src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Mon Mar 29 15:50:18 2010 +0200 (2010-03-29)
changeset 36062 194cb6e3c13f
parent 35994 9cc3df9a606e
child 36126 00d550b6cfd4
permissions -rw-r--r--
get rid of Polyhash, since it's no longer used
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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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    skolemize: bool,
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    star_linear_preds: bool,
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    uncurry: 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 : theory -> typ -> bool
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  val is_univ_typedef : theory -> typ -> bool
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  val is_datatype : theory -> (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 : theory -> styp -> bool
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  val is_rep_fun : theory -> 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 : theory -> styp -> styp
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  val is_constr_like : theory -> styp -> bool
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  val is_stale_constr : theory -> styp -> bool
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  val is_constr : theory -> (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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    theory -> (typ option * bool) list -> styp -> term -> int -> typ -> term
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  val construct_value :
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    theory -> (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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    theory -> (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 : theory -> styp -> term list
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  val optimized_typedef_axioms : theory -> 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 : theory -> term -> bool
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  val is_constr_pattern_formula : theory -> 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 Sledgehammer_Util
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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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  skolemize: bool,
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  star_linear_preds: bool,
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  uncurry: 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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(* int -> string *)
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fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
blanchet@35311
   299
(* Proof.context -> typ -> string *)
blanchet@35311
   300
fun quot_normal_name_for_type ctxt T =
blanchet@35311
   301
  quot_normal_prefix ^ unyxml (Syntax.string_of_typ ctxt T)
blanchet@33192
   302
blanchet@33192
   303
(* string -> string * string *)
blanchet@33192
   304
val strip_first_name_sep =
blanchet@33192
   305
  Substring.full #> Substring.position name_sep ##> Substring.triml 1
blanchet@33192
   306
  #> pairself Substring.string
blanchet@33192
   307
(* string -> string *)
blanchet@33192
   308
fun original_name s =
blanchet@33192
   309
  if String.isPrefix nitpick_prefix s then
blanchet@33192
   310
    case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
blanchet@33192
   311
  else
blanchet@33192
   312
    s
blanchet@35718
   313
blanchet@35718
   314
(* term * term -> term *)
blanchet@35718
   315
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
blanchet@35718
   316
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
blanchet@35718
   317
  | s_betapply p = betapply p
blanchet@35718
   318
(* term * term list -> term *)
blanchet@35718
   319
val s_betapplys = Library.foldl s_betapply
blanchet@33192
   320
blanchet@34998
   321
(* term * term -> term *)
blanchet@34998
   322
fun s_conj (t1, @{const True}) = t1
blanchet@34998
   323
  | s_conj (@{const True}, t2) = t2
blanchet@34998
   324
  | s_conj (t1, t2) =
blanchet@34998
   325
    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
blanchet@34998
   326
    else HOLogic.mk_conj (t1, t2)
blanchet@34998
   327
fun s_disj (t1, @{const False}) = t1
blanchet@34998
   328
  | s_disj (@{const False}, t2) = t2
blanchet@34998
   329
  | s_disj (t1, t2) =
blanchet@34998
   330
    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
blanchet@34998
   331
    else HOLogic.mk_disj (t1, t2)
blanchet@34998
   332
blanchet@34998
   333
(* term -> term -> term list *)
blanchet@34998
   334
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
blanchet@34998
   335
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
blanchet@34998
   336
  | strip_connective _ t = [t]
blanchet@34998
   337
(* term -> term list * term *)
blanchet@35280
   338
fun strip_any_connective (t as (t0 $ _ $ _)) =
blanchet@34998
   339
    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
blanchet@34998
   340
      (strip_connective t0 t, t0)
blanchet@34998
   341
    else
blanchet@34998
   342
      ([t], @{const Not})
blanchet@34998
   343
  | strip_any_connective t = ([t], @{const Not})
blanchet@34998
   344
(* term -> term list *)
blanchet@35070
   345
val conjuncts_of = strip_connective @{const "op &"}
blanchet@35070
   346
val disjuncts_of = strip_connective @{const "op |"}
blanchet@34998
   347
blanchet@33192
   348
(* When you add constants to these lists, make sure to handle them in
blanchet@33232
   349
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
blanchet@33192
   350
   well. *)
blanchet@33192
   351
val built_in_consts =
blanchet@33192
   352
  [(@{const_name all}, 1),
blanchet@33192
   353
   (@{const_name "=="}, 2),
blanchet@33192
   354
   (@{const_name "==>"}, 2),
blanchet@33192
   355
   (@{const_name Pure.conjunction}, 2),
blanchet@33192
   356
   (@{const_name Trueprop}, 1),
blanchet@33192
   357
   (@{const_name Not}, 1),
blanchet@33192
   358
   (@{const_name False}, 0),
blanchet@33192
   359
   (@{const_name True}, 0),
blanchet@33192
   360
   (@{const_name All}, 1),
blanchet@33192
   361
   (@{const_name Ex}, 1),
blanchet@33192
   362
   (@{const_name "op ="}, 2),
blanchet@33192
   363
   (@{const_name "op &"}, 2),
blanchet@33192
   364
   (@{const_name "op |"}, 2),
blanchet@33192
   365
   (@{const_name "op -->"}, 2),
blanchet@33192
   366
   (@{const_name If}, 3),
blanchet@33192
   367
   (@{const_name Let}, 2),
blanchet@33192
   368
   (@{const_name Unity}, 0),
blanchet@33192
   369
   (@{const_name Pair}, 2),
blanchet@33192
   370
   (@{const_name fst}, 1),
blanchet@33192
   371
   (@{const_name snd}, 1),
blanchet@33192
   372
   (@{const_name Id}, 0),
blanchet@33192
   373
   (@{const_name insert}, 2),
blanchet@33192
   374
   (@{const_name converse}, 1),
blanchet@33192
   375
   (@{const_name trancl}, 1),
blanchet@33192
   376
   (@{const_name rel_comp}, 2),
blanchet@33192
   377
   (@{const_name image}, 2),
blanchet@33192
   378
   (@{const_name finite}, 1),
blanchet@34936
   379
   (@{const_name unknown}, 0),
blanchet@34936
   380
   (@{const_name is_unknown}, 1),
blanchet@35671
   381
   (@{const_name safe_The}, 1),
blanchet@35671
   382
   (@{const_name safe_Eps}, 1),
blanchet@33192
   383
   (@{const_name Frac}, 0),
blanchet@33192
   384
   (@{const_name norm_frac}, 0)]
blanchet@35220
   385
val built_in_nat_consts =
blanchet@35220
   386
  [(@{const_name Suc}, 0),
blanchet@35220
   387
   (@{const_name nat}, 0),
blanchet@35220
   388
   (@{const_name nat_gcd}, 0),
blanchet@35220
   389
   (@{const_name nat_lcm}, 0)]
blanchet@33192
   390
val built_in_descr_consts =
blanchet@33192
   391
  [(@{const_name The}, 1),
blanchet@33192
   392
   (@{const_name Eps}, 1)]
blanchet@33192
   393
val built_in_typed_consts =
blanchet@35220
   394
  [((@{const_name zero_class.zero}, int_T), 0),
blanchet@35220
   395
   ((@{const_name one_class.one}, int_T), 0),
blanchet@35220
   396
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   397
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   398
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
blanchet@35220
   399
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
blanchet@35220
   400
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
blanchet@35220
   401
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
blanchet@35220
   402
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
blanchet@35220
   403
val built_in_typed_nat_consts =
blanchet@35220
   404
  [((@{const_name zero_class.zero}, nat_T), 0),
blanchet@35220
   405
   ((@{const_name one_class.one}, nat_T), 0),
blanchet@35220
   406
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   407
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   408
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   409
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   410
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   411
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   412
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   413
val built_in_set_consts =
blanchet@35220
   414
  [(@{const_name semilattice_inf_class.inf}, 2),
blanchet@35220
   415
   (@{const_name semilattice_sup_class.sup}, 2),
blanchet@35220
   416
   (@{const_name minus_class.minus}, 2),
blanchet@35220
   417
   (@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   418
blanchet@33192
   419
(* typ -> typ *)
blanchet@35190
   420
fun unarize_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   421
  | unarize_type @{typ "signed_bit word"} = int_T
blanchet@35190
   422
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
blanchet@35190
   423
  | unarize_type T = T
blanchet@35665
   424
fun unarize_unbox_etc_type (Type (@{type_name fin_fun}, Ts)) =
blanchet@35665
   425
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   426
  | unarize_unbox_etc_type (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   427
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   428
  | unarize_unbox_etc_type (Type (@{type_name pair_box}, Ts)) =
blanchet@35665
   429
    Type (@{type_name "*"}, map unarize_unbox_etc_type Ts)
blanchet@35665
   430
  | unarize_unbox_etc_type @{typ "unsigned_bit word"} = nat_T
blanchet@35665
   431
  | unarize_unbox_etc_type @{typ "signed_bit word"} = int_T
blanchet@35665
   432
  | unarize_unbox_etc_type (Type (s, Ts as _ :: _)) =
blanchet@35665
   433
    Type (s, map unarize_unbox_etc_type Ts)
blanchet@35665
   434
  | unarize_unbox_etc_type T = T
blanchet@35280
   435
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   436
  | uniterize_type @{typ bisim_iterator} = nat_T
blanchet@35280
   437
  | uniterize_type T = T
blanchet@35665
   438
val uniterize_unarize_unbox_etc_type = uniterize_type o unarize_unbox_etc_type
blanchet@35280
   439
blanchet@33192
   440
(* Proof.context -> typ -> string *)
blanchet@35665
   441
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_unbox_etc_type
blanchet@33192
   442
blanchet@33192
   443
(* string -> string -> string *)
blanchet@33192
   444
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@33192
   445
(* string -> string *)
blanchet@34121
   446
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   447
(* string -> term -> term *)
blanchet@33192
   448
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@33192
   449
(* string -> string *)
blanchet@34121
   450
fun short_name s =
blanchet@33192
   451
  case space_explode name_sep s of
blanchet@33192
   452
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   453
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   454
(* typ -> typ *)
blanchet@34121
   455
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   456
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   457
  | shorten_names_in_type T = T
blanchet@33192
   458
(* term -> term *)
blanchet@34121
   459
val shorten_names_in_term =
blanchet@34121
   460
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   461
  #> map_types shorten_names_in_type
blanchet@33192
   462
blanchet@33192
   463
(* theory -> typ * typ -> bool *)
blanchet@35665
   464
fun strict_type_match thy (T1, T2) =
blanchet@33192
   465
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   466
  handle Type.TYPE_MATCH => false
blanchet@35665
   467
fun type_match thy = strict_type_match thy o pairself unarize_unbox_etc_type
blanchet@33192
   468
(* theory -> styp * styp -> bool *)
blanchet@33192
   469
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   470
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   471
(* theory -> term * term -> bool *)
blanchet@33192
   472
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   473
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   474
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   475
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   476
blanchet@35711
   477
(* typ -> term -> term -> term *)
blanchet@35711
   478
fun frac_from_term_pair T t1 t2 =
blanchet@35711
   479
  case snd (HOLogic.dest_number t1) of
blanchet@35711
   480
    0 => HOLogic.mk_number T 0
blanchet@35711
   481
  | n1 => case snd (HOLogic.dest_number t2) of
blanchet@35711
   482
            1 => HOLogic.mk_number T n1
blanchet@35711
   483
          | n2 => Const (@{const_name divide}, T --> T --> T)
blanchet@35711
   484
                  $ HOLogic.mk_number T n1 $ HOLogic.mk_number T n2
blanchet@35711
   485
blanchet@33192
   486
(* typ -> bool *)
blanchet@33192
   487
fun is_TFree (TFree _) = true
blanchet@33192
   488
  | is_TFree _ = false
blanchet@35665
   489
fun is_higher_order_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   490
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   491
  | is_higher_order_type _ = false
blanchet@35665
   492
fun is_fun_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   493
  | is_fun_type _ = false
blanchet@35665
   494
fun is_set_type (Type (@{type_name fun}, [_, @{typ bool}])) = true
blanchet@33192
   495
  | is_set_type _ = false
blanchet@35665
   496
fun is_pair_type (Type (@{type_name "*"}, _)) = true
blanchet@33192
   497
  | is_pair_type _ = false
blanchet@33192
   498
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   499
  | is_lfp_iterator_type _ = false
blanchet@33192
   500
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   501
  | is_gfp_iterator_type _ = false
blanchet@33192
   502
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   503
fun is_iterator_type T =
blanchet@35280
   504
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   505
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   506
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   507
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   508
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   509
  | is_word_type _ = false
blanchet@35280
   510
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   511
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   512
(* theory -> typ -> bool *)
blanchet@33192
   513
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   514
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   515
  | is_frac_type _ _ = false
blanchet@35220
   516
fun is_number_type thy = is_integer_like_type orf is_frac_type thy
blanchet@33192
   517
blanchet@33192
   518
(* bool -> styp -> typ *)
blanchet@33192
   519
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   520
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   521
        binder_types T)
blanchet@33192
   522
(* typ -> styp *)
blanchet@35718
   523
fun const_for_iterator_type (Type (s, Ts)) =
blanchet@35718
   524
    (strip_first_name_sep s |> snd, Ts ---> bool_T)
blanchet@33192
   525
  | const_for_iterator_type T =
blanchet@33232
   526
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   527
blanchet@35070
   528
(* int -> typ -> typ list * typ *)
blanchet@33192
   529
fun strip_n_binders 0 T = ([], T)
blanchet@35665
   530
  | strip_n_binders n (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
   531
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   532
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   533
    strip_n_binders n (Type (@{type_name fun}, Ts))
blanchet@33232
   534
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   535
(* typ -> typ *)
blanchet@33192
   536
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   537
blanchet@33192
   538
(* typ -> int *)
blanchet@35665
   539
fun num_factors_in_type (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
   540
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   541
  | num_factors_in_type _ = 1
blanchet@35665
   542
fun num_binder_types (Type (@{type_name fun}, [_, T2])) =
blanchet@35665
   543
    1 + num_binder_types T2
blanchet@33192
   544
  | num_binder_types _ = 0
blanchet@33192
   545
(* typ -> typ list *)
blanchet@33192
   546
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   547
fun maybe_curried_binder_types T =
blanchet@33192
   548
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   549
blanchet@33192
   550
(* typ -> term list -> term *)
blanchet@33192
   551
fun mk_flat_tuple _ [t] = t
blanchet@35665
   552
  | mk_flat_tuple (Type (@{type_name "*"}, [T1, T2])) (t :: ts) =
blanchet@33192
   553
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   554
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   555
(* int -> term -> term list *)
blanchet@33192
   556
fun dest_n_tuple 1 t = [t]
blanchet@33192
   557
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   558
blanchet@35220
   559
type typedef_info =
blanchet@35220
   560
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   561
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   562
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   563
blanchet@35220
   564
(* theory -> string -> typedef_info *)
blanchet@35220
   565
fun typedef_info thy s =
blanchet@35220
   566
  if is_frac_type thy (Type (s, [])) then
blanchet@35220
   567
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@35220
   568
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@35220
   569
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
wenzelm@35845
   570
                          |> Logic.varify_global,
blanchet@35220
   571
          set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
wenzelm@35743
   572
  else case Typedef.get_info_global thy s of
wenzelm@35743
   573
    (* FIXME handle multiple typedef interpretations (!??) *)
wenzelm@35994
   574
    [({abs_type, rep_type, Abs_name, Rep_name, ...}, {set_def, Rep, Abs_inverse,
wenzelm@35994
   575
          Rep_inverse, ...})] =>
blanchet@35220
   576
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@35220
   577
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@35220
   578
          set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@35220
   579
          Rep_inverse = SOME Rep_inverse}
wenzelm@35743
   580
  | _ => NONE
blanchet@35220
   581
blanchet@35220
   582
(* theory -> string -> bool *)
blanchet@35220
   583
val is_typedef = is_some oo typedef_info
blanchet@35220
   584
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   585
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   586
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   587
blanchet@34121
   588
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   589
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   590
(* theory -> (typ option * bool) list -> string -> bool *)
blanchet@35220
   591
fun is_basic_datatype thy stds s =
blanchet@35220
   592
  member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@35220
   593
                 @{type_name int}, "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   594
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   595
blanchet@33192
   596
(* theory -> typ -> typ -> typ -> typ *)
blanchet@33192
   597
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   598
  Same.commit (Envir.subst_type_same
blanchet@35311
   599
                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
blanchet@33192
   600
  handle Type.TYPE_MATCH =>
blanchet@33232
   601
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@35311
   602
fun varify_and_instantiate_type thy T1 T1' T2 =
wenzelm@35845
   603
  instantiate_type thy (Logic.varifyT_global T1) T1' (Logic.varifyT_global T2)
blanchet@33192
   604
blanchet@33192
   605
(* theory -> typ -> typ -> styp *)
blanchet@33192
   606
fun repair_constr_type thy body_T' T =
blanchet@35311
   607
  varify_and_instantiate_type thy (body_type T) body_T' T
blanchet@33192
   608
blanchet@33192
   609
(* string -> (string * string) list -> theory -> theory *)
blanchet@33192
   610
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   611
  let
blanchet@33583
   612
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   613
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   614
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   615
(* string -> theory -> theory *)
blanchet@33192
   616
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   617
blanchet@33192
   618
(* typ -> string -> styp list -> theory -> theory *)
blanchet@33192
   619
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   620
  let
blanchet@33583
   621
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   622
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   623
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   624
    val _ =
blanchet@34936
   625
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35665
   626
         co_s <> @{type_name fun} andalso
blanchet@35220
   627
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   628
        ()
blanchet@34121
   629
      else
blanchet@34121
   630
        raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   631
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   632
                                   codatatypes
blanchet@33583
   633
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   634
(* typ -> theory -> theory *)
blanchet@33192
   635
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   636
blanchet@33192
   637
(* theory -> typ -> bool *)
blanchet@35284
   638
fun is_quot_type thy (Type (s, _)) =
blanchet@35284
   639
    is_some (Quotient_Info.quotdata_lookup_raw thy s)
blanchet@34936
   640
  | is_quot_type _ _ = false
blanchet@35280
   641
fun is_codatatype thy (Type (s, _)) =
blanchet@33583
   642
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   643
               |> Option.map snd |> these))
blanchet@33192
   644
  | is_codatatype _ _ = false
blanchet@33192
   645
fun is_pure_typedef thy (T as Type (s, _)) =
blanchet@33192
   646
    is_typedef thy s andalso
blanchet@34936
   647
    not (is_real_datatype thy s orelse is_quot_type thy T orelse
blanchet@35220
   648
         is_codatatype thy T orelse is_record_type T orelse
blanchet@35220
   649
         is_integer_like_type T)
blanchet@33192
   650
  | is_pure_typedef _ _ = false
blanchet@33192
   651
fun is_univ_typedef thy (Type (s, _)) =
blanchet@33192
   652
    (case typedef_info thy s of
blanchet@33192
   653
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@35332
   654
       let
blanchet@35332
   655
         val t_opt =
blanchet@35332
   656
           case set_def of
blanchet@35332
   657
             SOME thm => try (snd o Logic.dest_equals o prop_of) thm
blanchet@35332
   658
           | NONE => try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop)
blanchet@35332
   659
                         prop_of_Rep
blanchet@35332
   660
       in
blanchet@35332
   661
         case t_opt of
blanchet@35332
   662
           SOME (Const (@{const_name top}, _)) => true
blanchet@35386
   663
           (* "Multiset.multiset" *)
blanchet@35332
   664
         | SOME (Const (@{const_name Collect}, _)
blanchet@35332
   665
                 $ Abs (_, _, Const (@{const_name finite}, _) $ _)) => true
blanchet@35386
   666
           (* "FinFun.finfun" *)
blanchet@35386
   667
         | SOME (Const (@{const_name Collect}, _) $ Abs (_, _,
blanchet@35386
   668
                     Const (@{const_name Ex}, _) $ Abs (_, _,
blanchet@35386
   669
                         Const (@{const_name finite}, _) $ _))) => true
blanchet@35332
   670
         | _ => false
blanchet@35332
   671
       end
blanchet@33192
   672
     | NONE => false)
blanchet@33192
   673
  | is_univ_typedef _ _ = false
blanchet@35220
   674
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   675
fun is_datatype thy stds (T as Type (s, _)) =
blanchet@34936
   676
    (is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind} orelse
blanchet@35220
   677
     is_quot_type thy T) andalso not (is_basic_datatype thy stds s)
blanchet@35220
   678
  | is_datatype _ _ _ = false
blanchet@33192
   679
blanchet@33192
   680
(* theory -> typ -> (string * typ) list * (string * typ) *)
blanchet@33192
   681
fun all_record_fields thy T =
blanchet@33192
   682
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   683
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   684
  end
blanchet@33192
   685
  handle TYPE _ => []
blanchet@33192
   686
(* styp -> bool *)
blanchet@35280
   687
fun is_record_constr (s, T) =
blanchet@33192
   688
  String.isSuffix Record.extN s andalso
blanchet@33192
   689
  let val dataT = body_type T in
blanchet@33192
   690
    is_record_type dataT andalso
blanchet@33192
   691
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   692
  end
blanchet@33192
   693
(* theory -> typ -> int *)
blanchet@33192
   694
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   695
(* theory -> string -> typ -> int *)
blanchet@33192
   696
fun no_of_record_field thy s T1 =
blanchet@34121
   697
  find_index (curry (op =) s o fst)
blanchet@34121
   698
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@33192
   699
(* theory -> styp -> bool *)
blanchet@35665
   700
fun is_record_get thy (s, Type (@{type_name fun}, [T1, _])) =
blanchet@34121
   701
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   702
  | is_record_get _ _ = false
blanchet@33192
   703
fun is_record_update thy (s, T) =
blanchet@33192
   704
  String.isSuffix Record.updateN s andalso
blanchet@34121
   705
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   706
         (all_record_fields thy (body_type T))
blanchet@33192
   707
  handle TYPE _ => false
blanchet@35665
   708
fun is_abs_fun thy (s, Type (@{type_name fun}, [_, Type (s', _)])) =
blanchet@33192
   709
    (case typedef_info thy s' of
blanchet@33192
   710
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   711
     | NONE => false)
blanchet@33192
   712
  | is_abs_fun _ _ = false
blanchet@35665
   713
fun is_rep_fun thy (s, Type (@{type_name fun}, [Type (s', _), _])) =
blanchet@33192
   714
    (case typedef_info thy s' of
blanchet@33192
   715
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   716
     | NONE => false)
blanchet@33192
   717
  | is_rep_fun _ _ = false
blanchet@34936
   718
(* Proof.context -> styp -> bool *)
blanchet@35665
   719
fun is_quot_abs_fun ctxt
blanchet@35665
   720
                    (x as (_, Type (@{type_name fun}, [_, Type (s', _)]))) =
blanchet@35284
   721
    (try (Quotient_Term.absrep_const_chk Quotient_Term.AbsF ctxt) s'
blanchet@35284
   722
     = SOME (Const x))
blanchet@34936
   723
  | is_quot_abs_fun _ _ = false
blanchet@35665
   724
fun is_quot_rep_fun ctxt
blanchet@35665
   725
                    (x as (_, Type (@{type_name fun}, [Type (s', _), _]))) =
blanchet@35284
   726
    (try (Quotient_Term.absrep_const_chk Quotient_Term.RepF ctxt) s'
blanchet@35284
   727
     = SOME (Const x))
blanchet@34936
   728
  | is_quot_rep_fun _ _ = false
blanchet@33192
   729
blanchet@33192
   730
(* theory -> styp -> styp *)
blanchet@35665
   731
fun mate_of_rep_fun thy (x as (_, Type (@{type_name fun},
blanchet@35665
   732
                                        [T1 as Type (s', _), T2]))) =
blanchet@33192
   733
    (case typedef_info thy s' of
blanchet@35665
   734
       SOME {Abs_name, ...} => (Abs_name, Type (@{type_name fun}, [T2, T1]))
blanchet@33232
   735
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   736
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@34936
   737
(* theory -> typ -> typ *)
blanchet@35284
   738
fun rep_type_for_quot_type thy (T as Type (s, _)) =
blanchet@35284
   739
  let val {qtyp, rtyp, ...} = Quotient_Info.quotdata_lookup thy s in
blanchet@35284
   740
    instantiate_type thy qtyp T rtyp
blanchet@35284
   741
  end
blanchet@34936
   742
(* theory -> typ -> term *)
blanchet@35284
   743
fun equiv_relation_for_quot_type thy (Type (s, Ts)) =
blanchet@35284
   744
    let
blanchet@35284
   745
      val {qtyp, equiv_rel, ...} = Quotient_Info.quotdata_lookup thy s
blanchet@35284
   746
      val Ts' = qtyp |> dest_Type |> snd
blanchet@35284
   747
    in subst_atomic_types (Ts' ~~ Ts) equiv_rel end
blanchet@34936
   748
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   749
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   750
blanchet@33192
   751
(* theory -> styp -> bool *)
blanchet@33192
   752
fun is_coconstr thy (s, T) =
blanchet@33192
   753
  let
blanchet@33583
   754
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   755
    val co_T = body_type T
blanchet@33192
   756
    val co_s = dest_Type co_T |> fst
blanchet@33192
   757
  in
blanchet@33192
   758
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   759
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   760
  end
blanchet@33192
   761
  handle TYPE ("dest_Type", _, _) => false
blanchet@33192
   762
fun is_constr_like thy (s, T) =
blanchet@35665
   763
  member (op =) [@{const_name FinFun}, @{const_name FunBox},
blanchet@35665
   764
                 @{const_name PairBox}, @{const_name Quot},
blanchet@35665
   765
                 @{const_name Zero_Rep}, @{const_name Suc_Rep}] s orelse
blanchet@35665
   766
  let val (x as (_, T)) = (s, unarize_unbox_etc_type T) in
blanchet@34936
   767
    Refute.is_IDT_constructor thy x orelse is_record_constr x orelse
blanchet@34936
   768
    (is_abs_fun thy x andalso is_pure_typedef thy (range_type T)) orelse
blanchet@34936
   769
    is_coconstr thy x
blanchet@33192
   770
  end
blanchet@33581
   771
fun is_stale_constr thy (x as (_, T)) =
blanchet@34936
   772
  is_codatatype thy (body_type T) andalso is_constr_like thy x andalso
blanchet@34936
   773
  not (is_coconstr thy x)
blanchet@35220
   774
(* theory -> (typ option * bool) list -> styp -> bool *)
blanchet@35220
   775
fun is_constr thy stds (x as (_, T)) =
blanchet@34936
   776
  is_constr_like thy x andalso
blanchet@35220
   777
  not (is_basic_datatype thy stds
blanchet@35220
   778
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@34936
   779
  not (is_stale_constr thy x)
blanchet@33192
   780
(* string -> bool *)
blanchet@33192
   781
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   782
val is_sel_like_and_no_discr =
blanchet@35665
   783
  String.isPrefix sel_prefix orf
blanchet@35665
   784
  (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   785
blanchet@33192
   786
(* boxability -> boxability *)
blanchet@33192
   787
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   788
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   789
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   790
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   791
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   792
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   793
blanchet@35070
   794
(* hol_context -> boxability -> typ -> bool *)
blanchet@35070
   795
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   796
  case T of
blanchet@35665
   797
    Type (@{type_name fun}, _) =>
blanchet@34936
   798
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   799
    not (is_boolean_type (body_type T))
blanchet@35665
   800
  | Type (@{type_name "*"}, Ts) =>
blanchet@34936
   801
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   802
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   803
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   804
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   805
  | _ => false
blanchet@35070
   806
(* hol_context -> boxability -> string * typ list -> string *)
blanchet@35280
   807
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   808
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   809
    SOME (SOME box_me) => box_me
blanchet@35070
   810
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   811
(* hol_context -> boxability -> typ -> typ *)
blanchet@35070
   812
and box_type hol_ctxt boxy T =
blanchet@33192
   813
  case T of
blanchet@35665
   814
    Type (z as (@{type_name fun}, [T1, T2])) =>
blanchet@34936
   815
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   816
       should_box_type hol_ctxt boxy z then
blanchet@33192
   817
      Type (@{type_name fun_box},
blanchet@35070
   818
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   819
    else
blanchet@35070
   820
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   821
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@35665
   822
  | Type (z as (@{type_name "*"}, Ts)) =>
blanchet@34982
   823
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   824
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   825
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   826
    else
blanchet@35665
   827
      Type (@{type_name "*"},
blanchet@35665
   828
            map (box_type hol_ctxt
blanchet@34121
   829
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   830
                           else InPair)) Ts)
blanchet@33192
   831
  | _ => T
blanchet@33192
   832
blanchet@35190
   833
(* typ -> typ *)
blanchet@35190
   834
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   835
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   836
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   837
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   838
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   839
(* term -> term *)
blanchet@35190
   840
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   841
blanchet@33192
   842
(* styp -> styp *)
blanchet@33192
   843
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   844
blanchet@33192
   845
(* typ -> int *)
blanchet@33192
   846
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   847
(* string -> int -> string *)
blanchet@33192
   848
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   849
  if s = @{const_name Pair} then
blanchet@33192
   850
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   851
  else
blanchet@33192
   852
    sel_prefix_for n ^ s
blanchet@33192
   853
(* styp -> int -> styp *)
blanchet@33192
   854
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   855
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   856
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   857
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   858
(* hol_context -> bool -> styp -> int -> styp *)
blanchet@35190
   859
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   860
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   861
  oo nth_sel_for_constr
blanchet@33192
   862
blanchet@33192
   863
(* string -> int *)
blanchet@33192
   864
fun sel_no_from_name s =
blanchet@33192
   865
  if String.isPrefix discr_prefix s then
blanchet@33192
   866
    ~1
blanchet@33192
   867
  else if String.isPrefix sel_prefix s then
blanchet@33192
   868
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   869
  else if s = @{const_name snd} then
blanchet@33192
   870
    1
blanchet@33192
   871
  else
blanchet@33192
   872
    0
blanchet@33192
   873
blanchet@35078
   874
(* term -> term *)
blanchet@35078
   875
val close_form =
blanchet@35078
   876
  let
blanchet@35078
   877
    (* (indexname * typ) list -> (indexname * typ) list -> term -> term *)
blanchet@35078
   878
    fun close_up zs zs' =
blanchet@35078
   879
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   880
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   881
           (take (length zs' - length zs) zs')
blanchet@35078
   882
    (* (indexname * typ) list -> term -> term *)
blanchet@35078
   883
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   884
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   885
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   886
        end
blanchet@35078
   887
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   888
  in aux [] end
blanchet@35078
   889
blanchet@33192
   890
(* typ list -> term -> int -> term *)
blanchet@33192
   891
fun eta_expand _ t 0 = t
blanchet@33192
   892
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   893
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   894
  | eta_expand Ts t n =
blanchet@33192
   895
    fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
blanchet@33192
   896
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   897
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   898
blanchet@33192
   899
(* term -> term *)
blanchet@33192
   900
fun extensionalize t =
blanchet@33192
   901
  case t of
blanchet@33192
   902
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   903
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   904
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   905
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   906
    end
blanchet@33192
   907
  | _ => t
blanchet@33192
   908
blanchet@33192
   909
(* typ -> term list -> term *)
blanchet@33192
   910
fun distinctness_formula T =
blanchet@33192
   911
  all_distinct_unordered_pairs_of
blanchet@33192
   912
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   913
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   914
blanchet@33192
   915
(* typ -> term *)
blanchet@35220
   916
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   917
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   918
blanchet@35220
   919
(* hol_context -> typ -> styp list *)
blanchet@35220
   920
fun uncached_datatype_constrs ({thy, stds, ...} : hol_context)
blanchet@35220
   921
                              (T as Type (s, Ts)) =
blanchet@33583
   922
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@34982
   923
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   924
     | _ =>
blanchet@35220
   925
       if is_datatype thy stds T then
blanchet@33581
   926
         case Datatype.get_info thy s of
blanchet@33581
   927
           SOME {index, descr, ...} =>
blanchet@33581
   928
           let
blanchet@33581
   929
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   930
           in
blanchet@33581
   931
             map (fn (s', Us) =>
blanchet@33581
   932
                     (s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us
blanchet@33581
   933
                          ---> T)) constrs
blanchet@33581
   934
           end
blanchet@33581
   935
         | NONE =>
blanchet@33581
   936
           if is_record_type T then
blanchet@33581
   937
             let
blanchet@33581
   938
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   939
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   940
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   941
             in [(s', T')] end
blanchet@34936
   942
           else if is_quot_type thy T then
blanchet@34936
   943
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@33581
   944
           else case typedef_info thy s of
blanchet@33581
   945
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@35311
   946
             [(Abs_name,
blanchet@35311
   947
               varify_and_instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   948
           | NONE =>
blanchet@33581
   949
             if T = @{typ ind} then
blanchet@33581
   950
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   951
             else
blanchet@33581
   952
               []
blanchet@33581
   953
       else
blanchet@33581
   954
         [])
blanchet@33580
   955
  | uncached_datatype_constrs _ _ = []
blanchet@35070
   956
(* hol_context -> typ -> styp list *)
blanchet@35220
   957
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   958
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   959
    SOME xs => xs
blanchet@33580
   960
  | NONE =>
blanchet@35220
   961
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   962
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   963
    end
blanchet@35190
   964
(* hol_context -> bool -> typ -> styp list *)
blanchet@35190
   965
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   966
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   967
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@35070
   968
(* hol_context -> typ -> int *)
blanchet@33192
   969
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   970
blanchet@33192
   971
(* string -> string *)
blanchet@33192
   972
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   973
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   974
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   975
(* hol_context -> bool -> styp -> styp *)
blanchet@35190
   976
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   977
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   978
    AList.lookup (op =)
blanchet@35190
   979
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   980
        s
blanchet@33192
   981
    |> the |> pair s
blanchet@33192
   982
  end
blanchet@34982
   983
blanchet@35070
   984
(* hol_context -> styp -> term *)
blanchet@35070
   985
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   986
  let val dataT = body_type T in
blanchet@33192
   987
    if s = @{const_name Suc} then
blanchet@33192
   988
      Abs (Name.uu, dataT,
blanchet@33192
   989
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
   990
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
   991
      Const (discr_for_constr x)
blanchet@33192
   992
    else
blanchet@33192
   993
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   994
  end
blanchet@35070
   995
(* hol_context -> styp -> term -> term *)
blanchet@35280
   996
fun discriminate_value (hol_ctxt as {thy, ...}) x t =
blanchet@35280
   997
  case head_of t of
blanchet@35280
   998
    Const x' =>
blanchet@33192
   999
    if x = x' then @{const True}
blanchet@33192
  1000
    else if is_constr_like thy x' then @{const False}
blanchet@35070
  1001
    else betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@35070
  1002
  | _ => betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
  1003
blanchet@35220
  1004
(* theory -> (typ option * bool) list -> styp -> term -> term *)
blanchet@35220
  1005
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
  1006
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
  1007
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
  1008
      @{term "%n::nat. n - 1"}
blanchet@33192
  1009
    else if is_pair_type dataT then
blanchet@33192
  1010
      Const (nth_sel_for_constr x n)
blanchet@33192
  1011
    else
blanchet@33192
  1012
      let
blanchet@33192
  1013
        (* int -> typ -> int * term *)
blanchet@35665
  1014
        fun aux m (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
  1015
            let
blanchet@33192
  1016
              val (m, t1) = aux m T1
blanchet@33192
  1017
              val (m, t2) = aux m T2
blanchet@33192
  1018
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
  1019
          | aux m T =
blanchet@33192
  1020
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
  1021
                    $ Bound 0)
blanchet@33192
  1022
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
  1023
                     (List.take (arg_Ts, n)) 0
blanchet@33192
  1024
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
  1025
  end
blanchet@35220
  1026
(* theory -> (typ option * bool) list -> styp -> term -> int -> typ -> term *)
blanchet@35220
  1027
fun select_nth_constr_arg thy stds x t n res_T =
blanchet@35220
  1028
  (case strip_comb t of
blanchet@35220
  1029
     (Const x', args) =>
blanchet@35220
  1030
     if x = x' then nth args n
blanchet@35220
  1031
     else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
blanchet@35220
  1032
     else raise SAME ()
blanchet@35220
  1033
   | _ => raise SAME())
blanchet@35220
  1034
  handle SAME () => betapply (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@33192
  1035
blanchet@35220
  1036
(* theory -> (typ option * bool) list -> styp -> term list -> term *)
blanchet@35220
  1037
fun construct_value _ _ x [] = Const x
blanchet@35220
  1038
  | construct_value thy stds (x as (s, _)) args =
blanchet@33192
  1039
    let val args = map Envir.eta_contract args in
blanchet@33192
  1040
      case hd args of
blanchet@35280
  1041
        Const (s', _) $ t =>
blanchet@34936
  1042
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
  1043
           constr_name_for_sel_like s' = s andalso
blanchet@35220
  1044
           forall (fn (n, t') =>
blanchet@35220
  1045
                      select_nth_constr_arg thy stds x t n dummyT = t')
blanchet@34936
  1046
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  1047
          t
blanchet@33192
  1048
        else
blanchet@33192
  1049
          list_comb (Const x, args)
blanchet@33192
  1050
      | _ => list_comb (Const x, args)
blanchet@33192
  1051
    end
blanchet@33192
  1052
blanchet@35665
  1053
(* hol_context -> typ -> term -> term *)
blanchet@35665
  1054
fun constr_expand (hol_ctxt as {thy, stds, ...}) T t =
blanchet@35665
  1055
  (case head_of t of
blanchet@35665
  1056
     Const x => if is_constr_like thy x then t else raise SAME ()
blanchet@35665
  1057
   | _ => raise SAME ())
blanchet@35665
  1058
  handle SAME () =>
blanchet@35665
  1059
         let
blanchet@35665
  1060
           val x' as (_, T') =
blanchet@35665
  1061
             if is_pair_type T then
blanchet@35665
  1062
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@35665
  1063
                 (@{const_name Pair}, T1 --> T2 --> T)
blanchet@35665
  1064
               end
blanchet@35665
  1065
             else
blanchet@35665
  1066
               datatype_constrs hol_ctxt T |> hd
blanchet@35665
  1067
           val arg_Ts = binder_types T'
blanchet@35665
  1068
         in
blanchet@35665
  1069
           list_comb (Const x', map2 (select_nth_constr_arg thy stds x' t)
blanchet@35665
  1070
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@35665
  1071
         end
blanchet@35665
  1072
blanchet@35665
  1073
(* (term -> term) -> int -> term -> term *)
blanchet@35665
  1074
fun coerce_bound_no f j t =
blanchet@35665
  1075
  case t of
blanchet@35665
  1076
    t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
blanchet@35665
  1077
  | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
blanchet@35665
  1078
  | Bound j' => if j' = j then f t else t
blanchet@35665
  1079
  | _ => t
blanchet@35665
  1080
(* hol_context -> typ -> typ -> term -> term *)
blanchet@35665
  1081
fun coerce_bound_0_in_term hol_ctxt new_T old_T =
blanchet@35665
  1082
  old_T <> new_T ? coerce_bound_no (coerce_term hol_ctxt [new_T] old_T new_T) 0
blanchet@35665
  1083
(* hol_context -> typ list -> typ -> typ -> term -> term *)
blanchet@35665
  1084
and coerce_term (hol_ctxt as {thy, stds, fast_descrs, ...}) Ts new_T old_T t =
blanchet@35665
  1085
  if old_T = new_T then
blanchet@35665
  1086
    t
blanchet@35665
  1087
  else
blanchet@35665
  1088
    case (new_T, old_T) of
blanchet@35665
  1089
      (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1090
       Type (@{type_name fun}, [old_T1, old_T2])) =>
blanchet@35665
  1091
      (case eta_expand Ts t 1 of
blanchet@35665
  1092
         Abs (s, _, t') =>
blanchet@35665
  1093
         Abs (s, new_T1,
blanchet@35665
  1094
              t' |> coerce_bound_0_in_term hol_ctxt new_T1 old_T1
blanchet@35665
  1095
                 |> coerce_term hol_ctxt (new_T1 :: Ts) new_T2 old_T2)
blanchet@35665
  1096
         |> Envir.eta_contract
blanchet@35665
  1097
         |> new_s <> @{type_name fun}
blanchet@35665
  1098
            ? construct_value thy stds
blanchet@35665
  1099
                  (if new_s = @{type_name fin_fun} then @{const_name FinFun}
blanchet@35665
  1100
                   else @{const_name FunBox},
blanchet@35665
  1101
                   Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1102
              o single
blanchet@35665
  1103
       | t' => raise TERM ("Nitpick_HOL.coerce_term", [t']))
blanchet@35665
  1104
    | (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1105
       Type (old_s, old_Ts as [old_T1, old_T2])) =>
blanchet@35665
  1106
      if old_s = @{type_name fin_fun} orelse old_s = @{type_name fun_box} orelse
blanchet@35665
  1107
         old_s = @{type_name pair_box} orelse old_s = @{type_name "*"} then
blanchet@35665
  1108
        case constr_expand hol_ctxt old_T t of
blanchet@35665
  1109
          Const (old_s, _) $ t1 =>
blanchet@35665
  1110
          if new_s = @{type_name fun} then
blanchet@35665
  1111
            coerce_term hol_ctxt Ts new_T (Type (@{type_name fun}, old_Ts)) t1
blanchet@35665
  1112
          else
blanchet@35665
  1113
            construct_value thy stds
blanchet@35665
  1114
                (old_s, Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1115
                [coerce_term hol_ctxt Ts (Type (@{type_name fun}, new_Ts))
blanchet@35665
  1116
                             (Type (@{type_name fun}, old_Ts)) t1]
blanchet@35665
  1117
        | Const _ $ t1 $ t2 =>
blanchet@35665
  1118
          construct_value thy stds
blanchet@35665
  1119
              (if new_s = @{type_name "*"} then @{const_name Pair}
blanchet@35665
  1120
               else @{const_name PairBox}, new_Ts ---> new_T)
blanchet@35665
  1121
              (map3 (coerce_term hol_ctxt Ts) [new_T1, new_T2] [old_T1, old_T2]
blanchet@35665
  1122
                    [t1, t2])
blanchet@35665
  1123
        | t' => raise TERM ("Nitpick_HOL.coerce_term", [t'])
blanchet@35665
  1124
      else
blanchet@35665
  1125
        raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1126
    | _ => raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1127
blanchet@33192
  1128
(* (typ * int) list -> typ -> int *)
blanchet@35665
  1129
fun card_of_type assigns (Type (@{type_name fun}, [T1, T2])) =
blanchet@34123
  1130
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@35665
  1131
  | card_of_type assigns (Type (@{type_name "*"}, [T1, T2])) =
blanchet@34123
  1132
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1133
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1134
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1135
  | card_of_type _ @{typ bool} = 2
blanchet@33192
  1136
  | card_of_type _ @{typ unit} = 1
blanchet@34123
  1137
  | card_of_type assigns T =
blanchet@34123
  1138
    case AList.lookup (op =) assigns T of
blanchet@33192
  1139
      SOME k => k
blanchet@33192
  1140
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1141
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@33192
  1142
(* int -> (typ * int) list -> typ -> int *)
blanchet@35665
  1143
fun bounded_card_of_type max default_card assigns
blanchet@35665
  1144
                         (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
  1145
    let
blanchet@34123
  1146
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1147
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1148
    in
blanchet@33192
  1149
      if k1 = max orelse k2 = max then max
blanchet@33192
  1150
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1151
    end
blanchet@35665
  1152
  | bounded_card_of_type max default_card assigns
blanchet@35665
  1153
                         (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
  1154
    let
blanchet@34123
  1155
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1156
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1157
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1158
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1159
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1160
                    card_of_type assigns T
blanchet@33192
  1161
                  else
blanchet@34123
  1162
                    card_of_type assigns T
blanchet@33232
  1163
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1164
                           default_card)
blanchet@35385
  1165
(* hol_context -> typ list -> int -> (typ * int) list -> typ -> int *)
blanchet@35385
  1166
fun bounded_exact_card_of_type hol_ctxt finitizable_dataTs max default_card
blanchet@35385
  1167
                               assigns T =
blanchet@33192
  1168
  let
blanchet@33192
  1169
    (* typ list -> typ -> int *)
blanchet@33192
  1170
    fun aux avoid T =
blanchet@34121
  1171
      (if member (op =) avoid T then
blanchet@33192
  1172
         0
blanchet@35385
  1173
       else if member (op =) finitizable_dataTs T then
blanchet@35385
  1174
         raise SAME ()
blanchet@33192
  1175
       else case T of
blanchet@35665
  1176
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
  1177
         let
blanchet@33192
  1178
           val k1 = aux avoid T1
blanchet@33192
  1179
           val k2 = aux avoid T2
blanchet@33192
  1180
         in
blanchet@33192
  1181
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1182
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1183
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1184
         end
blanchet@35665
  1185
       | Type (@{type_name "*"}, [T1, T2]) =>
blanchet@33192
  1186
         let
blanchet@33192
  1187
           val k1 = aux avoid T1
blanchet@33192
  1188
           val k2 = aux avoid T2
blanchet@33192
  1189
         in
blanchet@33192
  1190
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1191
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1192
           else Int.min (max, k1 * k2)
blanchet@33192
  1193
         end
blanchet@33192
  1194
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1195
       | @{typ prop} => 2
blanchet@33192
  1196
       | @{typ bool} => 2
blanchet@33192
  1197
       | @{typ unit} => 1
blanchet@33192
  1198
       | Type _ =>
blanchet@35070
  1199
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1200
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1201
                  else raise SAME ()
blanchet@33192
  1202
          | constrs =>
blanchet@33192
  1203
            let
blanchet@33192
  1204
              val constr_cards =
blanchet@35280
  1205
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1206
                    constrs
blanchet@33192
  1207
            in
blanchet@34121
  1208
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1209
              else Integer.sum constr_cards
blanchet@33192
  1210
            end)
blanchet@33192
  1211
       | _ => raise SAME ())
blanchet@34123
  1212
      handle SAME () =>
blanchet@34123
  1213
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1214
  in Int.min (max, aux [] T) end
blanchet@33192
  1215
blanchet@35665
  1216
val small_type_max_card = 5
blanchet@35665
  1217
blanchet@35070
  1218
(* hol_context -> typ -> bool *)
blanchet@35384
  1219
fun is_finite_type hol_ctxt T =
blanchet@35665
  1220
  bounded_exact_card_of_type hol_ctxt [] 1 2 [] T > 0
blanchet@35665
  1221
(* hol_context -> typ -> bool *)
blanchet@35665
  1222
fun is_small_finite_type hol_ctxt T =
blanchet@35665
  1223
  let val n = bounded_exact_card_of_type hol_ctxt [] 1 2 [] T in
blanchet@35665
  1224
    n > 0 andalso n <= small_type_max_card
blanchet@35665
  1225
  end
blanchet@33192
  1226
blanchet@33192
  1227
(* term -> bool *)
blanchet@33192
  1228
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1229
  | is_ground_term (Const _) = true
blanchet@33192
  1230
  | is_ground_term _ = false
blanchet@33192
  1231
blanchet@33192
  1232
(* term -> word -> word *)
blanchet@36062
  1233
fun hashw_term (t1 $ t2) = hashw (hashw_term t1, hashw_term t2)
blanchet@36062
  1234
  | hashw_term (Const (s, _)) = hashw_string (s, 0w0)
blanchet@33192
  1235
  | hashw_term _ = 0w0
blanchet@33192
  1236
(* term -> int *)
blanchet@33192
  1237
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1238
blanchet@33192
  1239
(* term list -> (indexname * typ) list *)
blanchet@33192
  1240
fun special_bounds ts =
wenzelm@35408
  1241
  fold Term.add_vars ts [] |> sort (Term_Ord.fast_indexname_ord o pairself fst)
blanchet@33192
  1242
blanchet@33192
  1243
(* indexname * typ -> term -> term *)
blanchet@33192
  1244
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
  1245
blanchet@33571
  1246
(* theory -> string -> bool *)
blanchet@33571
  1247
fun is_funky_typedef_name thy s =
blanchet@34121
  1248
  member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@34936
  1249
                 @{type_name int}] s orelse
blanchet@34936
  1250
  is_frac_type thy (Type (s, []))
blanchet@35070
  1251
(* theory -> typ -> bool *)
blanchet@33571
  1252
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
  1253
  | is_funky_typedef _ _ = false
blanchet@33192
  1254
(* term -> bool *)
blanchet@33192
  1255
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1256
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1257
  | is_arity_type_axiom _ = false
blanchet@33192
  1258
(* theory -> bool -> term -> bool *)
blanchet@33197
  1259
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
blanchet@33197
  1260
    is_typedef_axiom thy boring t2
blanchet@33197
  1261
  | is_typedef_axiom thy boring
blanchet@33192
  1262
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@35665
  1263
         $ Const (_, Type (@{type_name fun}, [Type (s, _), _]))
blanchet@35665
  1264
         $ Const _ $ _)) =
blanchet@33571
  1265
    boring <> is_funky_typedef_name thy s andalso is_typedef thy s
blanchet@33192
  1266
  | is_typedef_axiom _ _ _ = false
blanchet@35893
  1267
(* term -> bool *)
blanchet@35893
  1268
fun is_class_axiom t =
blanchet@35893
  1269
  (t |> Logic.strip_horn |> swap |> op :: |> map Logic.dest_of_class; true)
blanchet@35893
  1270
  handle TERM _ => false
blanchet@33192
  1271
blanchet@33192
  1272
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1273
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1274
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1275
   using "typedef_info". *)
blanchet@33192
  1276
(* theory -> (string * term) list -> string list -> term list * term list *)
blanchet@33192
  1277
fun partition_axioms_by_definitionality thy axioms def_names =
blanchet@33192
  1278
  let
blanchet@33192
  1279
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1280
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1281
    val nondefs =
blanchet@33192
  1282
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1283
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
blanchet@33192
  1284
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1285
blanchet@33197
  1286
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1287
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1288
   commands. *)
blanchet@33192
  1289
(* theory -> bool *)
blanchet@33192
  1290
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1291
blanchet@33192
  1292
(* term -> bool *)
blanchet@35283
  1293
val is_trivial_definition =
blanchet@35283
  1294
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1295
val is_plain_definition =
blanchet@33192
  1296
  let
blanchet@33192
  1297
    (* term -> bool *)
blanchet@33192
  1298
    fun do_lhs t1 =
blanchet@33192
  1299
      case strip_comb t1 of
blanchet@34936
  1300
        (Const _, args) =>
blanchet@34936
  1301
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1302
      | _ => false
blanchet@33192
  1303
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1304
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1305
        do_lhs t1
blanchet@33192
  1306
      | do_eq _ = false
blanchet@33192
  1307
  in do_eq end
blanchet@33192
  1308
blanchet@35335
  1309
(* theory -> (term * term) list -> term list * term list * term list *)
blanchet@35335
  1310
fun all_axioms_of thy subst =
blanchet@33192
  1311
  let
blanchet@33192
  1312
    (* theory list -> term list *)
blanchet@35335
  1313
    val axioms_of_thys =
blanchet@35893
  1314
      maps Thm.axioms_of
blanchet@35893
  1315
      #> map (apsnd (subst_atomic subst o prop_of))
blanchet@35893
  1316
      #> filter_out (is_class_axiom o snd)
blanchet@33192
  1317
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1318
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1319
                    |> OrdList.make fast_string_ord
blanchet@33192
  1320
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1321
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1322
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1323
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1324
    val (built_in_defs, built_in_nondefs) =
blanchet@33192
  1325
      partition_axioms_by_definitionality thy built_in_axioms def_names
blanchet@33197
  1326
      ||> filter (is_typedef_axiom thy false)
blanchet@33192
  1327
    val (user_defs, user_nondefs) =
blanchet@33192
  1328
      partition_axioms_by_definitionality thy user_axioms def_names
blanchet@33197
  1329
    val (built_in_nondefs, user_nondefs) =
blanchet@33197
  1330
      List.partition (is_typedef_axiom thy false) user_nondefs
blanchet@33197
  1331
      |>> append built_in_nondefs
blanchet@34121
  1332
    val defs =
blanchet@34121
  1333
      (thy |> PureThy.all_thms_of
blanchet@34121
  1334
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1335
           |> map (prop_of o snd)
blanchet@35283
  1336
           |> filter_out is_trivial_definition
blanchet@35283
  1337
           |> filter is_plain_definition) @
blanchet@34121
  1338
      user_defs @ built_in_defs
blanchet@33192
  1339
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1340
blanchet@35220
  1341
(* theory -> (typ option * bool) list -> bool -> styp -> int option *)
blanchet@35220
  1342
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1343
  if s = @{const_name If} then
blanchet@33192
  1344
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1345
  else
blanchet@35220
  1346
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1347
      case AList.lookup (op =)
blanchet@35220
  1348
                    (built_in_consts
blanchet@35220
  1349
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1350
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1351
        SOME n => SOME n
blanchet@35220
  1352
      | NONE =>
blanchet@35220
  1353
        case AList.lookup (op =)
blanchet@35220
  1354
                 (built_in_typed_consts
blanchet@35220
  1355
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1356
                 (s, unarize_type T) of
blanchet@35220
  1357
          SOME n => SOME n
blanchet@35220
  1358
        | NONE =>
blanchet@35280
  1359
          case s of
blanchet@35280
  1360
            @{const_name zero_class.zero} =>
blanchet@35280
  1361
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1362
          | @{const_name Suc} =>
blanchet@35280
  1363
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1364
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1365
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1366
                 else
blanchet@35280
  1367
                   NONE
blanchet@35220
  1368
    end
blanchet@35220
  1369
(* theory -> (typ option * bool) list -> bool -> styp -> bool *)
blanchet@35220
  1370
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1371
blanchet@33192
  1372
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1373
   simplification rules (equational specifications). *)
blanchet@33192
  1374
(* term -> term *)
blanchet@33192
  1375
fun term_under_def t =
blanchet@33192
  1376
  case t of
blanchet@33192
  1377
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1378
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1379
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1380
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1381
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1382
  | t1 $ _ => term_under_def t1
blanchet@33192
  1383
  | _ => t
blanchet@33192
  1384
blanchet@33192
  1385
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
blanchet@33192
  1386
   traversal of the term, without which the wrong occurrence of a constant could
blanchet@33192
  1387
   be matched in the face of overloading. *)
blanchet@35220
  1388
(* theory -> (typ option * bool) list -> bool -> const_table -> styp
blanchet@35220
  1389
   -> term list *)
blanchet@35220
  1390
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1391
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1392
    []
blanchet@33192
  1393
  else
blanchet@33192
  1394
    these (Symtab.lookup table s)
blanchet@33192
  1395
    |> map_filter (try (Refute.specialize_type thy x))
blanchet@34121
  1396
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1397
blanchet@35280
  1398
(* term -> term option *)
blanchet@35280
  1399
fun normalized_rhs_of t =
blanchet@33192
  1400
  let
blanchet@33743
  1401
    (* term option -> term option *)
blanchet@33743
  1402
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1403
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1404
      | aux _ _ = NONE
blanchet@33192
  1405
    val (lhs, rhs) =
blanchet@33192
  1406
      case t of
blanchet@33192
  1407
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1408
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1409
        (t1, t2)
blanchet@33232
  1410
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1411
    val args = strip_comb lhs |> snd
blanchet@33743
  1412
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1413
blanchet@33192
  1414
(* theory -> const_table -> styp -> term option *)
blanchet@33192
  1415
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1416
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1417
     original_name s <> s then
blanchet@33192
  1418
    NONE
blanchet@33192
  1419
  else
blanchet@35220
  1420
    x |> def_props_for_const thy [(NONE, false)] false table |> List.last
blanchet@35280
  1421
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1422
    handle List.Empty => NONE
blanchet@33192
  1423
blanchet@33192
  1424
(* term -> fixpoint_kind *)
blanchet@33192
  1425
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1426
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1427
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1428
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1429
blanchet@33192
  1430
(* theory -> const_table -> term -> bool *)
blanchet@33192
  1431
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1432
  let
blanchet@33192
  1433
    (* term -> bool *)
blanchet@33192
  1434
    fun is_good_arg (Bound _) = true
blanchet@33192
  1435
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1436
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1437
        s = @{const_name undefined}
blanchet@33192
  1438
      | is_good_arg _ = false
blanchet@33192
  1439
  in
blanchet@33192
  1440
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1441
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1442
      (case def_of_const thy table x of
blanchet@33192
  1443
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1444
       | NONE => false)
blanchet@33192
  1445
    | _ => false
blanchet@33192
  1446
  end
blanchet@33192
  1447
(* theory -> const_table -> term -> term *)
blanchet@33192
  1448
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1449
  map_aterms (fn t as Const x =>
blanchet@33192
  1450
                 (case def_of_const thy table x of
blanchet@33192
  1451
                    SOME t' =>
blanchet@33192
  1452
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1453
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1454
                      else t
blanchet@33192
  1455
                    end
blanchet@33192
  1456
                 | NONE => t)
blanchet@33192
  1457
               | t => t)
blanchet@33192
  1458
blanchet@35220
  1459
(* theory -> (typ option * bool) list -> (string * int) list *)
blanchet@35220
  1460
fun case_const_names thy stds =
blanchet@33192
  1461
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@35220
  1462
                  if is_basic_datatype thy stds dtype_s then
blanchet@33192
  1463
                    I
blanchet@33192
  1464
                  else
blanchet@33192
  1465
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1466
                                     |> the |> #3 |> length))
blanchet@33192
  1467
              (Datatype.get_all thy) [] @
blanchet@33583
  1468
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1469
blanchet@35718
  1470
(* theory -> const_table -> string * typ -> fixpoint_kind *)
blanchet@35718
  1471
fun fixpoint_kind_of_const thy table x =
blanchet@35718
  1472
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@35718
  1473
    NoFp
blanchet@35718
  1474
  else
blanchet@35718
  1475
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@35718
  1476
    handle Option.Option => NoFp
blanchet@33192
  1477
blanchet@35718
  1478
(* hol_context -> styp -> bool *)
blanchet@35718
  1479
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35718
  1480
                             ...} : hol_context) x =
blanchet@35718
  1481
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35718
  1482
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@35718
  1483
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@35718
  1484
                             ...} : hol_context) x =
blanchet@35718
  1485
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@35718
  1486
                                                     x)))
blanchet@35718
  1487
         [!simp_table, psimp_table]
blanchet@35718
  1488
fun is_inductive_pred hol_ctxt =
blanchet@35718
  1489
  is_real_inductive_pred hol_ctxt andf (not o is_real_equational_fun hol_ctxt)
blanchet@35718
  1490
fun is_equational_fun hol_ctxt =
blanchet@35718
  1491
  (is_real_equational_fun hol_ctxt orf is_real_inductive_pred hol_ctxt orf
blanchet@35718
  1492
   (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1493
blanchet@35718
  1494
(* term -> term *)
blanchet@35718
  1495
fun lhs_of_equation t =
blanchet@35718
  1496
  case t of
blanchet@35718
  1497
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1498
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1499
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1500
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@35718
  1501
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@35718
  1502
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@35718
  1503
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@35718
  1504
  | _ => NONE
blanchet@35718
  1505
(* theory -> term -> bool *)
blanchet@35718
  1506
fun is_constr_pattern _ (Bound _) = true
blanchet@35718
  1507
  | is_constr_pattern _ (Var _) = true
blanchet@35718
  1508
  | is_constr_pattern thy t =
blanchet@35718
  1509
    case strip_comb t of
blanchet@35718
  1510
      (Const x, args) =>
blanchet@35718
  1511
      is_constr_like thy x andalso forall (is_constr_pattern thy) args
blanchet@35718
  1512
    | _ => false
blanchet@35718
  1513
fun is_constr_pattern_lhs thy t =
blanchet@35718
  1514
  forall (is_constr_pattern thy) (snd (strip_comb t))
blanchet@35718
  1515
fun is_constr_pattern_formula thy t =
blanchet@35718
  1516
  case lhs_of_equation t of
blanchet@35718
  1517
    SOME t' => is_constr_pattern_lhs thy t'
blanchet@35718
  1518
  | NONE => false
blanchet@35718
  1519
blanchet@35807
  1520
(* Similar to "Refute.specialize_type" but returns all matches rather than only
blanchet@35807
  1521
   the first (preorder) match. *)
blanchet@35807
  1522
(* theory -> styp -> term -> term list *)
blanchet@35807
  1523
fun multi_specialize_type thy slack (s, T) t =
blanchet@35807
  1524
  let
blanchet@35807
  1525
    (* term -> (typ * term) list -> (typ * term) list *)
blanchet@35807
  1526
    fun aux (Const (s', T')) ys =
blanchet@35807
  1527
        if s = s' then
blanchet@35807
  1528
          ys |> (if AList.defined (op =) ys T' then
blanchet@35807
  1529
                   I
blanchet@35807
  1530
                 else
blanchet@35807
  1531
                   cons (T', Refute.monomorphic_term
blanchet@35807
  1532
                                 (Sign.typ_match thy (T', T) Vartab.empty) t)
blanchet@35807
  1533
                   handle Type.TYPE_MATCH => I
blanchet@35807
  1534
                        | Refute.REFUTE _ =>
blanchet@35807
  1535
                          if slack then
blanchet@35807
  1536
                            I
blanchet@35807
  1537
                          else
blanchet@35807
  1538
                            raise NOT_SUPPORTED ("too much polymorphism in \
blanchet@35807
  1539
                                                 \axiom involving " ^ quote s))
blanchet@35807
  1540
        else
blanchet@35807
  1541
          ys
blanchet@35807
  1542
      | aux _ ys = ys
blanchet@35807
  1543
  in map snd (fold_aterms aux t []) end
blanchet@35807
  1544
(* theory -> bool -> const_table -> styp -> term list *)
blanchet@35807
  1545
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@35807
  1546
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@35807
  1547
blanchet@35807
  1548
(* term -> term *)
blanchet@35807
  1549
fun unvarify_term (t1 $ t2) = unvarify_term t1 $ unvarify_term t2
blanchet@35807
  1550
  | unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@35807
  1551
  | unvarify_term (Abs (s, T, t')) = Abs (s, T, unvarify_term t')
blanchet@35807
  1552
  | unvarify_term t = t
blanchet@35807
  1553
(* theory -> term -> term *)
blanchet@35807
  1554
fun axiom_for_choice_spec thy =
blanchet@35807
  1555
  unvarify_term
blanchet@35807
  1556
  #> Object_Logic.atomize_term thy
blanchet@35807
  1557
  #> Choice_Specification.close_form
blanchet@35807
  1558
  #> HOLogic.mk_Trueprop
blanchet@35807
  1559
(* hol_context -> styp -> bool *)
blanchet@35807
  1560
fun is_choice_spec_fun ({thy, def_table, nondef_table, choice_spec_table, ...}
blanchet@35807
  1561
                        : hol_context) x =
blanchet@35807
  1562
  case nondef_props_for_const thy true choice_spec_table x of
blanchet@35807
  1563
    [] => false
blanchet@35807
  1564
  | ts => case def_of_const thy def_table x of
blanchet@35807
  1565
            SOME (Const (@{const_name Eps}, _) $ _) => true
blanchet@35807
  1566
          | SOME _ => false
blanchet@35807
  1567
          | NONE =>
blanchet@35807
  1568
            let val ts' = nondef_props_for_const thy true nondef_table x in
blanchet@35807
  1569
              length ts' = length ts andalso
blanchet@35807
  1570
              forall (fn t =>
blanchet@35807
  1571
                         exists (curry (op aconv) (axiom_for_choice_spec thy t))
blanchet@35807
  1572
                                ts') ts
blanchet@35807
  1573
            end
blanchet@35807
  1574
blanchet@35807
  1575
(* theory -> const_table -> term -> bool *)
blanchet@35807
  1576
fun is_choice_spec_axiom thy choice_spec_table t =
blanchet@35807
  1577
  Symtab.exists (fn (_, ts) =>
blanchet@35807
  1578
                    exists (curry (op aconv) t o axiom_for_choice_spec thy) ts)
blanchet@35807
  1579
                choice_spec_table
blanchet@35807
  1580
blanchet@35718
  1581
(** Constant unfolding **)
blanchet@33192
  1582
blanchet@35220
  1583
(* theory -> (typ option * bool) list -> int * styp -> term *)
blanchet@35220
  1584
fun constr_case_body thy stds (j, (x as (_, T))) =
blanchet@33192
  1585
  let val arg_Ts = binder_types T in
blanchet@35220
  1586
    list_comb (Bound j, map2 (select_nth_constr_arg thy stds x (Bound 0))
blanchet@33192
  1587
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1588
  end
blanchet@35070
  1589
(* hol_context -> typ -> int * styp -> term -> term *)
blanchet@35220
  1590
fun add_constr_case (hol_ctxt as {thy, stds, ...}) res_T (j, x) res_t =
blanchet@34124
  1591
  Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@35220
  1592
  $ discriminate_value hol_ctxt x (Bound 0) $ constr_case_body thy stds (j, x)
blanchet@33580
  1593
  $ res_t
blanchet@35070
  1594
(* hol_context -> typ -> typ -> term *)
blanchet@35220
  1595
fun optimized_case_def (hol_ctxt as {thy, stds, ...}) dataT res_T =
blanchet@33192
  1596
  let
blanchet@35070
  1597
    val xs = datatype_constrs hol_ctxt dataT
blanchet@35179
  1598
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs
blanchet@35179
  1599
    val (xs', x) = split_last xs
blanchet@33192
  1600
  in
blanchet@35220
  1601
    constr_case_body thy stds (1, x)
blanchet@35179
  1602
    |> fold_rev (add_constr_case hol_ctxt res_T) (length xs downto 2 ~~ xs')
blanchet@33192
  1603
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1604
  end
blanchet@35070
  1605
(* hol_context -> string -> typ -> typ -> term -> term *)
blanchet@35220
  1606
fun optimized_record_get (hol_ctxt as {thy, stds, ...}) s rec_T res_T t =
blanchet@35070
  1607
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1608
    case no_of_record_field thy s rec_T of
blanchet@33192
  1609
      ~1 => (case rec_T of
blanchet@33192
  1610
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1611
               let
blanchet@33192
  1612
                 val rec_T' = List.last Ts
blanchet@33192
  1613
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1614
               in
blanchet@35220
  1615
                 select_nth_constr_arg thy stds constr_x t j res_T
blanchet@35070
  1616
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1617
               end
blanchet@33232
  1618
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1619
                                []))
blanchet@35220
  1620
    | j => select_nth_constr_arg thy stds constr_x t j res_T
blanchet@33192
  1621
  end
blanchet@35070
  1622
(* hol_context -> string -> typ -> term -> term -> term *)
blanchet@35220
  1623
fun optimized_record_update (hol_ctxt as {thy, stds, ...}) s rec_T fun_t rec_t =
blanchet@33192
  1624
  let
blanchet@35070
  1625
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1626
    val Ts = binder_types constr_T
blanchet@33192
  1627
    val n = length Ts
blanchet@33192
  1628
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1629
    val ts =
blanchet@35220
  1630
      map2 (fn j => fn T =>
blanchet@35220
  1631
               let val t = select_nth_constr_arg thy stds constr_x rec_t j T in
blanchet@35220
  1632
                 if j = special_j then
blanchet@35220
  1633
                   betapply (fun_t, t)
blanchet@35220
  1634
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1635
                   optimized_record_update hol_ctxt s
blanchet@35220
  1636
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1637
                 else
blanchet@35220
  1638
                   t
blanchet@35220
  1639
               end) (index_seq 0 n) Ts
blanchet@33192
  1640
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1641
blanchet@35070
  1642
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1643
val unfold_max_depth = 255
blanchet@33192
  1644
blanchet@35070
  1645
(* hol_context -> term -> term *)
blanchet@35284
  1646
fun unfold_defs_in_term (hol_ctxt as {thy, ctxt, stds, fast_descrs, case_names,
blanchet@35280
  1647
                                      def_table, ground_thm_table, ersatz_table,
blanchet@35280
  1648
                                      ...}) =
blanchet@33192
  1649
  let
blanchet@33192
  1650
    (* int -> typ list -> term -> term *)
blanchet@33192
  1651
    fun do_term depth Ts t =
blanchet@33192
  1652
      case t of
blanchet@33192
  1653
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@35665
  1654
                      Type (@{type_name fun}, [_, ran_T]))) $ t1 =>
blanchet@33192
  1655
        ((if is_number_type thy ran_T then
blanchet@33192
  1656
            let
blanchet@33192
  1657
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1658
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1659
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1660
            in
blanchet@35220
  1661
              if is_integer_like_type ran_T then
blanchet@35220
  1662
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1663
                  Const (s, ran_T)
blanchet@35220
  1664
                else
blanchet@35220
  1665
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1666
              else
blanchet@33192
  1667
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1668
                                  $ Const (s, int_T))
blanchet@33192
  1669
            end
blanchet@33192
  1670
            handle TERM _ => raise SAME ()
blanchet@33192
  1671
          else
blanchet@33192
  1672
            raise SAME ())
blanchet@33192
  1673
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1674
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1675
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1676
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1677
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1678
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1679
      | Const (x as (@{const_name distinct},
blanchet@35665
  1680
               Type (@{type_name fun}, [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1681
        $ (t1 as _ $ _) =>
blanchet@33192
  1682
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1683
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1684
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1685
        if is_ground_term t1 andalso
blanchet@34936
  1686
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1687
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1688
          do_term depth Ts t2
blanchet@33192
  1689
        else
blanchet@33192
  1690
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1691
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1692
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1693
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1694
      | Const x => do_const depth Ts t x []
blanchet@33192
  1695
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1696
      | Free _ => t
blanchet@33192
  1697
      | Var _ => t
blanchet@33192
  1698
      | Bound _ => t
blanchet@33192
  1699
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1700
    (* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
blanchet@33192
  1701
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1702
        (Abs (Name.uu, body_type T,
blanchet@35220
  1703
              select_nth_constr_arg thy stds x (Bound 0) n res_T), [])
blanchet@33192
  1704
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@35220
  1705
        (select_nth_constr_arg thy stds x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1706
    (* int -> typ list -> term -> styp -> term list -> term *)
blanchet@33192
  1707
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1708
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1709
        SOME s' =>
blanchet@33192
  1710
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1711
      | NONE =>
blanchet@33192
  1712
        let
blanchet@33192
  1713
          val (const, ts) =
blanchet@35220
  1714
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1715
              (Const x, ts)
blanchet@33192
  1716
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1717
              SOME n =>
blanchet@33192
  1718
              let
blanchet@33192
  1719
                val (dataT, res_T) = nth_range_type n T
blanchet@33705
  1720
                                     |> pairf domain_type range_type
blanchet@33192
  1721
              in
blanchet@35070
  1722
                (optimized_case_def hol_ctxt dataT res_T
blanchet@33192
  1723
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1724
              end
blanchet@33192
  1725
            | _ =>
blanchet@35220
  1726
              if is_constr thy stds x then
blanchet@33192
  1727
                (Const x, ts)
blanchet@33581
  1728
              else if is_stale_constr thy x then
blanchet@34936
  1729
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1730
                                     \(\"" ^ s ^ "\")")
blanchet@35284
  1731
              else if is_quot_abs_fun ctxt x then
blanchet@34936
  1732
                let
blanchet@34936
  1733
                  val rep_T = domain_type T
blanchet@34936
  1734
                  val abs_T = range_type T
blanchet@34936
  1735
                in
blanchet@34936
  1736
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1737
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@35311
  1738
                               $ (Const (quot_normal_name_for_type ctxt abs_T,
blanchet@34936
  1739
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1740
                end
blanchet@35284
  1741
              else if is_quot_rep_fun ctxt x then
blanchet@34936
  1742
                let
blanchet@34936
  1743
                  val abs_T = domain_type T
blanchet@34936
  1744
                  val rep_T = range_type T
blanchet@34936
  1745
                  val x' = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1746
                in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
blanchet@33192
  1747
              else if is_record_get thy x then
blanchet@33192
  1748
                case length ts of
blanchet@33192
  1749
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1750
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1751
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1752
              else if is_record_update thy x then
blanchet@33192
  1753
                case length ts of
blanchet@35070
  1754
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1755
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1756
                            (do_term depth Ts (hd ts))
blanchet@33580
  1757
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1758
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@33192
  1759
              else if is_rep_fun thy x then
blanchet@33192
  1760
                let val x' = mate_of_rep_fun thy x in
blanchet@35220
  1761
                  if is_constr thy stds x' then
blanchet@33192
  1762
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1763
                                                    (range_type T)
blanchet@33192
  1764
                  else
blanchet@33192
  1765
                    (Const x, ts)
blanchet@33192
  1766
                end
blanchet@35807
  1767
              else if is_equational_fun hol_ctxt x orelse
blanchet@35807
  1768
                      is_choice_spec_fun hol_ctxt x then
blanchet@33192
  1769
                (Const x, ts)
blanchet@33192
  1770
              else case def_of_const thy def_table x of
blanchet@33192
  1771
                SOME def =>
blanchet@33192
  1772
                if depth > unfold_max_depth then
blanchet@34124
  1773
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1774
                                   "too many nested definitions (" ^
blanchet@34124
  1775
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1776
                                   quote s)
blanchet@33192
  1777
                else if s = @{const_name wfrec'} then
blanchet@33192
  1778
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1779
                else
blanchet@33192
  1780
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1781
              | NONE => (Const x, ts)
blanchet@33192
  1782
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1783
  in do_term 0 [] end
blanchet@33192
  1784
blanchet@35718
  1785
(** Axiom extraction/generation **)
blanchet@35718
  1786
blanchet@35807
  1787
(* term -> string * term *)
blanchet@35807
  1788
fun pair_for_prop t =
blanchet@35807
  1789
  case term_under_def t of
blanchet@35807
  1790
    Const (s, _) => (s, t)
blanchet@35807
  1791
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@35807
  1792
(* (Proof.context -> term list) -> Proof.context -> (term * term) list
blanchet@35807
  1793
   -> const_table *)
blanchet@35807
  1794
fun def_table_for get ctxt subst =
blanchet@35807
  1795
  ctxt |> get |> map (pair_for_prop o subst_atomic subst)
blanchet@35807
  1796
       |> AList.group (op =) |> Symtab.make
blanchet@35807
  1797
(* term -> string * term *)
blanchet@35807
  1798
fun paired_with_consts t = map (rpair t) (Term.add_const_names t [])
blanchet@35718
  1799
(* Proof.context -> (term * term) list -> term list -> const_table *)
blanchet@35718
  1800
fun const_def_table ctxt subst ts =
blanchet@35807
  1801
  def_table_for (map prop_of o Nitpick_Defs.get) ctxt subst
blanchet@35718
  1802
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@35718
  1803
          (map pair_for_prop ts)
blanchet@35718
  1804
(* term list -> const_table *)
blanchet@35718
  1805
fun const_nondef_table ts =
blanchet@35807
  1806
  fold (append o paired_with_consts) ts [] |> AList.group (op =) |> Symtab.make
blanchet@35718
  1807
(* Proof.context -> (term * term) list -> const_table *)
blanchet@35807
  1808
val const_simp_table = def_table_for (map prop_of o Nitpick_Simps.get)
blanchet@35807
  1809
val const_psimp_table = def_table_for (map prop_of o Nitpick_Psimps.get)
blanchet@35807
  1810
fun const_choice_spec_table ctxt subst =
blanchet@35807
  1811
  map (subst_atomic subst o prop_of) (Nitpick_Choice_Specs.get ctxt)
blanchet@35807
  1812
  |> const_nondef_table
blanchet@35718
  1813
(* Proof.context -> (term * term) list -> const_table -> const_table *)
blanchet@35718
  1814
fun inductive_intro_table ctxt subst def_table =
blanchet@35807
  1815
  def_table_for
blanchet@35807
  1816
      (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
blanchet@35807
  1817
                                            def_table o prop_of)
blanchet@35807
  1818
           o Nitpick_Intros.get) ctxt subst
blanchet@35718
  1819
(* theory -> term list Inttab.table *)
blanchet@35718
  1820
fun ground_theorem_table thy =
blanchet@35718
  1821
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@35718
  1822
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@35718
  1823
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@35718
  1824
blanchet@35807
  1825
(* TODO: Move to "Nitpick.thy" *)
blanchet@35718
  1826
val basic_ersatz_table =
blanchet@35718
  1827
  [(@{const_name prod_case}, @{const_name split}),
blanchet@35718
  1828
   (@{const_name card}, @{const_name card'}),
blanchet@35718
  1829
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@35718
  1830
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@35718
  1831
   (@{const_name wf}, @{const_name wf'}),
blanchet@35718
  1832
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@35718
  1833
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@35718
  1834
blanchet@35718
  1835
(* theory -> (string * string) list *)
blanchet@35718
  1836
fun ersatz_table thy =
blanchet@35718
  1837
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@35718
  1838
blanchet@35718
  1839
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
blanchet@35718
  1840
fun add_simps simp_table s eqs =
blanchet@35718
  1841
  Unsynchronized.change simp_table
blanchet@35718
  1842
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@35718
  1843
blanchet@35718
  1844
(* theory -> styp -> term list *)
blanchet@35718
  1845
fun inverse_axioms_for_rep_fun thy (x as (_, T)) =
blanchet@35718
  1846
  let val abs_T = domain_type T in
blanchet@35718
  1847
    typedef_info thy (fst (dest_Type abs_T)) |> the
blanchet@35718
  1848
    |> pairf #Abs_inverse #Rep_inverse
blanchet@35718
  1849
    |> pairself (Refute.specialize_type thy x o prop_of o the)
blanchet@35718
  1850
    ||> single |> op ::
blanchet@35718
  1851
  end
blanchet@35718
  1852
(* theory -> string * typ list -> term list *)
blanchet@35718
  1853
fun optimized_typedef_axioms thy (abs_z as (abs_s, _)) =
blanchet@35718
  1854
  let val abs_T = Type abs_z in
blanchet@35718
  1855
    if is_univ_typedef thy abs_T then
blanchet@35718
  1856
      []
blanchet@35718
  1857
    else case typedef_info thy abs_s of
blanchet@35718
  1858
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@35718
  1859
      let
blanchet@35718
  1860
        val rep_T = varify_and_instantiate_type thy abs_type abs_T rep_type
blanchet@35718
  1861
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@35718
  1862
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@35718
  1863
        val set_t' =
blanchet@35718
  1864
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@35718
  1865
                      |> Refute.specialize_type thy (dest_Const rep_t)
blanchet@35718
  1866
                      |> HOLogic.dest_mem |> snd
blanchet@35718
  1867
      in
blanchet@35718
  1868
        [HOLogic.all_const abs_T
blanchet@35718
  1869
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@35718
  1870
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@35718
  1871
        |> map HOLogic.mk_Trueprop
blanchet@35718
  1872
      end
blanchet@35718
  1873
    | NONE => []
blanchet@35718
  1874
  end
blanchet@35718
  1875
(* Proof.context -> string * typ list -> term list *)
blanchet@35718
  1876
fun optimized_quot_type_axioms ctxt stds abs_z =
blanchet@35718
  1877
  let
blanchet@35718
  1878
    val thy = ProofContext.theory_of ctxt
blanchet@35718
  1879
    val abs_T = Type abs_z
blanchet@35718
  1880
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@35718
  1881
    val equiv_rel = equiv_relation_for_quot_type thy abs_T
blanchet@35718
  1882
    val a_var = Var (("a", 0), abs_T)
blanchet@35718
  1883
    val x_var = Var (("x", 0), rep_T)
blanchet@35718
  1884
    val y_var = Var (("y", 0), rep_T)
blanchet@35718
  1885
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@35718
  1886
    val sel_a_t = select_nth_constr_arg thy stds x a_var 0 rep_T
blanchet@35718
  1887
    val normal_t = Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T)
blanchet@35718
  1888
    val normal_x = normal_t $ x_var
blanchet@35718
  1889
    val normal_y = normal_t $ y_var
blanchet@35718
  1890
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@35718
  1891
  in
blanchet@35718
  1892
    [Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
blanchet@35718
  1893
     Logic.list_implies
blanchet@35718
  1894
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@35718
  1895
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@35718
  1896
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@35718
  1897
           Logic.mk_equals (normal_x, normal_y)),
blanchet@35718
  1898
     Logic.list_implies
blanchet@35718
  1899
         ([HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)),
blanchet@35718
  1900
           HOLogic.mk_Trueprop (@{const Not} $ HOLogic.mk_eq (normal_x, x_var))],
blanchet@35718
  1901
          HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@35718
  1902
  end
blanchet@35718
  1903
blanchet@35070
  1904
(* hol_context -> typ -> term list *)
blanchet@35220
  1905
fun codatatype_bisim_axioms (hol_ctxt as {thy, stds, ...}) T =
blanchet@33192
  1906
  let
blanchet@35070
  1907
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1908
    val set_T = T --> bool_T
blanchet@33192
  1909
    val iter_T = @{typ bisim_iterator}
blanchet@34124
  1910
    val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1911
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1912
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1913
    val n_var_minus_1 =
blanchet@35671
  1914
      Const (@{const_name safe_The}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1915
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1916
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1917
    val x_var = Var (("x", 0), T)
blanchet@33192
  1918
    val y_var = Var (("y", 0), T)
blanchet@33192
  1919
    (* styp -> int -> typ -> term *)
blanchet@33192
  1920
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1921
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1922
       else HOLogic.eq_const nth_T)
blanchet@35220
  1923
      $ select_nth_constr_arg thy stds x x_var n nth_T
blanchet@35220
  1924
      $ select_nth_constr_arg thy stds x y_var n nth_T
blanchet@33192
  1925
    (* styp -> term *)
blanchet@33192
  1926
    fun case_func (x as (_, T)) =
blanchet@33192
  1927
      let
blanchet@33192
  1928
        val arg_Ts = binder_types T
blanchet@33192
  1929
        val core_t =
blanchet@35070
  1930
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1931
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1932
          |> foldr1 s_conj
blanchet@33192
  1933
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1934
  in
blanchet@33192
  1935
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1936
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@35070
  1937
        $ (betapplys (optimized_case_def hol_ctxt T bool_T,
blanchet@33192
  1938
                      map case_func xs @ [x_var]))),
blanchet@33192
  1939
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@34124
  1940
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  1941
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  1942
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1943
  end
blanchet@33192
  1944
blanchet@33192
  1945
exception NO_TRIPLE of unit
blanchet@33192
  1946
blanchet@33192
  1947
(* theory -> styp -> term -> term list * term list * term *)
blanchet@33192
  1948
fun triple_for_intro_rule thy x t =
blanchet@33192
  1949
  let
wenzelm@35625
  1950
    val prems = Logic.strip_imp_prems t |> map (Object_Logic.atomize_term thy)
wenzelm@35625
  1951
    val concl = Logic.strip_imp_concl t |> Object_Logic.atomize_term thy
blanchet@34121
  1952
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@33192
  1953
    (* term -> bool *)
blanchet@34121
  1954
     val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  1955
  in
blanchet@33192
  1956
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1957
  end
blanchet@33192
  1958
blanchet@33192
  1959
(* term -> term *)
blanchet@33192
  1960
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1961
blanchet@33192
  1962
(* indexname * typ -> term list -> term -> term -> term *)
blanchet@33192
  1963
fun wf_constraint_for rel side concl main =
blanchet@33192
  1964
  let
blanchet@33192
  1965
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1966
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1967
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1968
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1969
  in
blanchet@33192
  1970
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1971
                      HOLogic.all_const T
blanchet@33192
  1972
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1973
                  (t, vars)
blanchet@33192
  1974
  end
blanchet@33192
  1975
blanchet@33192
  1976
(* indexname * typ -> term list * term list * term -> term *)
blanchet@33192
  1977
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1978
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1979
blanchet@33192
  1980
(* Proof.context -> Time.time option -> thm
blanchet@33192
  1981
   -> (Proof.context -> tactic -> tactic) -> bool *)
blanchet@33192
  1982
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1983
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1984
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1985
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1986
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1987
blanchet@35181
  1988
val max_cached_wfs = 50
blanchet@35181
  1989
val cached_timeout =
blanchet@35181
  1990
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  1991
val cached_wf_props =
blanchet@35181
  1992
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  1993
krauss@33351
  1994
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1995
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1996
blanchet@35070
  1997
(* hol_context -> const_table -> styp -> bool *)
blanchet@33580
  1998
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  1999
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  2000
         : hol_context) (x as (_, T)) =
blanchet@35220
  2001
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  2002
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  2003
                      [Const x])
blanchet@33192
  2004
  | intro_ts =>
blanchet@33192
  2005
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  2006
          |> filter_out (null o #2) of
blanchet@33192
  2007
       [] => true
blanchet@33192
  2008
     | triples =>
blanchet@33192
  2009
       let
blanchet@33192
  2010
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  2011
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  2012
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  2013
         val rel = (("R", j), rel_T)
blanchet@33192
  2014
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  2015
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  2016
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  2017
         val _ = if debug then
blanchet@33192
  2018
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  2019
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  2020
                 else
blanchet@33192
  2021
                   ()
blanchet@33192
  2022
       in
blanchet@35181
  2023
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  2024
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  2025
           ()
blanchet@33557
  2026
         else
blanchet@35181
  2027
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  2028
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  2029
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  2030
           SOME wf => wf
blanchet@33192
  2031
         | NONE =>
blanchet@33192
  2032
           let
blanchet@33192
  2033
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  2034
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  2035
                             termination_tacs
blanchet@35181
  2036
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  2037
       end)
blanchet@35309
  2038
    handle List.Empty => false | NO_TRIPLE () => false
blanchet@33192
  2039
blanchet@35070
  2040
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  2041
blanchet@35070
  2042
(* hol_context -> styp -> bool *)
blanchet@33192
  2043
fun is_well_founded_inductive_pred
blanchet@35070
  2044
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  2045
        (x as (s, _)) =
blanchet@33192
  2046
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  2047
    SOME (SOME b) => b
blanchet@34936
  2048
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  2049
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  2050
           SOME (_, wf) => wf
blanchet@35181
  2051
         | NONE =>
blanchet@35181
  2052
           let
blanchet@35181
  2053
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  2054
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  2055
           in
blanchet@35181
  2056
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  2057
           end
blanchet@33192
  2058
blanchet@35280
  2059
(* typ list -> typ -> term -> term *)
blanchet@35280
  2060
fun ap_curry [_] _ t = t
blanchet@35280
  2061
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  2062
    let val n = length arg_Ts in
blanchet@33192
  2063
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  2064
                incr_boundvars n t
blanchet@33192
  2065
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  2066
    end
blanchet@33192
  2067
blanchet@33192
  2068
(* int -> term -> int *)
blanchet@33192
  2069
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  2070
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  2071
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  2072
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  2073
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  2074
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  2075
blanchet@33192
  2076
(* term -> bool *)
blanchet@33192
  2077
val is_linear_inductive_pred_def =
blanchet@33192
  2078
  let
blanchet@33192
  2079
    (* int -> term -> bool *)
blanchet@33192
  2080
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  2081
        do_disjunct (j + 1) t2
blanchet@33192
  2082
      | do_disjunct j t =
blanchet@33192
  2083
        case num_occs_of_bound_in_term j t of
blanchet@33192
  2084
          0 => true
blanchet@35070
  2085
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  2086
        | _ => false
blanchet@33192
  2087
    (* term -> bool *)
blanchet@33192
  2088
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2089
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  2090
          case length xs of
blanchet@33192
  2091
            1 => false
blanchet@35070
  2092
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  2093
        end
blanchet@33192
  2094
      | do_lfp_def _ = false
blanchet@33192
  2095
  in do_lfp_def o strip_abs_body end
blanchet@33192
  2096
blanchet@33851
  2097
(* int -> int list list *)
blanchet@33851
  2098
fun n_ptuple_paths 0 = []
blanchet@33851
  2099
  | n_ptuple_paths 1 = []
blanchet@33851
  2100
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  2101
(* int -> typ -> typ -> term -> term *)
blanchet@33851
  2102
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  2103
blanchet@33192
  2104
(* term -> term * term *)
blanchet@33192
  2105
val linear_pred_base_and_step_rhss =
blanchet@33192
  2106
  let
blanchet@33192
  2107
    (* term -> term *)
blanchet@33192
  2108
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2109
        let
blanchet@33192
  2110
          val (xs, body) = strip_abs t2
blanchet@33192
  2111
          val arg_Ts = map snd (tl xs)
blanchet@33192
  2112
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  2113
          val j = length arg_Ts
blanchet@33192
  2114
          (* int -> term -> term *)
blanchet@33192
  2115
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  2116
              Const (@{const_name Ex}, T1)
blanchet@33192
  2117
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  2118
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  2119
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  2120
            | repair_rec j t =
blanchet@33192
  2121
              let val (head, args) = strip_comb t in
blanchet@33192
  2122
                if head = Bound j then
blanchet@33192
  2123
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  2124
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  2125
                else
blanchet@33192
  2126
                  t
blanchet@33192
  2127
              end
blanchet@33192
  2128
          val (nonrecs, recs) =
blanchet@34121
  2129
            List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
blanchet@35070
  2130
                           (disjuncts_of body)
blanchet@33192
  2131
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  2132
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  2133
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  2134
        in
blanchet@33192
  2135
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  2136
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  2137
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  2138
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  2139
        end
blanchet@33192
  2140
      | aux t =
blanchet@33232
  2141
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  2142
  in aux end
blanchet@33192
  2143
blanchet@35070
  2144
(* hol_context -> styp -> term -> term *)
blanchet@35280
  2145
fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (s, T) def =
blanchet@33192
  2146
  let
blanchet@33192
  2147
    val j = maxidx_of_term def + 1
blanchet@33192
  2148
    val (outer, fp_app) = strip_abs def
blanchet@33192
  2149
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2150
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  2151
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  2152
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  2153
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  2154
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  2155
    val set_T = tuple_T --> bool_T
blanchet@33192
  2156
    val curried_T = tuple_T --> set_T
blanchet@35665
  2157
    val uncurried_T = Type (@{type_name "*"}, [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  2158
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  2159
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  2160
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  2161
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2162
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  2163
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  2164
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  2165
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2166
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  2167
  in
blanchet@33192
  2168
    list_abs (outer,
blanchet@33192
  2169
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  2170
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192