383
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1384
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@35718
  1385
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1386
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1387
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1388
  | _ => NONE
blanchet@35718
  1389
fun is_constr_pattern _ (Bound _) = true
blanchet@35718
  1390
  | is_constr_pattern _ (Var _) = true
blanchet@37256
  1391
  | is_constr_pattern ctxt t =
blanchet@35718
  1392
    case strip_comb t of
blanchet@35718
  1393
      (Const x, args) =>
blanchet@37256
  1394
      is_constr_like ctxt x andalso forall (is_constr_pattern ctxt) args
blanchet@35718
  1395
    | _ => false
blanchet@37256
  1396
fun is_constr_pattern_lhs ctxt t =
blanchet@37256
  1397
  forall (is_constr_pattern ctxt) (snd (strip_comb t))
blanchet@37256
  1398
fun is_constr_pattern_formula ctxt t =
blanchet@35718
  1399
  case lhs_of_equation t of
blanchet@37256
  1400
    SOME t' => is_constr_pattern_lhs ctxt t'
blanchet@35718
  1401
  | NONE => false
blanchet@35718
  1402
blanchet@36555
  1403
(* Similar to "specialize_type" but returns all matches rather than only the
blanchet@36555
  1404
   first (preorder) match. *)
blanchet@35807
  1405
fun multi_specialize_type thy slack (s, T) t =
blanchet@35807
  1406
  let
blanchet@35807
  1407
    fun aux (Const (s', T')) ys =
blanchet@35807
  1408
        if s = s' then
blanchet@35807
  1409
          ys |> (if AList.defined (op =) ys T' then
blanchet@35807
  1410
                   I
blanchet@35807
  1411
                 else
blanchet@36555
  1412
                   cons (T', monomorphic_term (Sign.typ_match thy (T', T)
blanchet@36555
  1413
                                                              Vartab.empty) t)
blanchet@35807
  1414
                   handle Type.TYPE_MATCH => I
blanchet@36575
  1415
                        | TERM _ =>
blanchet@35807
  1416
                          if slack then
blanchet@35807
  1417
                            I
blanchet@35807
  1418
                          else
blanchet@37253
  1419
                            raise NOT_SUPPORTED
blanchet@37253
  1420
                                      ("too much polymorphism in axiom \"" ^
blanchet@37253
  1421
                                       Syntax.string_of_term_global thy t ^
blanchet@37253
  1422
                                       "\" involving " ^ quote s))
blanchet@35807
  1423
        else
blanchet@35807
  1424
          ys
blanchet@35807
  1425
      | aux _ ys = ys
blanchet@35807
  1426
  in map snd (fold_aterms aux t []) end
blanchet@35807
  1427
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@35807
  1428
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@35807
  1429
blanchet@35807
  1430
fun unvarify_term (t1 $ t2) = unvarify_term t1 $ unvarify_term t2
blanchet@35807
  1431
  | unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@35807
  1432
  | unvarify_term (Abs (s, T, t')) = Abs (s, T, unvarify_term t')
blanchet@35807
  1433
  | unvarify_term t = t
blanchet@35807
  1434
fun axiom_for_choice_spec thy =
blanchet@35807
  1435
  unvarify_term
blanchet@35807
  1436
  #> Object_Logic.atomize_term thy
blanchet@35807
  1437
  #> Choice_Specification.close_form
blanchet@35807
  1438
  #> HOLogic.mk_Trueprop
blanchet@35807
  1439
fun is_choice_spec_fun ({thy, def_table, nondef_table, choice_spec_table, ...}
blanchet@35807
  1440
                        : hol_context) x =
blanchet@35807
  1441
  case nondef_props_for_const thy true choice_spec_table x of
blanchet@35807
  1442
    [] => false
blanchet@35807
  1443
  | ts => case def_of_const thy def_table x of
blanchet@35807
  1444
            SOME (Const (@{const_name Eps}, _) $ _) => true
blanchet@35807
  1445
          | SOME _ => false
blanchet@35807
  1446
          | NONE =>
blanchet@35807
  1447
            let val ts' = nondef_props_for_const thy true nondef_table x in
blanchet@35807
  1448
              length ts' = length ts andalso
blanchet@35807
  1449
              forall (fn t =>
blanchet@35807
  1450
                         exists (curry (op aconv) (axiom_for_choice_spec thy t))
blanchet@35807
  1451
                                ts') ts
blanchet@35807
  1452
            end
blanchet@35807
  1453
blanchet@35807
  1454
fun is_choice_spec_axiom thy choice_spec_table t =
blanchet@35807
  1455
  Symtab.exists (fn (_, ts) =>
blanchet@35807
  1456
                    exists (curry (op aconv) t o axiom_for_choice_spec thy) ts)
blanchet@35807
  1457
                choice_spec_table
blanchet@35807
  1458
blanchet@35718
  1459
(** Constant unfolding **)
blanchet@33192
  1460
blanchet@37256
  1461
fun constr_case_body ctxt stds (j, (x as (_, T))) =
blanchet@33192
  1462
  let val arg_Ts = binder_types T in
blanchet@37256
  1463
    list_comb (Bound j, map2 (select_nth_constr_arg ctxt stds x (Bound 0))
blanchet@33192
  1464
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1465
  end
blanchet@37256
  1466
fun add_constr_case (hol_ctxt as {ctxt, stds, ...}) res_T (j, x) res_t =
blanchet@34124
  1467
  Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@37256
  1468
  $ discriminate_value hol_ctxt x (Bound 0) $ constr_case_body ctxt stds (j, x)
blanchet@33580
  1469
  $ res_t
blanchet@37256
  1470
fun optimized_case_def (hol_ctxt as {ctxt, stds, ...}) dataT res_T =
blanchet@33192
  1471
  let
blanchet@35070
  1472
    val xs = datatype_constrs hol_ctxt dataT
blanchet@35179
  1473
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs
blanchet@35179
  1474
    val (xs', x) = split_last xs
blanchet@33192
  1475
  in
blanchet@37256
  1476
    constr_case_body ctxt stds (1, x)
blanchet@35179
  1477
    |> fold_rev (add_constr_case hol_ctxt res_T) (length xs downto 2 ~~ xs')
blanchet@33192
  1478
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1479
  end
blanchet@37256
  1480
fun optimized_record_get (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T res_T t =
blanchet@35070
  1481
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1482
    case no_of_record_field thy s rec_T of
blanchet@33192
  1483
      ~1 => (case rec_T of
blanchet@33192
  1484
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1485
               let
blanchet@33192
  1486
                 val rec_T' = List.last Ts
blanchet@33192
  1487
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1488
               in
blanchet@37256
  1489
                 select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@35070
  1490
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1491
               end
blanchet@33232
  1492
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1493
                                []))
blanchet@37256
  1494
    | j => select_nth_constr_arg ctxt stds constr_x t j res_T
blanchet@33192
  1495
  end
blanchet@37256
  1496
fun optimized_record_update (hol_ctxt as {thy, ctxt, stds, ...}) s rec_T fun_t
blanchet@37256
  1497
                            rec_t =
blanchet@33192
  1498
  let
blanchet@35070
  1499
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1500
    val Ts = binder_types constr_T
blanchet@33192
  1501
    val n = length Ts
blanchet@33192
  1502
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1503
    val ts =
blanchet@35220
  1504
      map2 (fn j => fn T =>
blanchet@37256
  1505
               let val t = select_nth_constr_arg ctxt stds constr_x rec_t j T in
blanchet@35220
  1506
                 if j = special_j then
blanchet@35220
  1507
                   betapply (fun_t, t)
blanchet@35220
  1508
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1509
                   optimized_record_update hol_ctxt s
blanchet@35220
  1510
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1511
                 else
blanchet@35220
  1512
                   t
blanchet@35220
  1513
               end) (index_seq 0 n) Ts
blanchet@33192
  1514
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1515
blanchet@35070
  1516
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1517
val unfold_max_depth = 255
blanchet@33192
  1518
blanchet@35284
  1519
fun unfold_defs_in_term (hol_ctxt as {thy, ctxt, stds, fast_descrs, case_names,
blanchet@35280
  1520
                                      def_table, ground_thm_table, ersatz_table,
blanchet@35280
  1521
                                      ...}) =
blanchet@33192
  1522
  let
blanchet@33192
  1523
    fun do_term depth Ts t =
blanchet@33192
  1524
      case t of
blanchet@33192
  1525
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@35665
  1526
                      Type (@{type_name fun}, [_, ran_T]))) $ t1 =>
blanchet@33192
  1527
        ((if is_number_type thy ran_T then
blanchet@33192
  1528
            let
blanchet@33192
  1529
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1530
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1531
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1532
            in
blanchet@35220
  1533
              if is_integer_like_type ran_T then
blanchet@35220
  1534
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1535
                  Const (s, ran_T)
blanchet@35220
  1536
                else
blanchet@35220
  1537
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1538
              else
blanchet@33192
  1539
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1540
                                  $ Const (s, int_T))
blanchet@33192
  1541
            end
blanchet@33192
  1542
            handle TERM _ => raise SAME ()
blanchet@33192
  1543
          else
blanchet@33192
  1544
            raise SAME ())
blanchet@33192
  1545
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1546
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1547
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1548
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1549
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1550
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1551
      | Const (x as (@{const_name distinct},
blanchet@35665
  1552
               Type (@{type_name fun}, [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1553
        $ (t1 as _ $ _) =>
blanchet@33192
  1554
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1555
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1556
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1557
        if is_ground_term t1 andalso
blanchet@34936
  1558
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1559
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1560
          do_term depth Ts t2
blanchet@33192
  1561
        else
blanchet@33192
  1562
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1563
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1564
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1565
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1566
      | Const x => do_const depth Ts t x []
blanchet@33192
  1567
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1568
      | Free _ => t
blanchet@33192
  1569
      | Var _ => t
blanchet@33192
  1570
      | Bound _ => t
blanchet@33192
  1571
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1572
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1573
        (Abs (Name.uu, body_type T,
blanchet@37256
  1574
              select_nth_constr_arg ctxt stds x (Bound 0) n res_T), [])
blanchet@33192
  1575
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@37256
  1576
        (select_nth_constr_arg ctxt stds x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1577
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1578
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1579
        SOME s' =>
blanchet@33192
  1580
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1581
      | NONE =>
blanchet@33192
  1582
        let
blanchet@33192
  1583
          val (const, ts) =
blanchet@35220
  1584
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1585
              (Const x, ts)
blanchet@33192
  1586
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1587
              SOME n =>
blanchet@33192
  1588
              let
blanchet@33192
  1589
                val (dataT, res_T) = nth_range_type n T
blanchet@33705
  1590
                                     |> pairf domain_type range_type
blanchet@33192
  1591
              in
blanchet@35070
  1592
                (optimized_case_def hol_ctxt dataT res_T
blanchet@33192
  1593
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1594
              end
blanchet@33192
  1595
            | _ =>
blanchet@37256
  1596
              if is_constr ctxt stds x then
blanchet@33192
  1597
                (Const x, ts)
blanchet@37256
  1598
              else if is_stale_constr ctxt x then
blanchet@34936
  1599
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1600
                                     \(\"" ^ s ^ "\")")
blanchet@35284
  1601
              else if is_quot_abs_fun ctxt x then
blanchet@34936
  1602
                let
blanchet@34936
  1603
                  val rep_T = domain_type T
blanchet@34936
  1604
                  val abs_T = range_type T
blanchet@34936
  1605
                in
blanchet@34936
  1606
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1607
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@35311
  1608
                               $ (Const (quot_normal_name_for_type ctxt abs_T,
blanchet@34936
  1609
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1610
                end
blanchet@35284
  1611
              else if is_quot_rep_fun ctxt x then
blanchet@34936
  1612
                let
blanchet@34936
  1613
                  val abs_T = domain_type T
blanchet@34936
  1614
                  val rep_T = range_type T
blanchet@34936
  1615
                  val x' = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1616
                in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
blanchet@33192
  1617
              else if is_record_get thy x then
blanchet@33192
  1618
                case length ts of
blanchet@33192
  1619
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1620
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1621
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1622
              else if is_record_update thy x then
blanchet@33192
  1623
                case length ts of
blanchet@35070
  1624
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1625
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1626
                            (do_term depth Ts (hd ts))
blanchet@33580
  1627
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1628
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@37256
  1629
              else if is_rep_fun ctxt x then
blanchet@37256
  1630
                let val x' = mate_of_rep_fun ctxt x in
blanchet@37256
  1631
                  if is_constr ctxt stds x' then
blanchet@33192
  1632
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1633
                                                    (range_type T)
blanchet@33192
  1634
                  else
blanchet@33192
  1635
                    (Const x, ts)
blanchet@33192
  1636
                end
blanchet@35807
  1637
              else if is_equational_fun hol_ctxt x orelse
blanchet@35807
  1638
                      is_choice_spec_fun hol_ctxt x then
blanchet@33192
  1639
                (Const x, ts)
blanchet@33192
  1640
              else case def_of_const thy def_table x of
blanchet@33192
  1641
                SOME def =>
blanchet@33192
  1642
                if depth > unfold_max_depth then
blanchet@34124
  1643
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1644
                                   "too many nested definitions (" ^
blanchet@34124
  1645
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1646
                                   quote s)
blanchet@33192
  1647
                else if s = @{const_name wfrec'} then
blanchet@33192
  1648
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1649
                else
blanchet@33192
  1650
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1651
              | NONE => (Const x, ts)
blanchet@33192
  1652
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1653
  in do_term 0 [] end
blanchet@33192
  1654
blanchet@35718
  1655
(** Axiom extraction/generation **)
blanchet@35718
  1656
blanchet@35807
  1657
fun pair_for_prop t =
blanchet@35807
  1658
  case term_under_def t of
blanchet@35807
  1659
    Const (s, _) => (s, t)
blanchet@35807
  1660
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@35807
  1661
fun def_table_for get ctxt subst =
blanchet@35807
  1662
  ctxt |> get |> map (pair_for_prop o subst_atomic subst)
blanchet@35807
  1663
       |> AList.group (op =) |> Symtab.make
blanchet@35807
  1664
fun paired_with_consts t = map (rpair t) (Term.add_const_names t [])
blanchet@35718
  1665
fun const_def_table ctxt subst ts =
blanchet@35807
  1666
  def_table_for (map prop_of o Nitpick_Defs.get) ctxt subst
blanchet@35718
  1667
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@35718
  1668
          (map pair_for_prop ts)
blanchet@35718
  1669
fun const_nondef_table ts =
blanchet@35807
  1670
  fold (append o paired_with_consts) ts [] |> AList.group (op =) |> Symtab.make
blanchet@35807
  1671
val const_simp_table = def_table_for (map prop_of o Nitpick_Simps.get)
blanchet@35807
  1672
val const_psimp_table = def_table_for (map prop_of o Nitpick_Psimps.get)
blanchet@35807
  1673
fun const_choice_spec_table ctxt subst =
blanchet@35807
  1674
  map (subst_atomic subst o prop_of) (Nitpick_Choice_Specs.get ctxt)
blanchet@35807
  1675
  |> const_nondef_table
blanchet@35718
  1676
fun inductive_intro_table ctxt subst def_table =
blanchet@37264
  1677
  let val thy = ProofContext.theory_of ctxt in
blanchet@37264
  1678
    def_table_for
blanchet@37264
  1679
        (maps (map (unfold_mutually_inductive_preds thy def_table o prop_of)
blanchet@37264
  1680
               o snd o snd)
blanchet@37264
  1681
         o filter (fn (cat, _) => cat = Spec_Rules.Inductive orelse
blanchet@37264
  1682
                                  cat = Spec_Rules.Co_Inductive)
blanchet@37264
  1683
         o Spec_Rules.get) ctxt subst
blanchet@37264
  1684
  end
blanchet@35718
  1685
fun ground_theorem_table thy =
blanchet@35718
  1686
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@35718
  1687
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@35718
  1688
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@35718
  1689
blanchet@35807
  1690
(* TODO: Move to "Nitpick.thy" *)
blanchet@35718
  1691
val basic_ersatz_table =
blanchet@37213
  1692
  [(@{const_name card}, @{const_name card'}),
blanchet@35718
  1693
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@35718
  1694
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@35718
  1695
   (@{const_name wf}, @{const_name wf'}),
blanchet@35718
  1696
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@35718
  1697
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@35718
  1698
blanchet@35718
  1699
fun ersatz_table thy =
blanchet@35718
  1700
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@35718
  1701
blanchet@35718
  1702
fun add_simps simp_table s eqs =
blanchet@35718
  1703
  Unsynchronized.change simp_table
blanchet@35718
  1704
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@35718
  1705
blanchet@37256
  1706
fun inverse_axioms_for_rep_fun ctxt (x as (_, T)) =
blanchet@37256
  1707
  let
blanchet@37256
  1708
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1709
    val abs_T = domain_type T
blanchet@37256
  1710
  in
blanchet@37256
  1711
    typedef_info ctxt (fst (dest_Type abs_T)) |> the
blanchet@35718
  1712
    |> pairf #Abs_inverse #Rep_inverse
blanchet@36555
  1713
    |> pairself (specialize_type thy x o prop_of o the)
blanchet@35718
  1714
    ||> single |> op ::
blanchet@35718
  1715
  end
blanchet@37256
  1716
fun optimized_typedef_axioms ctxt (abs_z as (abs_s, _)) =
blanchet@37256
  1717
  let
blanchet@37256
  1718
    val thy = ProofContext.theory_of ctxt
blanchet@37256
  1719
    val abs_T = Type abs_z
blanchet@37256
  1720
  in
blanchet@37256
  1721
    if is_univ_typedef ctxt abs_T then
blanchet@35718
  1722
      []
blanchet@37256
  1723
    else case typedef_info ctxt abs_s of
blanchet@35718
  1724
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@35718
  1725
      let
blanchet@35718
  1726
        val rep_T = varify_and_instantiate_type thy abs_type abs_T rep_type
blanchet@35718
  1727
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@35718
  1728
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@35718
  1729
        val set_t' =
blanchet@35718
  1730
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@36555
  1731
                      |> specialize_type thy (dest_Const rep_t)
blanchet@35718
  1732
                      |> HOLogic.dest_mem |> snd
blanchet@35718
  1733
      in
blanchet@35718
  1734
        [HOLogic.all_const abs_T
blanchet@35718
  1735
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@35718
  1736
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@35718
  1737
        |> map HOLogic.mk_Trueprop
blanchet@35718
  1738
      end
blanchet@35718
  1739
    | NONE => []
blanchet@35718
  1740
  end
blanchet@35718
  1741
fun optimized_quot_type_axioms ctxt stds abs_z =
blanchet@35718
  1742
  let
blanchet@35718
  1743
    val thy = ProofContext.theory_of ctxt
blanchet@35718
  1744
    val abs_T = Type abs_z
blanchet@35718
  1745
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@35718
  1746
    val equiv_rel = equiv_relation_for_quot_type thy abs_T
blanchet@35718
  1747
    val a_var = Var (("a", 0), abs_T)
blanchet@35718
  1748
    val x_var = Var (("x", 0), rep_T)
blanchet@35718
  1749
    val y_var = Var (("y", 0), rep_T)
blanchet@35718
  1750
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@37256
  1751
    val sel_a_t = select_nth_constr_arg ctxt stds x a_var 0 rep_T
blanchet@35718
  1752
    val normal_t = Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T)
blanchet@35718
  1753
    val normal_x = normal_t $ x_var
blanchet@35718
  1754
    val normal_y = normal_t $ y_var
blanchet@35718
  1755
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@35718
  1756
  in
blanchet@35718
  1757
    [Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
blanchet@35718
  1758
     Logic.list_implies
blanchet@35718
  1759
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@35718
  1760
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@35718
  1761
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@35718
  1762
           Logic.mk_equals (normal_x, normal_y)),
blanchet@35718
  1763
     Logic.list_implies
blanchet@35718
  1764
         ([HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)),
blanchet@35718
  1765
           HOLogic.mk_Trueprop (@{const Not} $ HOLogic.mk_eq (normal_x, x_var))],
blanchet@35718
  1766
          HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@35718
  1767
  end
blanchet@35718
  1768
blanchet@37256
  1769
fun codatatype_bisim_axioms (hol_ctxt as {ctxt, thy, stds, ...}) T =
blanchet@33192
  1770
  let
blanchet@35070
  1771
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1772
    val set_T = T --> bool_T
blanchet@33192
  1773
    val iter_T = @{typ bisim_iterator}
blanchet@34124
  1774
    val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1775
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1776
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1777
    val n_var_minus_1 =
blanchet@35671
  1778
      Const (@{const_name safe_The}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1779
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1780
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1781
    val x_var = Var (("x", 0), T)
blanchet@33192
  1782
    val y_var = Var (("y", 0), T)
blanchet@33192
  1783
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1784
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1785
       else HOLogic.eq_const nth_T)
blanchet@37256
  1786
      $ select_nth_constr_arg ctxt stds x x_var n nth_T
blanchet@37256
  1787
      $ select_nth_constr_arg ctxt stds x y_var n nth_T
blanchet@33192
  1788
    fun case_func (x as (_, T)) =
blanchet@33192
  1789
      let
blanchet@33192
  1790
        val arg_Ts = binder_types T
blanchet@33192
  1791
        val core_t =
blanchet@35070
  1792
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1793
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1794
          |> foldr1 s_conj
blanchet@33192
  1795
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1796
  in
blanchet@33192
  1797
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1798
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@35070
  1799
        $ (betapplys (optimized_case_def hol_ctxt T bool_T,
blanchet@33192
  1800
                      map case_func xs @ [x_var]))),
blanchet@33192
  1801
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@34124
  1802
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  1803
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  1804
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1805
  end
blanchet@33192
  1806
blanchet@33192
  1807
exception NO_TRIPLE of unit
blanchet@33192
  1808
blanchet@33192
  1809
fun triple_for_intro_rule thy x t =
blanchet@33192
  1810
  let
wenzelm@35625
  1811
    val prems = Logic.strip_imp_prems t |> map (Object_Logic.atomize_term thy)
wenzelm@35625
  1812
    val concl = Logic.strip_imp_concl t |> Object_Logic.atomize_term thy
blanchet@34121
  1813
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@36385
  1814
    val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  1815
  in
blanchet@33192
  1816
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1817
  end
blanchet@33192
  1818
blanchet@33192
  1819
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1820
blanchet@33192
  1821
fun wf_constraint_for rel side concl main =
blanchet@33192
  1822
  let
blanchet@33192
  1823
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1824
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1825
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1826
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1827
  in
blanchet@33192
  1828
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1829
                      HOLogic.all_const T
blanchet@33192
  1830
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1831
                  (t, vars)
blanchet@33192
  1832
  end
blanchet@33192
  1833
blanchet@33192
  1834
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1835
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1836
blanchet@33192
  1837
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1838
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1839
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1840
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1841
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1842
blanchet@35181
  1843
val max_cached_wfs = 50
blanchet@35181
  1844
val cached_timeout =
blanchet@35181
  1845
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  1846
val cached_wf_props =
blanchet@35181
  1847
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  1848
krauss@33351
  1849
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1850
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1851
blanchet@33580
  1852
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  1853
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  1854
         : hol_context) (x as (_, T)) =
blanchet@35220
  1855
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  1856
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  1857
                      [Const x])
blanchet@33192
  1858
  | intro_ts =>
blanchet@33192
  1859
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1860
          |> filter_out (null o #2) of
blanchet@33192
  1861
       [] => true
blanchet@33192
  1862
     | triples =>
blanchet@33192
  1863
       let
blanchet@33192
  1864
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1865
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  1866
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  1867
         val rel = (("R", j), rel_T)
blanchet@33192
  1868
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1869
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1870
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1871
         val _ = if debug then
blanchet@33192
  1872
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1873
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1874
                 else
blanchet@33192
  1875
                   ()
blanchet@33192
  1876
       in
blanchet@35181
  1877
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  1878
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  1879
           ()
blanchet@33557
  1880
         else
blanchet@35181
  1881
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  1882
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  1883
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  1884
           SOME wf => wf
blanchet@33192
  1885
         | NONE =>
blanchet@33192
  1886
           let
blanchet@33192
  1887
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  1888
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  1889
                             termination_tacs
blanchet@35181
  1890
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1891
       end)
blanchet@35309
  1892
    handle List.Empty => false | NO_TRIPLE () => false
blanchet@33192
  1893
blanchet@35070
  1894
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  1895
blanchet@33192
  1896
fun is_well_founded_inductive_pred
blanchet@35070
  1897
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  1898
        (x as (s, _)) =
blanchet@33192
  1899
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1900
    SOME (SOME b) => b
blanchet@34936
  1901
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  1902
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  1903
           SOME (_, wf) => wf
blanchet@35181
  1904
         | NONE =>
blanchet@35181
  1905
           let
blanchet@35181
  1906
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  1907
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  1908
           in
blanchet@35181
  1909
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  1910
           end
blanchet@33192
  1911
blanchet@35280
  1912
fun ap_curry [_] _ t = t
blanchet@35280
  1913
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  1914
    let val n = length arg_Ts in
blanchet@33192
  1915
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1916
                incr_boundvars n t
blanchet@33192
  1917
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1918
    end
blanchet@33192
  1919
blanchet@33192
  1920
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1921
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  1922
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  1923
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1924
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1925
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1926
blanchet@33192
  1927
val is_linear_inductive_pred_def =
blanchet@33192
  1928
  let
blanchet@33192
  1929
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  1930
        do_disjunct (j + 1) t2
blanchet@33192
  1931
      | do_disjunct j t =
blanchet@33192
  1932
        case num_occs_of_bound_in_term j t of
blanchet@33192
  1933
          0 => true
blanchet@35070
  1934
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  1935
        | _ => false
blanchet@33192
  1936
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1937
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  1938
          case length xs of
blanchet@33192
  1939
            1 => false
blanchet@35070
  1940
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  1941
        end
blanchet@33192
  1942
      | do_lfp_def _ = false
blanchet@33192
  1943
  in do_lfp_def o strip_abs_body end
blanchet@33192
  1944
blanchet@33851
  1945
fun n_ptuple_paths 0 = []
blanchet@33851
  1946
  | n_ptuple_paths 1 = []
blanchet@33851
  1947
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  1948
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  1949
blanchet@33192
  1950
val linear_pred_base_and_step_rhss =
blanchet@33192
  1951
  let
blanchet@33192
  1952
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1953
        let
blanchet@33192
  1954
          val (xs, body) = strip_abs t2
blanchet@33192
  1955
          val arg_Ts = map snd (tl xs)
blanchet@33192
  1956
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  1957
          val j = length arg_Ts
blanchet@33192
  1958
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  1959
              Const (@{const_name Ex}, T1)
blanchet@33192
  1960
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  1961
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  1962
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  1963
            | repair_rec j t =
blanchet@33192
  1964
              let val (head, args) = strip_comb t in
blanchet@33192
  1965
                if head = Bound j then
blanchet@33192
  1966
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  1967
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  1968
                else
blanchet@33192
  1969
                  t
blanchet@33192
  1970
              end
blanchet@33192
  1971
          val (nonrecs, recs) =
blanchet@34121
  1972
            List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
blanchet@35070
  1973
                           (disjuncts_of body)
blanchet@33192
  1974
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  1975
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  1976
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  1977
        in
blanchet@33192
  1978
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  1979
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  1980
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  1981
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  1982
        end
blanchet@33192
  1983
      | aux t =
blanchet@33232
  1984
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  1985
  in aux end
blanchet@33192
  1986
blanchet@35280
  1987
fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (s, T) def =
blanchet@33192
  1988
  let
blanchet@33192
  1989
    val j = maxidx_of_term def + 1
blanchet@33192
  1990
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1991
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1992
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  1993
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  1994
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  1995
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  1996
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  1997
    val set_T = tuple_T --> bool_T
blanchet@33192
  1998
    val curried_T = tuple_T --> set_T
blanchet@35665
  1999
    val uncurried_T = Type (@{type_name "*"}, [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  2000
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  2001
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  2002
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  2003
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2004
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  2005
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  2006
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  2007
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2008
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  2009
  in
blanchet@33192
  2010
    list_abs (outer,
blanchet@33192
  2011
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  2012
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  2013
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  2014
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  2015
              $ list_comb (Const base_x, outer_bounds)
blanchet@35280
  2016
              |> ap_curry tuple_arg_Ts tuple_T)
blanchet@35070
  2017
    |> unfold_defs_in_term hol_ctxt
blanchet@33192
  2018
  end
blanchet@33192
  2019
blanchet@35070
  2020
fun unrolled_inductive_pred_const (hol_ctxt as {thy, star_linear_preds,
blanchet@33192
  2021
                                                def_table, simp_table, ...})
blanchet@33192
  2022
                                  gfp (x as (s, T)) =
blanchet@33192
  2023
  let
blanchet@33192
  2024
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  2025
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  2026
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  2027
    val def = the (def_of_const thy def_table x)
blanchet@33192
  2028
  in
blanchet@35070
  2029
    if is_equational_fun hol_ctxt x' then
blanchet@33192
  2030
      unrolled_const (* already done *)
blanchet@34936
  2031
    else if not gfp andalso is_linear_inductive_pred_def def andalso
blanchet@34936
  2032
         star_linear_preds then
blanchet@35070
  2033
      starred_linear_pred_const hol_ctxt x def
blanchet@33192
  2034
    else
blanchet@33192
  2035
      let
blanchet@33192
  2036
        val j = maxidx_of_term def + 1
blanchet@33192
  2037
        val (outer, fp_app) = strip_abs def
blanchet@33192
  2038
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2039
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  2040
        val next = suc_const iter_T $ cur
blanchet@33192
  2041
        val rhs = case fp_app of
blanchet@33192
  2042
                    Const _ $ t =>
blanchet@33192
  2043
                    betapply (t, list_comb (Const x', next :: outer_bounds))
blanchet@33232
  2044
                  | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_\
blanchet@33232
  2045
                                     \const", [fp_app])
blanchet@33192
  2046
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  2047
        val all = outer @ inner
blanchet@33192
  2048
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  2049
        val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  2050
        val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
blanchet@33192
  2051
                 |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  2052
        val _ = add_simps simp_table s' [eq]
blanchet@33192
  2053
      in unrolled_const end
blanchet@33192
  2054
  end
blanchet@33192
  2055
blanchet@35070
  2056
fun raw_inductive_pred_axiom ({thy, def_table, ...} : hol_context) x =
blanchet@33192
  2057
  let
blanchet@33192
  2058
    val def = the (def_of_const thy def_table x)
blanchet@33192
  2059
    val (outer, fp_app) = strip_abs def
blanchet@33192
  2060
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2061
    val rhs = case fp_app of
blanchet@33192
  2062
                Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
blanchet@33232
  2063
              | _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom",
blanchet@33192
  2064
                                 [fp_app])
blanchet@33192
  2065
    val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  2066
    val all = outer @ inner
blanchet@33192
  2067
    val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  2068
    val j = maxidx_of_term def + 1
blanchet@33192
  2069
    val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  2070
  in
blanchet@33192
  2071
    HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
blanchet@33192
  2072
    |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  2073
  end
blanchet@35070
  2074
fun inductive_pred_axiom hol_ctxt (x as (s, T)) =
blanchet@33192
  2075
  if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
blanchet@35718
  2076
    let val x' = (strip_first_name_sep s |> snd, T) in
blanchet@35070
  2077
      raw_inductive_pred_axiom hol_ctxt x' |> subst_atomic [(Const x', Const x)]
blanchet@33192
  2078
    end
blanchet@33192
  2079
  else
blanchet@35070
  2080
    raw_inductive_pred_axiom hol_ctxt x
blanchet@33192
  2081
blanchet@35220
  2082
fun raw_equational_fun_axioms (hol_ctxt as {thy, stds, fast_descrs, simp_table,
blanchet@35280
  2083
                                            psimp_table, ...}) x =
blanchet@35220
  2084
  case def_props_for_const thy stds fast_descrs (!simp_table) x of
blanchet@35220
  2085
    [] => (case def_props_for_const thy stds fast_descrs psimp_table x of
blanchet@35070
  2086
             [] => [inductive_pred_axiom hol_ctxt x]
blanchet@33192
  2087
           | psimps => psimps)
blanchet@33192
  2088
  | simps => simps
blanchet@33192
  2089
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
blanchet@35070
  2090
fun is_equational_fun_surely_complete hol_ctxt x =
blanchet@35070
  2091
  case raw_equational_fun_axioms hol_ctxt x of
blanchet@35070
  2092
    [@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)] =>
blanchet@35070
  2093
    strip_comb t1 |> snd |> forall is_Var
blanchet@35070
  2094
  | _ => false
blanchet@33192
  2095
blanchet@35718
  2096
(** Type preprocessing **)
blanchet@35718
  2097
blanchet@33556
  2098
fun merge_type_vars_in_terms ts =
blanchet@33192
  2099
  let
blanchet@33192
  2100
    fun add_type (TFree (s, S)) table =
blanchet@33192
  2101
        (case AList.lookup (op =) table S of
blanchet@33192
  2102
           SOME s' =>
blanchet@33192
  2103
           if string_ord (s', s) = LESS then AList.update (op =) (S, s') table
blanchet@33192
  2104
           else table
blanchet@33192
  2105
         | NONE => (S, s) :: table)
blanchet@33192
  2106
      | add_type _ table = table
blanchet@33192
  2107
    val table = fold (fold_types (fold_atyps add_type)) ts []
blanchet@35280
  2108
    fun coalesce (TFree (_, S)) = TFree (AList.lookup (op =) table S |> the, S)
blanchet@33192
  2109
      | coalesce T = T
blanchet@33192
  2110
  in map (map_types (map_atyps coalesce)) ts end
blanchet@33192
  2111
blanchet@35190
  2112
fun add_ground_types hol_ctxt binarize =
blanchet@35190
  2113
  let
blanchet@35190
  2114
    fun aux T accum =
blanchet@35190
  2115
      case T of
blanchet@35665
  2116
        Type (@{type_name fun}, Ts) => fold aux Ts accum
blanchet@35665
  2117
      | Type (@{type_name "*"}, Ts) => fold aux Ts accum
blanchet@35190
  2118
      | Type (@{type_name itself}, [T1]) => aux T1 accum
blanchet@35190
  2119
      | Type (_, Ts) =>
blanchet@35190
  2120
        if member (op =) (@{typ prop} :: @{typ bool} :: @{typ unit} :: accum)
blanchet@35190
  2121
                  T then
blanchet@35190
  2122
          accum
blanchet@35190
  2123
        else
blanchet@35190
  2124
          T :: accum
blanchet@35190
  2125
          |> fold aux (case binarized_and_boxed_datatype_constrs hol_ctxt
blanchet@35190
  2126
                                                                 binarize T of
blanchet@35190
  2127
                         [] => Ts
blanchet@35190
  2128
                       | xs => map snd xs)
blanchet@35190
  2129
      | _ => insert (op =) T accum
blanchet@35190
  2130
  in aux end
blanchet@33192
  2131
blanchet@35190
  2132
fun ground_types_in_type hol_ctxt binarize T =
blanchet@35190
  2133
  add_ground_types hol_ctxt binarize T []
blanchet@35190
  2134
fun ground_types_in_terms hol_ctxt binarize ts =
blanchet@35190
  2135
  fold (fold_types (add_ground_types hol_ctxt binarize)) ts []
blanchet@33192
  2136
blanchet@33192
  2137
end;