src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Tue Feb 02 11:38:38 2010 +0100 (2010-02-02)
changeset 34982 7b8c366e34a2
parent 34936 c4f04bee79f3
child 34998 5e492a862b34
permissions -rw-r--r--
added support for nonstandard models to Nitpick (based on an idea by Koen Claessen) and did other fixes to Nitpick
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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 extended_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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    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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  val name_sep : string
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  val numeral_prefix : string
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  val skolem_prefix : string
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  val eval_prefix : string
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  val original_name : string -> string
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  val unbit_and_unbox_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 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 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_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_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 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 instantiate_type : theory -> typ -> typ -> typ -> typ
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  val is_real_datatype : theory -> string -> 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 -> 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 is_constr : theory -> styp -> bool
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  val is_stale_constr : theory -> 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 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 boxed_nth_sel_for_constr : extended_context -> styp -> int -> styp
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  val sel_no_from_name : string -> int
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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 : extended_context -> typ -> styp list
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  val boxed_datatype_constrs : extended_context -> typ -> styp list
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  val num_datatype_constrs : extended_context -> typ -> int
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  val constr_name_for_sel_like : string -> string
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  val boxed_constr_for_sel : extended_context -> styp -> styp
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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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    extended_context -> int -> int -> (typ * int) list -> typ -> int
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  val is_finite_type : extended_context -> typ -> bool
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  val all_axioms_of : theory -> term list * term list * term list
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  val arity_of_built_in_const : bool -> styp -> int option
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  val is_built_in_const : bool -> styp -> bool
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  val case_const_names : theory -> (string * int) list
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  val const_def_table : Proof.context -> 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 -> const_table
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  val const_psimp_table : Proof.context -> const_table
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  val inductive_intro_table : Proof.context -> 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 def_of_const : theory -> const_table -> styp -> term option
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  val is_inductive_pred : extended_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 merge_type_vars_in_terms : term list -> term list
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  val ground_types_in_type : extended_context -> typ -> typ list
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  val ground_types_in_terms : extended_context -> term list -> typ list
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  val format_type : int list -> int list -> typ -> typ
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  val format_term_type :
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    theory -> const_table -> (term option * int list) list -> term -> typ
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  val user_friendly_const :
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   extended_context -> string * string -> (term option * int list) list
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   -> styp -> term * typ
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  val assign_operator_for_const : styp -> string
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  val preprocess_term :
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    extended_context -> term -> ((term list * term list) * (bool * bool)) * term
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end;
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structure Nitpick_HOL : NITPICK_HOL =
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struct
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open Nitpick_Util
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type const_table = term list Symtab.table
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type special_fun = (styp * int list * term list) * styp
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type unrolled = styp * styp
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type wf_cache = (styp * (bool * bool)) list
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type extended_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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  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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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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(* term * term -> term *)
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fun s_conj (t1, @{const True}) = t1
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  | s_conj (@{const True}, t2) = t2
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  | s_conj (t1, t2) =
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    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
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    else HOLogic.mk_conj (t1, t2)
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fun s_disj (t1, @{const False}) = t1
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  | s_disj (@{const False}, t2) = t2
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  | s_disj (t1, t2) =
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    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
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    else HOLogic.mk_disj (t1, t2)
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(* term -> term -> term *)
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fun mk_exists v t =
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  HOLogic.exists_const (fastype_of v) $ lambda v (incr_boundvars 1 t)
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(* term -> term -> term list *)
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fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
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    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
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  | strip_connective _ t = [t]
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(* term -> term list * term *)
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fun strip_any_connective (t as (t0 $ t1 $ t2)) =
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    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
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      (strip_connective t0 t, t0)
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    else
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      ([t], @{const Not})
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  | strip_any_connective t = ([t], @{const Not})
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(* term -> term list *)
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val conjuncts = strip_connective @{const "op &"}
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val disjuncts = strip_connective @{const "op |"}
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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 nwf_prefix = nitpick_prefix ^ "nwf" ^ 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 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 bound_var_prefix = "b"
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val cong_var_prefix = "c"
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val iter_var_prefix = "i"
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val val_var_prefix = nitpick_prefix ^ "v"
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val arg_var_prefix = "x"
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(* int -> string *)
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fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
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fun special_prefix_for j = special_prefix ^ string_of_int j ^ name_sep
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(* int -> int -> string *)
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fun skolem_prefix_for k j =
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  skolem_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
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fun uncurry_prefix_for k j =
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  uncurry_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
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(* string -> string * string *)
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val strip_first_name_sep =
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  Substring.full #> Substring.position name_sep ##> Substring.triml 1
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  #> pairself Substring.string
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(* string -> string *)
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fun original_name s =
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  if String.isPrefix nitpick_prefix s then
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    case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
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  else
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    s
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val after_name_sep = snd o strip_first_name_sep
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(* When you add constants to these lists, make sure to handle them in
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   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
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   well. *)
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val built_in_consts =
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  [(@{const_name all}, 1),
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   (@{const_name "=="}, 2),
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   (@{const_name "==>"}, 2),
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   (@{const_name Pure.conjunction}, 2),
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   (@{const_name Trueprop}, 1),
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   (@{const_name Not}, 1),
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   (@{const_name False}, 0),
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   (@{const_name True}, 0),
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   (@{const_name All}, 1),
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   (@{const_name Ex}, 1),
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   (@{const_name "op ="}, 2),
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   (@{const_name "op &"}, 2),
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   (@{const_name "op |"}, 2),
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   (@{const_name "op -->"}, 2),
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   (@{const_name If}, 3),
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   (@{const_name Let}, 2),
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   (@{const_name Unity}, 0),
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   (@{const_name Pair}, 2),
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   303
   (@{const_name fst}, 1),
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   304
   (@{const_name snd}, 1),
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   305
   (@{const_name Id}, 0),
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   306
   (@{const_name insert}, 2),
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   307
   (@{const_name converse}, 1),
blanchet@33192
   308
   (@{const_name trancl}, 1),
blanchet@33192
   309
   (@{const_name rel_comp}, 2),
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   310
   (@{const_name image}, 2),
blanchet@33192
   311
   (@{const_name Suc}, 0),
blanchet@33192
   312
   (@{const_name finite}, 1),
blanchet@33192
   313
   (@{const_name nat}, 0),
blanchet@33192
   314
   (@{const_name zero_nat_inst.zero_nat}, 0),
blanchet@33192
   315
   (@{const_name one_nat_inst.one_nat}, 0),
blanchet@33192
   316
   (@{const_name plus_nat_inst.plus_nat}, 0),
blanchet@33192
   317
   (@{const_name minus_nat_inst.minus_nat}, 0),
blanchet@33192
   318
   (@{const_name times_nat_inst.times_nat}, 0),
blanchet@33192
   319
   (@{const_name div_nat_inst.div_nat}, 0),
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   320
   (@{const_name ord_nat_inst.less_nat}, 2),
blanchet@33192
   321
   (@{const_name ord_nat_inst.less_eq_nat}, 2),
blanchet@33192
   322
   (@{const_name nat_gcd}, 0),
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   323
   (@{const_name nat_lcm}, 0),
blanchet@33192
   324
   (@{const_name zero_int_inst.zero_int}, 0),
blanchet@33192
   325
   (@{const_name one_int_inst.one_int}, 0),
blanchet@33192
   326
   (@{const_name plus_int_inst.plus_int}, 0),
blanchet@33192
   327
   (@{const_name minus_int_inst.minus_int}, 0),
blanchet@33192
   328
   (@{const_name times_int_inst.times_int}, 0),
blanchet@33192
   329
   (@{const_name div_int_inst.div_int}, 0),
blanchet@33571
   330
   (@{const_name uminus_int_inst.uminus_int}, 0),
blanchet@33192
   331
   (@{const_name ord_int_inst.less_int}, 2),
blanchet@33192
   332
   (@{const_name ord_int_inst.less_eq_int}, 2),
blanchet@34936
   333
   (@{const_name unknown}, 0),
blanchet@34936
   334
   (@{const_name is_unknown}, 1),
blanchet@33192
   335
   (@{const_name Tha}, 1),
blanchet@33192
   336
   (@{const_name Frac}, 0),
blanchet@33192
   337
   (@{const_name norm_frac}, 0)]
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   338
val built_in_descr_consts =
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   339
  [(@{const_name The}, 1),
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   340
   (@{const_name Eps}, 1)]
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   341
val built_in_typed_consts =
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   342
  [((@{const_name of_nat}, nat_T --> int_T), 0),
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   343
   ((@{const_name of_nat}, @{typ "unsigned_bit word => signed_bit word"}), 0)]
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   344
val built_in_set_consts =
blanchet@33192
   345
  [(@{const_name lower_semilattice_fun_inst.inf_fun}, 2),
blanchet@33192
   346
   (@{const_name upper_semilattice_fun_inst.sup_fun}, 2),
blanchet@33192
   347
   (@{const_name minus_fun_inst.minus_fun}, 2),
blanchet@33192
   348
   (@{const_name ord_fun_inst.less_eq_fun}, 2)]
blanchet@33192
   349
blanchet@33192
   350
(* typ -> typ *)
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   351
fun unbit_type @{typ "unsigned_bit word"} = nat_T
blanchet@34124
   352
  | unbit_type @{typ "signed_bit word"} = int_T
blanchet@34124
   353
  | unbit_type @{typ bisim_iterator} = nat_T
blanchet@34124
   354
  | unbit_type (Type (s, Ts as _ :: _)) = Type (s, map unbit_type Ts)
blanchet@34124
   355
  | unbit_type T = T
blanchet@34124
   356
fun unbit_and_unbox_type (Type (@{type_name fun_box}, Ts)) =
blanchet@34124
   357
    unbit_and_unbox_type (Type ("fun", Ts))
blanchet@34124
   358
  | unbit_and_unbox_type (Type (@{type_name pair_box}, Ts)) =
blanchet@34124
   359
    Type ("*", map unbit_and_unbox_type Ts)
blanchet@34124
   360
  | unbit_and_unbox_type @{typ "unsigned_bit word"} = nat_T
blanchet@34124
   361
  | unbit_and_unbox_type @{typ "signed_bit word"} = int_T
blanchet@34124
   362
  | unbit_and_unbox_type @{typ bisim_iterator} = nat_T
blanchet@34124
   363
  | unbit_and_unbox_type (Type (s, Ts as _ :: _)) =
blanchet@34124
   364
    Type (s, map unbit_and_unbox_type Ts)
blanchet@34124
   365
  | unbit_and_unbox_type T = T
blanchet@33192
   366
(* Proof.context -> typ -> string *)
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   367
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unbit_and_unbox_type
blanchet@33192
   368
blanchet@33192
   369
(* string -> string -> string *)
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   370
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@33192
   371
(* string -> string *)
blanchet@34121
   372
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   373
(* string -> term -> term *)
blanchet@33192
   374
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@33192
   375
(* term -> term *)
blanchet@34121
   376
val shorten_abs_vars = Term.map_abs_vars shortest_name
blanchet@33192
   377
(* string -> string *)
blanchet@34121
   378
fun short_name s =
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   379
  case space_explode name_sep s of
blanchet@33192
   380
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
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   381
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   382
(* typ -> typ *)
blanchet@34121
   383
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   384
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   385
  | shorten_names_in_type T = T
blanchet@33192
   386
(* term -> term *)
blanchet@34121
   387
val shorten_names_in_term =
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   388
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   389
  #> map_types shorten_names_in_type
blanchet@33192
   390
blanchet@33192
   391
(* theory -> typ * typ -> bool *)
blanchet@33192
   392
fun type_match thy (T1, T2) =
blanchet@33192
   393
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   394
  handle Type.TYPE_MATCH => false
blanchet@33192
   395
(* theory -> styp * styp -> bool *)
blanchet@33192
   396
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   397
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   398
(* theory -> term * term -> bool *)
blanchet@33192
   399
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   400
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   401
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@33192
   402
  | term_match thy (t1, t2) = t1 aconv t2
blanchet@33192
   403
blanchet@33192
   404
(* typ -> bool *)
blanchet@33192
   405
fun is_TFree (TFree _) = true
blanchet@33192
   406
  | is_TFree _ = false
blanchet@33192
   407
fun is_higher_order_type (Type ("fun", _)) = true
blanchet@33192
   408
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   409
  | is_higher_order_type _ = false
blanchet@33192
   410
fun is_fun_type (Type ("fun", _)) = true
blanchet@33192
   411
  | is_fun_type _ = false
blanchet@33192
   412
fun is_set_type (Type ("fun", [_, @{typ bool}])) = true
blanchet@33192
   413
  | is_set_type _ = false
blanchet@33192
   414
fun is_pair_type (Type ("*", _)) = true
blanchet@33192
   415
  | is_pair_type _ = false
blanchet@33192
   416
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   417
  | is_lfp_iterator_type _ = false
blanchet@33192
   418
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   419
  | is_gfp_iterator_type _ = false
blanchet@33192
   420
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@34121
   421
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@33192
   422
val is_integer_type =
blanchet@33192
   423
  member (op =) [nat_T, int_T, @{typ bisim_iterator}] orf is_fp_iterator_type
blanchet@34124
   424
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   425
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   426
  | is_word_type _ = false
blanchet@33192
   427
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   428
(* theory -> typ -> bool *)
blanchet@33192
   429
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   430
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   431
  | is_frac_type _ _ = false
blanchet@33192
   432
fun is_number_type thy = is_integer_type orf is_frac_type thy
blanchet@33192
   433
blanchet@33192
   434
(* bool -> styp -> typ *)
blanchet@33192
   435
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   436
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   437
        binder_types T)
blanchet@33192
   438
(* typ -> styp *)
blanchet@33192
   439
fun const_for_iterator_type (Type (s, Ts)) = (after_name_sep s, Ts ---> bool_T)
blanchet@33192
   440
  | const_for_iterator_type T =
blanchet@33232
   441
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   442
blanchet@33192
   443
(* int -> typ -> typ * typ *)
blanchet@33192
   444
fun strip_n_binders 0 T = ([], T)
blanchet@33192
   445
  | strip_n_binders n (Type ("fun", [T1, T2])) =
blanchet@33192
   446
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   447
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@33192
   448
    strip_n_binders n (Type ("fun", Ts))
blanchet@33232
   449
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   450
(* typ -> typ *)
blanchet@33192
   451
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   452
blanchet@33192
   453
(* typ -> int *)
blanchet@33192
   454
fun num_factors_in_type (Type ("*", [T1, T2])) =
blanchet@33192
   455
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   456
  | num_factors_in_type _ = 1
blanchet@33192
   457
fun num_binder_types (Type ("fun", [_, T2])) = 1 + num_binder_types T2
blanchet@33192
   458
  | num_binder_types _ = 0
blanchet@33192
   459
(* typ -> typ list *)
blanchet@33192
   460
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   461
fun maybe_curried_binder_types T =
blanchet@33192
   462
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   463
blanchet@33192
   464
(* typ -> term list -> term *)
blanchet@33192
   465
fun mk_flat_tuple _ [t] = t
blanchet@33192
   466
  | mk_flat_tuple (Type ("*", [T1, T2])) (t :: ts) =
blanchet@33192
   467
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   468
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   469
(* int -> term -> term list *)
blanchet@33192
   470
fun dest_n_tuple 1 t = [t]
blanchet@33192
   471
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   472
blanchet@33192
   473
(* int -> typ -> typ list *)
blanchet@33192
   474
fun dest_n_tuple_type 1 T = [T]
blanchet@33192
   475
  | dest_n_tuple_type n (Type (_, [T1, T2])) =
blanchet@33192
   476
    T1 :: dest_n_tuple_type (n - 1) T2
blanchet@33232
   477
  | dest_n_tuple_type _ T =
blanchet@33232
   478
    raise TYPE ("Nitpick_HOL.dest_n_tuple_type", [T], [])
blanchet@33192
   479
blanchet@34121
   480
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   481
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@34121
   482
(* string -> bool *)
blanchet@34121
   483
val is_basic_datatype =
blanchet@34121
   484
    member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@34121
   485
                   @{type_name nat}, @{type_name int},
blanchet@34121
   486
                   "Code_Numeral.code_numeral"]
blanchet@34121
   487
blanchet@33192
   488
(* theory -> typ -> typ -> typ -> typ *)
blanchet@33192
   489
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   490
  Same.commit (Envir.subst_type_same
blanchet@33192
   491
                   (Sign.typ_match thy (Logic.varifyT T1, T1') Vartab.empty))
blanchet@33192
   492
              (Logic.varifyT T2)
blanchet@33192
   493
  handle Type.TYPE_MATCH =>
blanchet@33232
   494
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@33192
   495
blanchet@33192
   496
(* theory -> typ -> typ -> styp *)
blanchet@33192
   497
fun repair_constr_type thy body_T' T =
blanchet@33192
   498
  instantiate_type thy (body_type T) body_T' T
blanchet@33192
   499
blanchet@33192
   500
(* string -> (string * string) list -> theory -> theory *)
blanchet@33192
   501
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   502
  let
blanchet@33583
   503
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   504
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   505
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   506
(* string -> theory -> theory *)
blanchet@33192
   507
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   508
blanchet@33192
   509
(* typ -> string -> styp list -> theory -> theory *)
blanchet@33192
   510
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   511
  let
blanchet@33583
   512
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   513
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   514
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   515
    val _ =
blanchet@34936
   516
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@34936
   517
         co_s <> "fun" andalso not (is_basic_datatype co_s) then
blanchet@34121
   518
        ()
blanchet@34121
   519
      else
blanchet@34121
   520
        raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   521
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   522
                                   codatatypes
blanchet@33583
   523
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   524
(* typ -> theory -> theory *)
blanchet@33192
   525
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   526
blanchet@33192
   527
type typedef_info =
blanchet@33192
   528
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@33192
   529
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@33876
   530
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@33192
   531
blanchet@33192
   532
(* theory -> string -> typedef_info *)
blanchet@33192
   533
fun typedef_info thy s =
blanchet@33192
   534
  if is_frac_type thy (Type (s, [])) then
blanchet@33192
   535
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@33192
   536
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@33192
   537
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@33192
   538
                          |> Logic.varify,
blanchet@33876
   539
          set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@33192
   540
  else case Typedef.get_info thy s of
blanchet@33876
   541
    SOME {abs_type, rep_type, Abs_name, Rep_name, set_def, Rep, Abs_inverse,
blanchet@33876
   542
          Rep_inverse, ...} =>
blanchet@33192
   543
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@33192
   544
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@33876
   545
          set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@33876
   546
          Rep_inverse = SOME Rep_inverse}
blanchet@33192
   547
  | NONE => NONE
blanchet@33192
   548
blanchet@33192
   549
(* theory -> string -> bool *)
blanchet@33192
   550
val is_typedef = is_some oo typedef_info
blanchet@33192
   551
val is_real_datatype = is_some oo Datatype.get_info
blanchet@33192
   552
(* theory -> typ -> bool *)
blanchet@34982
   553
fun is_quot_type _ (Type ("IntEx.my_int", _)) = true (* FIXME *)
blanchet@34936
   554
  | is_quot_type _ _ = false
blanchet@33192
   555
fun is_codatatype thy (T as Type (s, _)) =
blanchet@33583
   556
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   557
               |> Option.map snd |> these))
blanchet@33192
   558
  | is_codatatype _ _ = false
blanchet@33192
   559
fun is_pure_typedef thy (T as Type (s, _)) =
blanchet@33192
   560
    is_typedef thy s andalso
blanchet@34936
   561
    not (is_real_datatype thy s orelse is_quot_type thy T orelse
blanchet@34936
   562
         is_codatatype thy T orelse is_record_type T orelse is_integer_type T)
blanchet@33192
   563
  | is_pure_typedef _ _ = false
blanchet@33192
   564
fun is_univ_typedef thy (Type (s, _)) =
blanchet@33192
   565
    (case typedef_info thy s of
blanchet@33192
   566
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@33192
   567
       (case set_def of
blanchet@33192
   568
          SOME thm =>
blanchet@33192
   569
          try (fst o dest_Const o snd o Logic.dest_equals o prop_of) thm
blanchet@33192
   570
        | NONE =>
blanchet@33192
   571
          try (fst o dest_Const o snd o HOLogic.dest_mem
blanchet@33864
   572
               o HOLogic.dest_Trueprop) prop_of_Rep) = SOME @{const_name top}
blanchet@33192
   573
     | NONE => false)
blanchet@33192
   574
  | is_univ_typedef _ _ = false
blanchet@33192
   575
fun is_datatype thy (T as Type (s, _)) =
blanchet@34936
   576
    (is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind} orelse
blanchet@34936
   577
     is_quot_type thy T) andalso
blanchet@34936
   578
    not (is_basic_datatype s)
blanchet@33192
   579
  | is_datatype _ _ = false
blanchet@33192
   580
blanchet@33192
   581
(* theory -> typ -> (string * typ) list * (string * typ) *)
blanchet@33192
   582
fun all_record_fields thy T =
blanchet@33192
   583
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   584
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   585
  end
blanchet@33192
   586
  handle TYPE _ => []
blanchet@33192
   587
(* styp -> bool *)
blanchet@33192
   588
fun is_record_constr (x as (s, T)) =
blanchet@33192
   589
  String.isSuffix Record.extN s andalso
blanchet@33192
   590
  let val dataT = body_type T in
blanchet@33192
   591
    is_record_type dataT andalso
blanchet@33192
   592
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   593
  end
blanchet@33192
   594
(* theory -> typ -> int *)
blanchet@33192
   595
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   596
(* theory -> string -> typ -> int *)
blanchet@33192
   597
fun no_of_record_field thy s T1 =
blanchet@34121
   598
  find_index (curry (op =) s o fst)
blanchet@34121
   599
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@33192
   600
(* theory -> styp -> bool *)
blanchet@33192
   601
fun is_record_get thy (s, Type ("fun", [T1, _])) =
blanchet@34121
   602
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   603
  | is_record_get _ _ = false
blanchet@33192
   604
fun is_record_update thy (s, T) =
blanchet@33192
   605
  String.isSuffix Record.updateN s andalso
blanchet@34121
   606
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   607
         (all_record_fields thy (body_type T))
blanchet@33192
   608
  handle TYPE _ => false
blanchet@33192
   609
fun is_abs_fun thy (s, Type ("fun", [_, Type (s', _)])) =
blanchet@33192
   610
    (case typedef_info thy s' of
blanchet@33192
   611
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   612
     | NONE => false)
blanchet@33192
   613
  | is_abs_fun _ _ = false
blanchet@33192
   614
fun is_rep_fun thy (s, Type ("fun", [Type (s', _), _])) =
blanchet@33192
   615
    (case typedef_info thy s' of
blanchet@33192
   616
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   617
     | NONE => false)
blanchet@33192
   618
  | is_rep_fun _ _ = false
blanchet@34936
   619
(* Proof.context -> styp -> bool *)
blanchet@34982
   620
fun is_quot_abs_fun _ ("IntEx.abs_my_int", _) = true (* FIXME *)
blanchet@34936
   621
  | is_quot_abs_fun _ _ = false
blanchet@34982
   622
fun is_quot_rep_fun _ ("IntEx.rep_my_int", _) = true (* FIXME *)
blanchet@34936
   623
  | is_quot_rep_fun _ _ = false
blanchet@33192
   624
blanchet@33192
   625
(* theory -> styp -> styp *)
blanchet@33192
   626
fun mate_of_rep_fun thy (x as (_, Type ("fun", [T1 as Type (s', _), T2]))) =
blanchet@33192
   627
    (case typedef_info thy s' of
blanchet@33192
   628
       SOME {Abs_name, ...} => (Abs_name, Type ("fun", [T2, T1]))
blanchet@33232
   629
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   630
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@34936
   631
(* theory -> typ -> typ *)
blanchet@34936
   632
fun rep_type_for_quot_type _ (Type ("IntEx.my_int", [])) = @{typ "nat * nat"}
blanchet@34936
   633
  | rep_type_for_quot_type _ T =
blanchet@34936
   634
    raise TYPE ("Nitpick_HOL.rep_type_for_quot_type", [T], [])
blanchet@34936
   635
(* theory -> typ -> term *)
blanchet@34936
   636
fun equiv_relation_for_quot_type _ (Type ("IntEx.my_int", [])) =
blanchet@34936
   637
    Const ("IntEx.intrel", @{typ "(nat * nat) => (nat * nat) => bool"})
blanchet@34936
   638
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   639
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   640
blanchet@33192
   641
(* theory -> styp -> bool *)
blanchet@33192
   642
fun is_coconstr thy (s, T) =
blanchet@33192
   643
  let
blanchet@33583
   644
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   645
    val co_T = body_type T
blanchet@33192
   646
    val co_s = dest_Type co_T |> fst
blanchet@33192
   647
  in
blanchet@33192
   648
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   649
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   650
  end
blanchet@33192
   651
  handle TYPE ("dest_Type", _, _) => false
blanchet@33192
   652
fun is_constr_like thy (s, T) =
blanchet@34982
   653
  member (op =) [@{const_name FunBox}, @{const_name PairBox},
blanchet@34982
   654
                 @{const_name Quot}, @{const_name Zero_Rep},
blanchet@34982
   655
                 @{const_name Suc_Rep}] s orelse
blanchet@34124
   656
  let val (x as (s, T)) = (s, unbit_and_unbox_type T) in
blanchet@34936
   657
    Refute.is_IDT_constructor thy x orelse is_record_constr x orelse
blanchet@34936
   658
    (is_abs_fun thy x andalso is_pure_typedef thy (range_type T)) orelse
blanchet@34936
   659
    x = (@{const_name zero_nat_inst.zero_nat}, nat_T) orelse
blanchet@34936
   660
    is_coconstr thy x
blanchet@33192
   661
  end
blanchet@33581
   662
fun is_stale_constr thy (x as (_, T)) =
blanchet@34936
   663
  is_codatatype thy (body_type T) andalso is_constr_like thy x andalso
blanchet@34936
   664
  not (is_coconstr thy x)
blanchet@33192
   665
fun is_constr thy (x as (_, T)) =
blanchet@34936
   666
  is_constr_like thy x andalso
blanchet@34936
   667
  not (is_basic_datatype (fst (dest_Type (unbit_type (body_type T))))) andalso
blanchet@34936
   668
  not (is_stale_constr thy x)
blanchet@33192
   669
(* string -> bool *)
blanchet@33192
   670
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   671
val is_sel_like_and_no_discr =
blanchet@33192
   672
  String.isPrefix sel_prefix
blanchet@33192
   673
  orf (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   674
blanchet@33192
   675
datatype boxability =
blanchet@33192
   676
  InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
blanchet@33192
   677
blanchet@33192
   678
(* boxability -> boxability *)
blanchet@33192
   679
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   680
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   681
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   682
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   683
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   684
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   685
blanchet@33192
   686
(* extended_context -> boxability -> typ -> bool *)
blanchet@33192
   687
fun is_boxing_worth_it (ext_ctxt : extended_context) boxy T =
blanchet@33192
   688
  case T of
blanchet@33192
   689
    Type ("fun", _) =>
blanchet@34936
   690
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   691
    not (is_boolean_type (body_type T))
blanchet@33192
   692
  | Type ("*", Ts) =>
blanchet@34936
   693
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   694
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@34936
   695
     exists (is_boxing_worth_it ext_ctxt InPair)
blanchet@34936
   696
            (map (box_type ext_ctxt InPair) Ts))
blanchet@33192
   697
  | _ => false
blanchet@33192
   698
(* extended_context -> boxability -> string * typ list -> string *)
blanchet@33192
   699
and should_box_type (ext_ctxt as {thy, boxes, ...}) boxy (z as (s, Ts)) =
blanchet@33192
   700
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   701
    SOME (SOME box_me) => box_me
blanchet@33192
   702
  | _ => is_boxing_worth_it ext_ctxt boxy (Type z)
blanchet@33192
   703
(* extended_context -> boxability -> typ -> typ *)
blanchet@33192
   704
and box_type ext_ctxt boxy T =
blanchet@33192
   705
  case T of
blanchet@33192
   706
    Type (z as ("fun", [T1, T2])) =>
blanchet@34936
   707
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@34936
   708
       should_box_type ext_ctxt boxy z then
blanchet@33192
   709
      Type (@{type_name fun_box},
blanchet@33192
   710
            [box_type ext_ctxt InFunLHS T1, box_type ext_ctxt InFunRHS1 T2])
blanchet@33192
   711
    else
blanchet@33192
   712
      box_type ext_ctxt (in_fun_lhs_for boxy) T1
blanchet@33192
   713
      --> box_type ext_ctxt (in_fun_rhs_for boxy) T2
blanchet@33192
   714
  | Type (z as ("*", Ts)) =>
blanchet@34982
   715
    if boxy <> InConstr andalso boxy <> InSel
blanchet@34982
   716
       andalso should_box_type ext_ctxt boxy z then
blanchet@33192
   717
      Type (@{type_name pair_box}, map (box_type ext_ctxt InSel) Ts)
blanchet@33192
   718
    else
blanchet@33192
   719
      Type ("*", map (box_type ext_ctxt
blanchet@34121
   720
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   721
                           else InPair)) Ts)
blanchet@33192
   722
  | _ => T
blanchet@33192
   723
blanchet@33192
   724
(* styp -> styp *)
blanchet@33192
   725
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   726
blanchet@33192
   727
(* typ -> int *)
blanchet@33192
   728
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   729
(* string -> int -> string *)
blanchet@33192
   730
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   731
  if s = @{const_name Pair} then
blanchet@33192
   732
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   733
  else
blanchet@33192
   734
    sel_prefix_for n ^ s
blanchet@33192
   735
(* styp -> int -> styp *)
blanchet@33192
   736
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   737
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   738
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   739
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@33192
   740
(* extended_context -> styp -> int -> styp *)
blanchet@33192
   741
fun boxed_nth_sel_for_constr ext_ctxt =
blanchet@33192
   742
  apsnd (box_type ext_ctxt InSel) oo nth_sel_for_constr
blanchet@33192
   743
blanchet@33192
   744
(* string -> int *)
blanchet@33192
   745
fun sel_no_from_name s =
blanchet@33192
   746
  if String.isPrefix discr_prefix s then
blanchet@33192
   747
    ~1
blanchet@33192
   748
  else if String.isPrefix sel_prefix s then
blanchet@33192
   749
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   750
  else if s = @{const_name snd} then
blanchet@33192
   751
    1
blanchet@33192
   752
  else
blanchet@33192
   753
    0
blanchet@33192
   754
blanchet@33192
   755
(* typ list -> term -> int -> term *)
blanchet@33192
   756
fun eta_expand _ t 0 = t
blanchet@33192
   757
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   758
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   759
  | eta_expand Ts t n =
blanchet@33192
   760
    fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
blanchet@33192
   761
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   762
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   763
blanchet@33192
   764
(* term -> term *)
blanchet@33192
   765
fun extensionalize t =
blanchet@33192
   766
  case t of
blanchet@33192
   767
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   768
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   769
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   770
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   771
    end
blanchet@33192
   772
  | _ => t
blanchet@33192
   773
blanchet@33192
   774
(* typ -> term list -> term *)
blanchet@33192
   775
fun distinctness_formula T =
blanchet@33192
   776
  all_distinct_unordered_pairs_of
blanchet@33192
   777
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   778
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   779
blanchet@33192
   780
(* typ -> term *)
blanchet@33192
   781
fun zero_const T = Const (@{const_name zero_nat_inst.zero_nat}, T)
blanchet@33192
   782
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   783
blanchet@34982
   784
(* extended_context -> typ -> styp list *)
blanchet@34982
   785
fun uncached_datatype_constrs ({thy, stds, ...} : extended_context)
blanchet@34982
   786
                              (T as Type (s, Ts)) =
blanchet@33583
   787
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@34982
   788
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   789
     | _ =>
blanchet@33581
   790
       if is_datatype thy T then
blanchet@33581
   791
         case Datatype.get_info thy s of
blanchet@33581
   792
           SOME {index, descr, ...} =>
blanchet@33581
   793
           let
blanchet@33581
   794
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   795
           in
blanchet@33581
   796
             map (fn (s', Us) =>
blanchet@33581
   797
                     (s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us
blanchet@33581
   798
                          ---> T)) constrs
blanchet@34982
   799
             |> (triple_lookup (type_match thy) stds T |> the |> not) ?
blanchet@34982
   800
                cons (@{const_name NonStd}, @{typ \<xi>} --> T)
blanchet@33581
   801
           end
blanchet@33581
   802
         | NONE =>
blanchet@33581
   803
           if is_record_type T then
blanchet@33581
   804
             let
blanchet@33581
   805
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   806
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   807
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   808
             in [(s', T')] end
blanchet@34936
   809
           else if is_quot_type thy T then
blanchet@34936
   810
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@33581
   811
           else case typedef_info thy s of
blanchet@33581
   812
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@33581
   813
             [(Abs_name, instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   814
           | NONE =>
blanchet@33581
   815
             if T = @{typ ind} then
blanchet@33581
   816
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   817
             else
blanchet@33581
   818
               []
blanchet@33581
   819
       else
blanchet@33581
   820
         [])
blanchet@33580
   821
  | uncached_datatype_constrs _ _ = []
blanchet@33192
   822
(* extended_context -> typ -> styp list *)
blanchet@34982
   823
fun datatype_constrs (ext_ctxt as {constr_cache, ...}) T =
blanchet@33580
   824
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   825
    SOME xs => xs
blanchet@33580
   826
  | NONE =>
blanchet@34982
   827
    let val xs = uncached_datatype_constrs ext_ctxt T in
blanchet@33580
   828
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   829
    end
blanchet@33580
   830
fun boxed_datatype_constrs ext_ctxt =
blanchet@33580
   831
  map (apsnd (box_type ext_ctxt InConstr)) o datatype_constrs ext_ctxt
blanchet@33580
   832
(* extended_context -> typ -> int *)
blanchet@33192
   833
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   834
blanchet@33192
   835
(* string -> string *)
blanchet@33192
   836
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   837
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   838
  | constr_name_for_sel_like s' = original_name s'
blanchet@33192
   839
(* extended_context -> styp -> styp *)
blanchet@33192
   840
fun boxed_constr_for_sel ext_ctxt (s', T') =
blanchet@33192
   841
  let val s = constr_name_for_sel_like s' in
blanchet@33192
   842
    AList.lookup (op =) (boxed_datatype_constrs ext_ctxt (domain_type T')) s
blanchet@33192
   843
    |> the |> pair s
blanchet@33192
   844
  end
blanchet@34982
   845
blanchet@33580
   846
(* extended_context -> styp -> term *)
blanchet@33580
   847
fun discr_term_for_constr ext_ctxt (x as (s, T)) =
blanchet@33192
   848
  let val dataT = body_type T in
blanchet@33192
   849
    if s = @{const_name Suc} then
blanchet@33192
   850
      Abs (Name.uu, dataT,
blanchet@33192
   851
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@33580
   852
    else if num_datatype_constrs ext_ctxt dataT >= 2 then
blanchet@33192
   853
      Const (discr_for_constr x)
blanchet@33192
   854
    else
blanchet@33192
   855
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   856
  end
blanchet@33580
   857
(* extended_context -> styp -> term -> term *)
blanchet@33580
   858
fun discriminate_value (ext_ctxt as {thy, ...}) (x as (_, T)) t =
blanchet@33192
   859
  case strip_comb t of
blanchet@33192
   860
    (Const x', args) =>
blanchet@33192
   861
    if x = x' then @{const True}
blanchet@33192
   862
    else if is_constr_like thy x' then @{const False}
blanchet@33580
   863
    else betapply (discr_term_for_constr ext_ctxt x, t)
blanchet@33580
   864
  | _ => betapply (discr_term_for_constr ext_ctxt x, t)
blanchet@33192
   865
blanchet@33192
   866
(* styp -> term -> term *)
blanchet@33192
   867
fun nth_arg_sel_term_for_constr (x as (s, T)) n =
blanchet@33192
   868
  let val (arg_Ts, dataT) = strip_type T in
blanchet@33192
   869
    if dataT = nat_T then
blanchet@33192
   870
      @{term "%n::nat. minus_nat_inst.minus_nat n one_nat_inst.one_nat"}
blanchet@33192
   871
    else if is_pair_type dataT then
blanchet@33192
   872
      Const (nth_sel_for_constr x n)
blanchet@33192
   873
    else
blanchet@33192
   874
      let
blanchet@33192
   875
        (* int -> typ -> int * term *)
blanchet@33192
   876
        fun aux m (Type ("*", [T1, T2])) =
blanchet@33192
   877
            let
blanchet@33192
   878
              val (m, t1) = aux m T1
blanchet@33192
   879
              val (m, t2) = aux m T2
blanchet@33192
   880
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   881
          | aux m T =
blanchet@33192
   882
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
   883
                    $ Bound 0)
blanchet@33192
   884
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
   885
                     (List.take (arg_Ts, n)) 0
blanchet@33192
   886
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
   887
  end
blanchet@33192
   888
(* theory -> styp -> term -> int -> typ -> term *)
blanchet@33192
   889
fun select_nth_constr_arg thy x t n res_T =
blanchet@33192
   890
  case strip_comb t of
blanchet@33192
   891
    (Const x', args) =>
blanchet@33192
   892
    if x = x' then nth args n
blanchet@33192
   893
    else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
blanchet@33192
   894
    else betapply (nth_arg_sel_term_for_constr x n, t)
blanchet@33192
   895
  | _ => betapply (nth_arg_sel_term_for_constr x n, t)
blanchet@33192
   896
blanchet@33192
   897
(* theory -> styp -> term list -> term *)
blanchet@33192
   898
fun construct_value _ x [] = Const x
blanchet@33192
   899
  | construct_value thy (x as (s, _)) args =
blanchet@33192
   900
    let val args = map Envir.eta_contract args in
blanchet@33192
   901
      case hd args of
blanchet@33192
   902
        Const (x' as (s', _)) $ t =>
blanchet@34936
   903
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
   904
           constr_name_for_sel_like s' = s andalso
blanchet@34936
   905
           forall (fn (n, t') => select_nth_constr_arg thy x t n dummyT = t')
blanchet@34936
   906
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
   907
          t
blanchet@33192
   908
        else
blanchet@33192
   909
          list_comb (Const x, args)
blanchet@33192
   910
      | _ => list_comb (Const x, args)
blanchet@33192
   911
    end
blanchet@33192
   912
blanchet@33580
   913
(* extended_context -> typ -> term -> term *)
blanchet@33580
   914
fun constr_expand (ext_ctxt as {thy, ...}) T t =
blanchet@33192
   915
  (case head_of t of
blanchet@33192
   916
     Const x => if is_constr_like thy x then t else raise SAME ()
blanchet@33192
   917
   | _ => raise SAME ())
blanchet@33192
   918
  handle SAME () =>
blanchet@33192
   919
         let
blanchet@33192
   920
           val x' as (_, T') =
blanchet@33192
   921
             if is_pair_type T then
blanchet@33192
   922
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@34124
   923
                 (@{const_name Pair}, T1 --> T2 --> T)
blanchet@33192
   924
               end
blanchet@33192
   925
             else
blanchet@34982
   926
               datatype_constrs ext_ctxt T |> hd
blanchet@33192
   927
           val arg_Ts = binder_types T'
blanchet@33192
   928
         in
blanchet@33192
   929
           list_comb (Const x', map2 (select_nth_constr_arg thy x' t)
blanchet@33192
   930
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
   931
         end
blanchet@33192
   932
blanchet@33192
   933
(* (typ * int) list -> typ -> int *)
blanchet@34123
   934
fun card_of_type assigns (Type ("fun", [T1, T2])) =
blanchet@34123
   935
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@34123
   936
  | card_of_type assigns (Type ("*", [T1, T2])) =
blanchet@34123
   937
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
   938
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
   939
  | card_of_type _ @{typ prop} = 2
blanchet@33192
   940
  | card_of_type _ @{typ bool} = 2
blanchet@33192
   941
  | card_of_type _ @{typ unit} = 1
blanchet@34123
   942
  | card_of_type assigns T =
blanchet@34123
   943
    case AList.lookup (op =) assigns T of
blanchet@33192
   944
      SOME k => k
blanchet@33192
   945
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
   946
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@33192
   947
(* int -> (typ * int) list -> typ -> int *)
blanchet@34123
   948
fun bounded_card_of_type max default_card assigns (Type ("fun", [T1, T2])) =
blanchet@33192
   949
    let
blanchet@34123
   950
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
   951
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
   952
    in
blanchet@33192
   953
      if k1 = max orelse k2 = max then max
blanchet@33192
   954
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
   955
    end
blanchet@34123
   956
  | bounded_card_of_type max default_card assigns (Type ("*", [T1, T2])) =
blanchet@33192
   957
    let
blanchet@34123
   958
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
   959
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
   960
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
   961
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
   962
    Int.min (max, if default_card = ~1 then
blanchet@34123
   963
                    card_of_type assigns T
blanchet@33192
   964
                  else
blanchet@34123
   965
                    card_of_type assigns T
blanchet@33232
   966
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
   967
                           default_card)
blanchet@33580
   968
(* extended_context -> int -> (typ * int) list -> typ -> int *)
blanchet@34123
   969
fun bounded_exact_card_of_type ext_ctxt max default_card assigns T =
blanchet@33192
   970
  let
blanchet@33192
   971
    (* typ list -> typ -> int *)
blanchet@33192
   972
    fun aux avoid T =
blanchet@34121
   973
      (if member (op =) avoid T then
blanchet@33192
   974
         0
blanchet@33192
   975
       else case T of
blanchet@33192
   976
         Type ("fun", [T1, T2]) =>
blanchet@33192
   977
         let
blanchet@33192
   978
           val k1 = aux avoid T1
blanchet@33192
   979
           val k2 = aux avoid T2
blanchet@33192
   980
         in
blanchet@33192
   981
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
   982
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
   983
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
   984
         end
blanchet@33192
   985
       | Type ("*", [T1, T2]) =>
blanchet@33192
   986
         let
blanchet@33192
   987
           val k1 = aux avoid T1
blanchet@33192
   988
           val k2 = aux avoid T2
blanchet@33192
   989
         in
blanchet@33192
   990
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
   991
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
   992
           else Int.min (max, k1 * k2)
blanchet@33192
   993
         end
blanchet@33192
   994
       | Type (@{type_name itself}, _) => 1
blanchet@33192
   995
       | @{typ prop} => 2
blanchet@33192
   996
       | @{typ bool} => 2
blanchet@33192
   997
       | @{typ unit} => 1
blanchet@33192
   998
       | Type _ =>
blanchet@33580
   999
         (case datatype_constrs ext_ctxt T of
blanchet@34126
  1000
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1001
                  else raise SAME ()
blanchet@33192
  1002
          | constrs =>
blanchet@33192
  1003
            let
blanchet@33192
  1004
              val constr_cards =
blanchet@33580
  1005
                datatype_constrs ext_ctxt T
blanchet@33192
  1006
                |> map (Integer.prod o map (aux (T :: avoid)) o binder_types
blanchet@33192
  1007
                        o snd)
blanchet@33192
  1008
            in
blanchet@34121
  1009
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1010
              else Integer.sum constr_cards
blanchet@33192
  1011
            end)
blanchet@33192
  1012
       | _ => raise SAME ())
blanchet@34123
  1013
      handle SAME () =>
blanchet@34123
  1014
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1015
  in Int.min (max, aux [] T) end
blanchet@33192
  1016
blanchet@33580
  1017
(* extended_context -> typ -> bool *)
blanchet@33580
  1018
fun is_finite_type ext_ctxt =
blanchet@34123
  1019
  not_equal 0 o bounded_exact_card_of_type ext_ctxt 1 2 []
blanchet@33192
  1020
blanchet@33192
  1021
(* term -> bool *)
blanchet@33192
  1022
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1023
  | is_ground_term (Const _) = true
blanchet@33192
  1024
  | is_ground_term _ = false
blanchet@33192
  1025
blanchet@33192
  1026
(* term -> word -> word *)
blanchet@33192
  1027
fun hashw_term (t1 $ t2) = Polyhash.hashw (hashw_term t1, hashw_term t2)
blanchet@33192
  1028
  | hashw_term (Const (s, _)) = Polyhash.hashw_string (s, 0w0)
blanchet@33192
  1029
  | hashw_term _ = 0w0
blanchet@33192
  1030
(* term -> int *)
blanchet@33192
  1031
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1032
blanchet@33192
  1033
(* term list -> (indexname * typ) list *)
blanchet@33192
  1034
fun special_bounds ts =
blanchet@33192
  1035
  fold Term.add_vars ts [] |> sort (TermOrd.fast_indexname_ord o pairself fst)
blanchet@33192
  1036
blanchet@33192
  1037
(* indexname * typ -> term -> term *)
blanchet@33192
  1038
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
  1039
blanchet@33571
  1040
(* theory -> string -> bool *)
blanchet@33571
  1041
fun is_funky_typedef_name thy s =
blanchet@34121
  1042
  member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@34936
  1043
                 @{type_name int}] s orelse
blanchet@34936
  1044
  is_frac_type thy (Type (s, []))
blanchet@33571
  1045
(* theory -> term -> bool *)
blanchet@33571
  1046
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
  1047
  | is_funky_typedef _ _ = false
blanchet@33192
  1048
(* term -> bool *)
blanchet@33192
  1049
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1050
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1051
  | is_arity_type_axiom _ = false
blanchet@33192
  1052
(* theory -> bool -> term -> bool *)
blanchet@33197
  1053
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
blanchet@33197
  1054
    is_typedef_axiom thy boring t2
blanchet@33197
  1055
  | is_typedef_axiom thy boring
blanchet@33192
  1056
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@33197
  1057
         $ Const (_, Type ("fun", [Type (s, _), _])) $ Const _ $ _)) =
blanchet@33571
  1058
    boring <> is_funky_typedef_name thy s andalso is_typedef thy s
blanchet@33192
  1059
  | is_typedef_axiom _ _ _ = false
blanchet@33192
  1060
blanchet@33192
  1061
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1062
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1063
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1064
   using "typedef_info". *)
blanchet@33192
  1065
(* theory -> (string * term) list -> string list -> term list * term list *)
blanchet@33192
  1066
fun partition_axioms_by_definitionality thy axioms def_names =
blanchet@33192
  1067
  let
blanchet@33192
  1068
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1069
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1070
    val nondefs =
blanchet@33192
  1071
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1072
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
blanchet@33192
  1073
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1074
blanchet@33197
  1075
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1076
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1077
   commands. *)
blanchet@33192
  1078
(* theory -> bool *)
blanchet@33192
  1079
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1080
blanchet@33192
  1081
(* term -> bool *)
blanchet@33192
  1082
val is_plain_definition =
blanchet@33192
  1083
  let
blanchet@33192
  1084
    (* term -> bool *)
blanchet@33192
  1085
    fun do_lhs t1 =
blanchet@33192
  1086
      case strip_comb t1 of
blanchet@34936
  1087
        (Const _, args) =>
blanchet@34936
  1088
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1089
      | _ => false
blanchet@33192
  1090
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1091
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1092
        do_lhs t1
blanchet@33192
  1093
      | do_eq _ = false
blanchet@33192
  1094
  in do_eq end
blanchet@33192
  1095
blanchet@33192
  1096
(* theory -> term list * term list * term list *)
blanchet@33192
  1097
fun all_axioms_of thy =
blanchet@33192
  1098
  let
blanchet@33192
  1099
    (* theory list -> term list *)
blanchet@33192
  1100
    val axioms_of_thys = maps Thm.axioms_of #> map (apsnd prop_of)
blanchet@33192
  1101
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1102
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1103
                    |> OrdList.make fast_string_ord
blanchet@33192
  1104
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1105
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1106
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1107
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1108
    val (built_in_defs, built_in_nondefs) =
blanchet@33192
  1109
      partition_axioms_by_definitionality thy built_in_axioms def_names
blanchet@33197
  1110
      ||> filter (is_typedef_axiom thy false)
blanchet@33192
  1111
    val (user_defs, user_nondefs) =
blanchet@33192
  1112
      partition_axioms_by_definitionality thy user_axioms def_names
blanchet@33197
  1113
    val (built_in_nondefs, user_nondefs) =
blanchet@33197
  1114
      List.partition (is_typedef_axiom thy false) user_nondefs
blanchet@33197
  1115
      |>> append built_in_nondefs
blanchet@34121
  1116
    val defs =
blanchet@34121
  1117
      (thy |> PureThy.all_thms_of
blanchet@34121
  1118
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@34121
  1119
           |> map (prop_of o snd) |> filter is_plain_definition) @
blanchet@34121
  1120
      user_defs @ built_in_defs
blanchet@33192
  1121
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1122
blanchet@33192
  1123
(* bool -> styp -> int option *)
blanchet@33192
  1124
fun arity_of_built_in_const fast_descrs (s, T) =
blanchet@33192
  1125
  if s = @{const_name If} then
blanchet@33192
  1126
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@33192
  1127
  else case AList.lookup (op =)
blanchet@33192
  1128
                (built_in_consts
blanchet@33192
  1129
                 |> fast_descrs ? append built_in_descr_consts) s of
blanchet@33192
  1130
    SOME n => SOME n
blanchet@33192
  1131
  | NONE =>
blanchet@33192
  1132
    case AList.lookup (op =) built_in_typed_consts (s, T) of
blanchet@33192
  1133
      SOME n => SOME n
blanchet@33192
  1134
    | NONE =>
blanchet@33192
  1135
      if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@33192
  1136
        AList.lookup (op =) built_in_set_consts s
blanchet@33192
  1137
      else
blanchet@33192
  1138
        NONE
blanchet@33192
  1139
(* bool -> styp -> bool *)
blanchet@33192
  1140
val is_built_in_const = is_some oo arity_of_built_in_const
blanchet@33192
  1141
blanchet@33192
  1142
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1143
   simplification rules (equational specifications). *)
blanchet@33192
  1144
(* term -> term *)
blanchet@33192
  1145
fun term_under_def t =
blanchet@33192
  1146
  case t of
blanchet@33192
  1147
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1148
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1149
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1150
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1151
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1152
  | t1 $ _ => term_under_def t1
blanchet@33192
  1153
  | _ => t
blanchet@33192
  1154
blanchet@33192
  1155
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
blanchet@33192
  1156
   traversal of the term, without which the wrong occurrence of a constant could
blanchet@33192
  1157
   be matched in the face of overloading. *)
blanchet@33192
  1158
(* theory -> bool -> const_table -> styp -> term list *)
blanchet@33192
  1159
fun def_props_for_const thy fast_descrs table (x as (s, _)) =
blanchet@33192
  1160
  if is_built_in_const fast_descrs x then
blanchet@33192
  1161
    []
blanchet@33192
  1162
  else
blanchet@33192
  1163
    these (Symtab.lookup table s)
blanchet@33192
  1164
    |> map_filter (try (Refute.specialize_type thy x))
blanchet@34121
  1165
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1166
blanchet@33743
  1167
(* theory -> term -> term option *)
blanchet@33192
  1168
fun normalized_rhs_of thy t =
blanchet@33192
  1169
  let
blanchet@33743
  1170
    (* term option -> term option *)
blanchet@33743
  1171
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@33743
  1172
      | aux (c as Const (@{const_name TYPE}, T)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1173
      | aux _ _ = NONE
blanchet@33192
  1174
    val (lhs, rhs) =
blanchet@33192
  1175
      case t of
blanchet@33192
  1176
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1177
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1178
        (t1, t2)
blanchet@33232
  1179
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1180
    val args = strip_comb lhs |> snd
blanchet@33743
  1181
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1182
blanchet@33192
  1183
(* theory -> const_table -> styp -> term option *)
blanchet@33192
  1184
fun def_of_const thy table (x as (s, _)) =
blanchet@33192
  1185
  if is_built_in_const false x orelse original_name s <> s then
blanchet@33192
  1186
    NONE
blanchet@33192
  1187
  else
blanchet@33192
  1188
    x |> def_props_for_const thy false table |> List.last
blanchet@33743
  1189
      |> normalized_rhs_of thy |> Option.map (prefix_abs_vars s)
blanchet@33192
  1190
    handle List.Empty => NONE
blanchet@33192
  1191
blanchet@33192
  1192
datatype fixpoint_kind = Lfp | Gfp | NoFp
blanchet@33192
  1193
blanchet@33192
  1194
(* term -> fixpoint_kind *)
blanchet@33192
  1195
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1196
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1197
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1198
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1199
blanchet@33192
  1200
(* theory -> const_table -> term -> bool *)
blanchet@33192
  1201
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1202
  let
blanchet@33192
  1203
    (* term -> bool *)
blanchet@33192
  1204
    fun is_good_arg (Bound _) = true
blanchet@33192
  1205
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1206
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1207
        s = @{const_name undefined}
blanchet@33192
  1208
      | is_good_arg _ = false
blanchet@33192
  1209
  in
blanchet@33192
  1210
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1211
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1212
      (case def_of_const thy table x of
blanchet@33192
  1213
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1214
       | NONE => false)
blanchet@33192
  1215
    | _ => false
blanchet@33192
  1216
  end
blanchet@33192
  1217
(* theory -> const_table -> term -> term *)
blanchet@33192
  1218
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1219
  map_aterms (fn t as Const x =>
blanchet@33192
  1220
                 (case def_of_const thy table x of
blanchet@33192
  1221
                    SOME t' =>
blanchet@33192
  1222
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1223
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1224
                      else t
blanchet@33192
  1225
                    end
blanchet@33192
  1226
                 | NONE => t)
blanchet@33192
  1227
               | t => t)
blanchet@33192
  1228
blanchet@33192
  1229
(* term -> string * term *)
blanchet@33192
  1230
fun pair_for_prop t =
blanchet@33192
  1231
  case term_under_def t of
blanchet@33192
  1232
    Const (s, _) => (s, t)
blanchet@33192
  1233
  | Free _ => raise NOT_SUPPORTED "local definitions"
blanchet@33232
  1234
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@33192
  1235
blanchet@33192
  1236
(* (Proof.context -> term list) -> Proof.context -> const_table *)
blanchet@33192
  1237
fun table_for get ctxt =
blanchet@33192
  1238
  get ctxt |> map pair_for_prop |> AList.group (op =) |> Symtab.make
blanchet@33192
  1239
blanchet@33192
  1240
(* theory -> (string * int) list *)
blanchet@33192
  1241
fun case_const_names thy =
blanchet@33192
  1242
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@33192
  1243
                  if is_basic_datatype dtype_s then
blanchet@33192
  1244
                    I
blanchet@33192
  1245
                  else
blanchet@33192
  1246
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1247
                                     |> the |> #3 |> length))
blanchet@33192
  1248
              (Datatype.get_all thy) [] @
blanchet@33583
  1249
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1250
blanchet@33192
  1251
(* Proof.context -> term list -> const_table *)
blanchet@33192
  1252
fun const_def_table ctxt ts =
blanchet@34126
  1253
  table_for (map prop_of o Nitpick_Defs.get) ctxt
blanchet@33192
  1254
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@33192
  1255
          (map pair_for_prop ts)
blanchet@33192
  1256
(* term list -> const_table *)
blanchet@33192
  1257
fun const_nondef_table ts =
blanchet@33192
  1258
  fold (fn t => append (map (fn s => (s, t)) (Term.add_const_names t []))) ts []
blanchet@33192
  1259
  |> AList.group (op =) |> Symtab.make
blanchet@33192
  1260
(* Proof.context -> const_table *)
blanchet@33192
  1261
val const_simp_table = table_for (map prop_of o Nitpick_Simps.get)
blanchet@33192
  1262
val const_psimp_table = table_for (map prop_of o Nitpick_Psimps.get)
blanchet@33192
  1263
(* Proof.context -> const_table -> const_table *)
blanchet@33192
  1264
fun inductive_intro_table ctxt def_table =
blanchet@33192
  1265
  table_for (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
blanchet@33192
  1266
                                                  def_table o prop_of)
blanchet@33192
  1267
             o Nitpick_Intros.get) ctxt
blanchet@33192
  1268
(* theory -> term list Inttab.table *)
blanchet@33192
  1269
fun ground_theorem_table thy =
blanchet@33192
  1270
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@33192
  1271
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@33192
  1272
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@33192
  1273
blanchet@33192
  1274
val basic_ersatz_table =
blanchet@33192
  1275
  [(@{const_name prod_case}, @{const_name split}),
blanchet@33192
  1276
   (@{const_name card}, @{const_name card'}),
blanchet@33192
  1277
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@33192
  1278
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@33192
  1279
   (@{const_name wf}, @{const_name wf'}),
blanchet@33192
  1280
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@33192
  1281
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@33192
  1282
blanchet@33192
  1283
(* theory -> (string * string) list *)
blanchet@33192
  1284
fun ersatz_table thy =
blanchet@33583
  1285
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@33192
  1286
blanchet@33192
  1287
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
blanchet@33192
  1288
fun add_simps simp_table s eqs =
blanchet@33192
  1289
  Unsynchronized.change simp_table
blanchet@33192
  1290
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@33192
  1291
blanchet@33192
  1292
(* Similar to "Refute.specialize_type" but returns all matches rather than only
blanchet@33192
  1293
   the first (preorder) match. *)
blanchet@33192
  1294
(* theory -> styp -> term -> term list *)
blanchet@33197
  1295
fun multi_specialize_type thy slack (x as (s, T)) t =
blanchet@33192
  1296
  let
blanchet@33192
  1297
    (* term -> (typ * term) list -> (typ * term) list *)
blanchet@33192
  1298
    fun aux (Const (s', T')) ys =
blanchet@33192
  1299
        if s = s' then
blanchet@33197
  1300
          ys |> (if AList.defined (op =) ys T' then
blanchet@33197
  1301
                   I
blanchet@33583
  1302
                 else
blanchet@33197
  1303
                  cons (T', Refute.monomorphic_term
blanchet@33197
  1304
                                (Sign.typ_match thy (T', T) Vartab.empty) t)
blanchet@33197
  1305
                  handle Type.TYPE_MATCH => I
blanchet@33197
  1306
                       | Refute.REFUTE _ =>
blanchet@33197
  1307
                         if slack then
blanchet@33197
  1308
                           I
blanchet@33197
  1309
                         else
blanchet@33197
  1310
                           raise NOT_SUPPORTED ("too much polymorphism in \
blanchet@33197
  1311
                                                \axiom involving " ^ quote s))
blanchet@33192
  1312
        else
blanchet@33192
  1313
          ys
blanchet@33192
  1314
      | aux _ ys = ys
blanchet@33192
  1315
  in map snd (fold_aterms aux t []) end
blanchet@33192
  1316
blanchet@33197
  1317
(* theory -> bool -> const_table -> styp -> term list *)
blanchet@33197
  1318
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@33197
  1319
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@33192
  1320
blanchet@34936
  1321
(* theory -> styp -> term list *)
blanchet@34936
  1322
fun inverse_axioms_for_rep_fun thy (x as (_, T)) =
blanchet@34936
  1323
  let val abs_T = domain_type T in
blanchet@34936
  1324
    typedef_info thy (fst (dest_Type abs_T)) |> the
blanchet@34936
  1325
    |> pairf #Abs_inverse #Rep_inverse
blanchet@34936
  1326
    |> pairself (Refute.specialize_type thy x o prop_of o the)
blanchet@34936
  1327
    ||> single |> op ::
blanchet@34936
  1328
  end
blanchet@33192
  1329
(* theory -> styp list -> term list *)
blanchet@34936
  1330
fun optimized_typedef_axioms thy (abs_z as (abs_s, abs_Ts)) =
blanchet@34936
  1331
  let val abs_T = Type abs_z in
blanchet@33192
  1332
    if is_univ_typedef thy abs_T then
blanchet@33192
  1333
      []
blanchet@33192
  1334
    else case typedef_info thy abs_s of
blanchet@33192
  1335
      SOME {abs_type, rep_type, Abs_name, Rep_name, prop_of_Rep, set_name,
blanchet@33192
  1336
            ...} =>
blanchet@33192
  1337
      let
blanchet@33192
  1338
        val rep_T = instantiate_type thy abs_type abs_T rep_type
blanchet@33192
  1339
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@33192
  1340
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@33192
  1341
        val set_t' =
blanchet@33192
  1342
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@33192
  1343
                      |> Refute.specialize_type thy (dest_Const rep_t)
blanchet@33192
  1344
                      |> HOLogic.dest_mem |> snd
blanchet@33192
  1345
      in
blanchet@33192
  1346
        [HOLogic.all_const abs_T
blanchet@33192
  1347
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@33192
  1348
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@33192
  1349
        |> map HOLogic.mk_Trueprop
blanchet@33192
  1350
      end
blanchet@33192
  1351
    | NONE => []
blanchet@33192
  1352
  end
blanchet@34936
  1353
fun optimized_quot_type_axioms thy abs_z =
blanchet@34936
  1354
  let
blanchet@34936
  1355
    val abs_T = Type abs_z
blanchet@34936
  1356
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@34936
  1357
    val equiv_rel = equiv_relation_for_quot_type thy abs_T
blanchet@34936
  1358
    val a_var = Var (("a", 0), abs_T)
blanchet@34936
  1359
    val x_var = Var (("x", 0), rep_T)
blanchet@34936
  1360
    val y_var = Var (("y", 0), rep_T)
blanchet@34936
  1361
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1362
    val sel_a_t = select_nth_constr_arg thy x a_var 0 rep_T
blanchet@34936
  1363
    val normal_t = Const (@{const_name quot_normal}, rep_T --> rep_T)
blanchet@34936
  1364
    val normal_x = normal_t $ x_var
blanchet@34936
  1365
    val normal_y = normal_t $ y_var
blanchet@34936
  1366
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@34936
  1367
  in
blanchet@34982
  1368
    [Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
blanchet@34936
  1369
     Logic.list_implies
blanchet@34982
  1370
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@34936
  1371
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@34936
  1372
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@34936
  1373
           Logic.mk_equals (normal_x, normal_y)),
blanchet@34936
  1374
     @{const "==>"}
blanchet@34936
  1375
         $ (HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)))
blanchet@34936
  1376
         $ (HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@33864
  1377
  end
blanchet@33192
  1378
blanchet@33192
  1379
(* theory -> int * styp -> term *)
blanchet@33192
  1380
fun constr_case_body thy (j, (x as (_, T))) =
blanchet@33192
  1381
  let val arg_Ts = binder_types T in
blanchet@33192
  1382
    list_comb (Bound j, map2 (select_nth_constr_arg thy x (Bound 0))
blanchet@33192
  1383
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1384
  end
blanchet@33580
  1385
(* extended_context -> typ -> int * styp -> term -> term *)
blanchet@33580
  1386
fun add_constr_case (ext_ctxt as {thy, ...}) res_T (j, x) res_t =
blanchet@34124
  1387
  Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@33580
  1388
  $ discriminate_value ext_ctxt x (Bound 0) $ constr_case_body thy (j, x)
blanchet@33580
  1389
  $ res_t
blanchet@33580
  1390
(* extended_context -> typ -> typ -> term *)
blanchet@33580
  1391
fun optimized_case_def (ext_ctxt as {thy, ...}) dataT res_T =
blanchet@33192
  1392
  let
blanchet@33580
  1393
    val xs = datatype_constrs ext_ctxt dataT
blanchet@34982
  1394
    val xs' = filter_out (fn (s, _) => s = @{const_name NonStd}) xs
blanchet@34982
  1395
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs'
blanchet@33192
  1396
  in
blanchet@34982
  1397
    (if length xs = length xs' then
blanchet@34982
  1398
       let
blanchet@34982
  1399
         val (xs'', x) = split_last xs'
blanchet@34982
  1400
       in
blanchet@34982
  1401
         constr_case_body thy (1, x)
blanchet@34982
  1402
         |> fold_rev (add_constr_case ext_ctxt res_T)
blanchet@34982
  1403
                     (length xs' downto 2 ~~ xs'')
blanchet@34982
  1404
       end
blanchet@34982
  1405
     else
blanchet@34982
  1406
       Const (@{const_name undefined}, dataT --> res_T) $ Bound 0
blanchet@34982
  1407
       |> fold_rev (add_constr_case ext_ctxt res_T)
blanchet@34982
  1408
                   (length xs' downto 1 ~~ xs'))
blanchet@33192
  1409
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1410
  end
blanchet@33192
  1411
blanchet@33580
  1412
(* extended_context -> string -> typ -> typ -> term -> term *)
blanchet@33580
  1413
fun optimized_record_get (ext_ctxt as {thy, ...}) s rec_T res_T t =
blanchet@34982
  1414
  let val constr_x = hd (datatype_constrs ext_ctxt rec_T) in
blanchet@33192
  1415
    case no_of_record_field thy s rec_T of
blanchet@33192
  1416
      ~1 => (case rec_T of
blanchet@33192
  1417
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1418
               let
blanchet@33192
  1419
                 val rec_T' = List.last Ts
blanchet@33192
  1420
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1421
               in
blanchet@33192
  1422
                 select_nth_constr_arg thy constr_x t j res_T
blanchet@33580
  1423
                 |> optimized_record_get ext_ctxt s rec_T' res_T
blanchet@33192
  1424
               end
blanchet@33232
  1425
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1426
                                []))
blanchet@33192
  1427
    | j => select_nth_constr_arg thy constr_x t j res_T
blanchet@33192
  1428
  end
blanchet@33580
  1429
(* extended_context -> string -> typ -> term -> term -> term *)
blanchet@33580
  1430
fun optimized_record_update (ext_ctxt as {thy, ...}) s rec_T fun_t rec_t =
blanchet@33192
  1431
  let
blanchet@34982
  1432
    val constr_x as (_, constr_T) = hd (datatype_constrs ext_ctxt rec_T)
blanchet@33192
  1433
    val Ts = binder_types constr_T
blanchet@33192
  1434
    val n = length Ts
blanchet@33192
  1435
    val special_j = no_of_record_field thy s rec_T
blanchet@33192
  1436
    val ts = map2 (fn j => fn T =>
blanchet@33192
  1437
                      let
blanchet@33192
  1438
                        val t = select_nth_constr_arg thy constr_x rec_t j T
blanchet@33192
  1439
                      in
blanchet@33192
  1440
                        if j = special_j then
blanchet@33192
  1441
                          betapply (fun_t, t)
blanchet@33192
  1442
                        else if j = n - 1 andalso special_j = ~1 then
blanchet@33580
  1443
                          optimized_record_update ext_ctxt s
blanchet@33192
  1444
                              (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@33192
  1445
                        else
blanchet@33192
  1446
                          t
blanchet@33192
  1447
                      end) (index_seq 0 n) Ts
blanchet@33192
  1448
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1449
blanchet@33192
  1450
(* Constants "c" whose definition is of the form "c == c'", where "c'" is also a
blanchet@33192
  1451
   constant, are said to be trivial. For those, we ignore the simplification
blanchet@33192
  1452
   rules and use the definition instead, to ensure that built-in symbols like
blanchet@33192
  1453
   "ord_nat_inst.less_eq_nat" are picked up correctly. *)
blanchet@33192
  1454
(* theory -> const_table -> styp -> bool *)
blanchet@33192
  1455
fun has_trivial_definition thy table x =
blanchet@33192
  1456
  case def_of_const thy table x of SOME (Const _) => true | _ => false
blanchet@33192
  1457
blanchet@33192
  1458
(* theory -> const_table -> string * typ -> fixpoint_kind *)
blanchet@33192
  1459
fun fixpoint_kind_of_const thy table x =
blanchet@33192
  1460
  if is_built_in_const false x then
blanchet@33192
  1461
    NoFp
blanchet@33192
  1462
  else
blanchet@33192
  1463
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@33192
  1464
    handle Option.Option => NoFp
blanchet@33192
  1465
blanchet@33192
  1466
(* extended_context -> styp -> bool *)
blanchet@33192
  1467
fun is_real_inductive_pred ({thy, fast_descrs, def_table, intro_table, ...}
blanchet@33192
  1468
                            : extended_context) x =
blanchet@34936
  1469
  not (null (def_props_for_const thy fast_descrs intro_table x)) andalso
blanchet@34936
  1470
  fixpoint_kind_of_const thy def_table x <> NoFp
blanchet@33192
  1471
fun is_real_equational_fun ({thy, fast_descrs, simp_table, psimp_table, ...}
blanchet@33192
  1472
                            : extended_context) x =
blanchet@33192
  1473
  exists (fn table => not (null (def_props_for_const thy fast_descrs table x)))
blanchet@33192
  1474
         [!simp_table, psimp_table]
blanchet@33192
  1475
fun is_inductive_pred ext_ctxt =
blanchet@33192
  1476
  is_real_inductive_pred ext_ctxt andf (not o is_real_equational_fun ext_ctxt)
blanchet@33192
  1477
fun is_equational_fun (ext_ctxt as {thy, def_table, ...}) =
blanchet@33192
  1478
  (is_real_equational_fun ext_ctxt orf is_real_inductive_pred ext_ctxt
blanchet@33192
  1479
   orf (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1480
  andf (not o has_trivial_definition thy def_table)
blanchet@33192
  1481
blanchet@33192
  1482
(* term * term -> term *)
blanchet@33192
  1483
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
blanchet@33192
  1484
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
blanchet@33192
  1485
  | s_betapply p = betapply p
blanchet@33192
  1486
(* term * term list -> term *)
blanchet@33192
  1487
val s_betapplys = Library.foldl s_betapply
blanchet@33192
  1488
blanchet@33192
  1489
(* term -> term *)
blanchet@33192
  1490
fun lhs_of_equation t =
blanchet@33192
  1491
  case t of
blanchet@33192
  1492
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1493
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1494
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1495
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@33192
  1496
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1497
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1498
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1499
  | _ => NONE
blanchet@33192
  1500
(* theory -> term -> bool *)
blanchet@33192
  1501
fun is_constr_pattern _ (Bound _) = true
blanchet@33864
  1502
  | is_constr_pattern _ (Var _) = true
blanchet@33192
  1503
  | is_constr_pattern thy t =
blanchet@33192
  1504
    case strip_comb t of
blanchet@33192
  1505
      (Const (x as (s, _)), args) =>
blanchet@33192
  1506
      is_constr_like thy x andalso forall (is_constr_pattern thy) args
blanchet@33192
  1507
    | _ => false
blanchet@33192
  1508
fun is_constr_pattern_lhs thy t =
blanchet@33192
  1509
  forall (is_constr_pattern thy) (snd (strip_comb t))
blanchet@33192
  1510
fun is_constr_pattern_formula thy t =
blanchet@33192
  1511
  case lhs_of_equation t of
blanchet@33192
  1512
    SOME t' => is_constr_pattern_lhs thy t'
blanchet@33192
  1513
  | NONE => false
blanchet@33192
  1514
blanchet@33747
  1515
val unfold_max_depth = 255
blanchet@33747
  1516
val axioms_max_depth = 255
blanchet@33192
  1517
blanchet@33192
  1518
(* extended_context -> term -> term *)
blanchet@33192
  1519
fun unfold_defs_in_term (ext_ctxt as {thy, destroy_constrs, fast_descrs,
blanchet@33192
  1520
                                      case_names, def_table, ground_thm_table,
blanchet@33192
  1521
                                      ersatz_table, ...}) =
blanchet@33192
  1522
  let
blanchet@33192
  1523
    (* int -> typ list -> term -> term *)
blanchet@33192
  1524
    fun do_term depth Ts t =
blanchet@33192
  1525
      case t of
blanchet@33192
  1526
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@33192
  1527
                      Type ("fun", [_, ran_T]))) $ t1 =>
blanchet@33192
  1528
        ((if is_number_type thy ran_T then
blanchet@33192
  1529
            let
blanchet@33192
  1530
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1531
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1532
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1533
            in
blanchet@33192
  1534
              if is_integer_type ran_T then
blanchet@33192
  1535
                Const (s, ran_T)
blanchet@33192
  1536
              else
blanchet@33192
  1537
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1538
                                  $ Const (s, int_T))
blanchet@33192
  1539
            end
blanchet@33192
  1540
            handle TERM _ => raise SAME ()
blanchet@33192
  1541
          else
blanchet@33192
  1542
            raise SAME ())
blanchet@33192
  1543
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1544
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1545
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@33192
  1546
      | (t0 as Const (x as (@{const_name Sigma}, T))) $ t1
blanchet@33192
  1547
        $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1548
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1549
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1550
      | Const (x as (@{const_name distinct},
blanchet@33192
  1551
               Type ("fun", [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1552
        $ (t1 as _ $ _) =>
blanchet@33192
  1553
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1554
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@33192
  1555
      | (t0 as Const (x as (@{const_name If}, _))) $ t1 $ t2 $ t3 =>
blanchet@34936
  1556
        if is_ground_term t1 andalso
blanchet@34936
  1557
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1558
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1559
          do_term depth Ts t2
blanchet@33192
  1560
        else
blanchet@33192
  1561
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1562
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1563
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1564
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1565
      | Const x => do_const depth Ts t x []
blanchet@33192
  1566
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1567
      | Free _ => t
blanchet@33192
  1568
      | Var _ => t
blanchet@33192
  1569
      | Bound _ => t
blanchet@33192
  1570
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1571
    (* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
blanchet@33192
  1572
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1573
        (Abs (Name.uu, body_type T,
blanchet@33192
  1574
              select_nth_constr_arg thy x (Bound 0) n res_T), [])
blanchet@33192
  1575
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@33192
  1576
        (select_nth_constr_arg thy x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1577
    (* int -> typ list -> term -> styp -> term list -> term *)
blanchet@33192
  1578
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1579
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1580
        SOME s' =>
blanchet@33192
  1581
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1582
      | NONE =>
blanchet@33192
  1583
        let
blanchet@33192
  1584
          val (const, ts) =
blanchet@33192
  1585
            if is_built_in_const fast_descrs x then
blanchet@33877
  1586
              (Const x, ts)
blanchet@33192
  1587
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1588
              SOME n =>
blanchet@33192
  1589
              let
blanchet@33192
  1590
                val (dataT, res_T) = nth_range_type n T
blanchet@33705
  1591
                                     |> pairf domain_type range_type
blanchet@33192
  1592
              in
blanchet@33580
  1593
                (optimized_case_def ext_ctxt dataT res_T
blanchet@33192
  1594
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1595
              end
blanchet@33192
  1596
            | _ =>
blanchet@33192
  1597
              if is_constr thy x then
blanchet@33192
  1598
                (Const x, ts)
blanchet@33581
  1599
              else if is_stale_constr thy x then
blanchet@34936
  1600
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1601
                                     \(\"" ^ s ^ "\")")
blanchet@34936
  1602
              else if is_quot_abs_fun thy x then
blanchet@34936
  1603
                let
blanchet@34936
  1604
                  val rep_T = domain_type T
blanchet@34936
  1605
                  val abs_T = range_type T
blanchet@34936
  1606
                in
blanchet@34936
  1607
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1608
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1609
                               $ (Const (@{const_name quot_normal},
blanchet@34936
  1610
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1611
                end
blanchet@34936
  1612
              else if is_quot_rep_fun thy x then
blanchet@34936
  1613
                let
blanchet@34936
  1614
                  val abs_T = domain_type T
blanchet@34936
  1615
                  val rep_T = range_type T
blanchet@34936
  1616
                  val x' = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1617
                in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
blanchet@33192
  1618
              else if is_record_get thy x then
blanchet@33192
  1619
                case length ts of
blanchet@33192
  1620
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@33580
  1621
                | _ => (optimized_record_get ext_ctxt s (domain_type T)
blanchet@34982
  1622
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1623
              else if is_record_update thy x then
blanchet@33192
  1624
                case length ts of
blanchet@33580
  1625
                  2 => (optimized_record_update ext_ctxt
blanchet@33580
  1626
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1627
                            (do_term depth Ts (hd ts))
blanchet@33580
  1628
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1629
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@33192
  1630
              else if is_rep_fun thy x then
blanchet@33192
  1631
                let val x' = mate_of_rep_fun thy x in
blanchet@33192
  1632
                  if is_constr thy x' then
blanchet@33192
  1633
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1634
                                                    (range_type T)
blanchet@33192
  1635
                  else
blanchet@33192
  1636
                    (Const x, ts)
blanchet@33192
  1637
                end
blanchet@33192
  1638
              else if is_equational_fun ext_ctxt x then
blanchet@33192
  1639
                (Const x, ts)
blanchet@33192
  1640
              else case def_of_const thy def_table x of
blanchet@33192
  1641
                SOME def =>
blanchet@33192
  1642
                if depth > unfold_max_depth then
blanchet@34124
  1643
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1644
                                   "too many nested definitions (" ^
blanchet@34124
  1645
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1646
                                   quote s)
blanchet@33192
  1647
                else if s = @{const_name wfrec'} then
blanchet@33192
  1648
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1649
                else
blanchet@33192
  1650
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1651
              | NONE => (Const x, ts)
blanchet@33192
  1652
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1653
  in do_term 0 [] end
blanchet@33192
  1654
blanchet@33580
  1655
(* extended_context -> typ -> term list *)
blanchet@33580
  1656
fun codatatype_bisim_axioms (ext_ctxt as {thy, ...}) T =
blanchet@33192
  1657
  let
blanchet@33580
  1658
    val xs = datatype_constrs ext_ctxt T
blanchet@33192
  1659
    val set_T = T --> bool_T
blanchet@33192
  1660
    val iter_T = @{typ bisim_iterator}
blanchet@34124
  1661
    val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1662
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1663
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1664
    val n_var_minus_1 =
blanchet@33192
  1665
      Const (@{const_name Tha}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1666
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1667
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1668
    val x_var = Var (("x", 0), T)
blanchet@33192
  1669
    val y_var = Var (("y", 0), T)
blanchet@33192
  1670
    (* styp -> int -> typ -> term *)
blanchet@33192
  1671
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1672
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1673
       else HOLogic.eq_const nth_T)
blanchet@33192
  1674
      $ select_nth_constr_arg thy x x_var n nth_T
blanchet@33192
  1675
      $ select_nth_constr_arg thy x y_var n nth_T
blanchet@33192
  1676
    (* styp -> term *)
blanchet@33192
  1677
    fun case_func (x as (_, T)) =
blanchet@33192
  1678
      let
blanchet@33192
  1679
        val arg_Ts = binder_types T
blanchet@33192
  1680
        val core_t =
blanchet@33580
  1681
          discriminate_value ext_ctxt x y_var ::
blanchet@33192
  1682
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1683
          |> foldr1 s_conj
blanchet@33192
  1684
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1685
  in
blanchet@33192
  1686
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1687
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@33580
  1688
        $ (betapplys (optimized_case_def ext_ctxt T bool_T,
blanchet@33192
  1689
                      map case_func xs @ [x_var]))),
blanchet@33192
  1690
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@34124
  1691
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@33192
  1692
        $ x_var $ Const (@{const_name bot_fun_inst.bot_fun}, set_T))]
blanchet@33192
  1693
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1694
  end
blanchet@33192
  1695
blanchet@33192
  1696
exception NO_TRIPLE of unit
blanchet@33192
  1697
blanchet@33192
  1698
(* theory -> styp -> term -> term list * term list * term *)
blanchet@33192
  1699
fun triple_for_intro_rule thy x t =
blanchet@33192
  1700
  let
blanchet@33192
  1701
    val prems = Logic.strip_imp_prems t |> map (ObjectLogic.atomize_term thy)
blanchet@33192
  1702
    val concl = Logic.strip_imp_concl t |> ObjectLogic.atomize_term thy
blanchet@34121
  1703
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@33192
  1704
    (* term -> bool *)
blanchet@34121
  1705
     val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  1706
  in
blanchet@33192
  1707
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1708
  end
blanchet@33192
  1709
blanchet@33192
  1710
(* term -> term *)
blanchet@33192
  1711
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1712
blanchet@33192
  1713
(* indexname * typ -> term list -> term -> term -> term *)
blanchet@33192
  1714
fun wf_constraint_for rel side concl main =
blanchet@33192
  1715
  let
blanchet@33192
  1716
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1717
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1718
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1719
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1720
  in
blanchet@33192
  1721
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1722
                      HOLogic.all_const T
blanchet@33192
  1723
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1724
                  (t, vars)
blanchet@33192
  1725
  end
blanchet@33192
  1726
blanchet@33192
  1727
(* indexname * typ -> term list * term list * term -> term *)
blanchet@33192
  1728
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1729
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1730
blanchet@33192
  1731
(* Proof.context -> Time.time option -> thm
blanchet@33192
  1732
   -> (Proof.context -> tactic -> tactic) -> bool *)
blanchet@33192
  1733
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1734
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1735
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1736
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1737
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1738
blanchet@33557
  1739
val max_cached_wfs = 100
blanchet@33192
  1740
val cached_timeout = Unsynchronized.ref (SOME Time.zeroTime)
blanchet@33192
  1741
val cached_wf_props : (term * bool) list Unsynchronized.ref =
blanchet@33192
  1742
  Unsynchronized.ref []
blanchet@33192
  1743
krauss@33351
  1744
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1745
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1746
blanchet@33192
  1747
(* extended_context -> const_table -> styp -> bool *)
blanchet@33580
  1748
fun uncached_is_well_founded_inductive_pred
blanchet@33192
  1749
        ({thy, ctxt, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@33192
  1750
         : extended_context) (x as (_, T)) =
blanchet@33192
  1751
  case def_props_for_const thy fast_descrs intro_table x of
blanchet@33580
  1752
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  1753
                      [Const x])
blanchet@33192
  1754
  | intro_ts =>
blanchet@33192
  1755
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1756
          |> filter_out (null o #2) of
blanchet@33192
  1757
       [] => true
blanchet@33192
  1758
     | triples =>
blanchet@33192
  1759
       let
blanchet@33192
  1760
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1761
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  1762
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  1763
         val rel = (("R", j), rel_T)
blanchet@33192
  1764
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1765
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1766
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1767
         val _ = if debug then
blanchet@33192
  1768
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1769
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1770
                 else
blanchet@33192
  1771
                   ()
blanchet@33192
  1772
       in
blanchet@34936
  1773
         if tac_timeout = (!cached_timeout) andalso
blanchet@34936
  1774
            length (!cached_wf_props) < max_cached_wfs then
blanchet@33557
  1775
           ()
blanchet@33557
  1776
         else
blanchet@33557
  1777
           (cached_wf_props := []; cached_timeout := tac_timeout);
blanchet@33192
  1778
         case AList.lookup (op =) (!cached_wf_props) prop of
blanchet@33192
  1779
           SOME wf => wf
blanchet@33192
  1780
         | NONE =>
blanchet@33192
  1781
           let
blanchet@33192
  1782
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  1783
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  1784
                             termination_tacs
blanchet@33192
  1785
           in Unsynchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1786
       end)
blanchet@33192
  1787
    handle List.Empty => false
blanchet@33192
  1788
         | NO_TRIPLE () => false
blanchet@33192
  1789
blanchet@33192
  1790
(* The type constraint below is a workaround for a Poly/ML bug. *)
blanchet@33192
  1791
blanchet@33192
  1792
(* extended_context -> styp -> bool *)
blanchet@33192
  1793
fun is_well_founded_inductive_pred
blanchet@33192
  1794
        (ext_ctxt as {thy, wfs, def_table, wf_cache, ...} : extended_context)
blanchet@33192
  1795
        (x as (s, _)) =
blanchet@33192
  1796
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1797
    SOME (SOME b) => b
blanchet@34936
  1798
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  1799
         case AList.lookup (op =) (!wf_cache) x of
blanchet@33192
  1800
                  SOME (_, wf) => wf
blanchet@33192
  1801
                | NONE =>
blanchet@33192
  1802
                  let
blanchet@33192
  1803
                    val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@33580
  1804
                    val wf = uncached_is_well_founded_inductive_pred ext_ctxt x
blanchet@33192
  1805
                  in
blanchet@33192
  1806
                    Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@33192
  1807
                  end
blanchet@33192
  1808
blanchet@33192
  1809
(* typ list -> typ -> typ -> term -> term *)
blanchet@33192
  1810
fun ap_curry [_] _ _ t = t
blanchet@33192
  1811
  | ap_curry arg_Ts tuple_T body_T t =
blanchet@33192
  1812
    let val n = length arg_Ts in
blanchet@33192
  1813
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1814
                incr_boundvars n t
blanchet@33192
  1815
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1816
    end
blanchet@33192
  1817
blanchet@33192
  1818
(* int -> term -> int *)
blanchet@33192
  1819
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1820
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@33192
  1821
  | num_occs_of_bound_in_term j (Abs (s, T, t')) =
blanchet@33192
  1822
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1823
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1824
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1825
blanchet@33192
  1826
(* term -> bool *)
blanchet@33192
  1827
val is_linear_inductive_pred_def =
blanchet@33192
  1828
  let
blanchet@33192
  1829
    (* int -> term -> bool *)
blanchet@33192
  1830
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  1831
        do_disjunct (j + 1) t2
blanchet@33192
  1832
      | do_disjunct j t =
blanchet@33192
  1833
        case num_occs_of_bound_in_term j t of
blanchet@33192
  1834
          0 => true
blanchet@34121
  1835
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts t)
blanchet@33192
  1836
        | _ => false
blanchet@33192
  1837
    (* term -> bool *)
blanchet@33192
  1838
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1839
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  1840
          case length xs of
blanchet@33192
  1841
            1 => false
blanchet@33192
  1842
          | n => forall (do_disjunct (n - 1)) (disjuncts body)
blanchet@33192
  1843
        end
blanchet@33192
  1844
      | do_lfp_def _ = false
blanchet@33192
  1845
  in do_lfp_def o strip_abs_body end
blanchet@33192
  1846
blanchet@33851
  1847
(* int -> int list list *)
blanchet@33851
  1848
fun n_ptuple_paths 0 = []
blanchet@33851
  1849
  | n_ptuple_paths 1 = []
blanchet@33851
  1850
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  1851
(* int -> typ -> typ -> term -> term *)
blanchet@33851
  1852
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  1853
blanchet@33192
  1854
(* term -> term * term *)
blanchet@33192
  1855
val linear_pred_base_and_step_rhss =
blanchet@33192
  1856
  let
blanchet@33192
  1857
    (* term -> term *)
blanchet@33192
  1858
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1859
        let
blanchet@33192
  1860
          val (xs, body) = strip_abs t2
blanchet@33192
  1861
          val arg_Ts = map snd (tl xs)
blanchet@33192
  1862
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  1863
          val j = length arg_Ts
blanchet@33192
  1864
          (* int -> term -> term *)
blanchet@33192
  1865
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  1866
              Const (@{const_name Ex}, T1)
blanchet@33192
  1867
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  1868
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  1869
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  1870
            | repair_rec j t =
blanchet@33192
  1871
              let val (head, args) = strip_comb t in
blanchet@33192
  1872
                if head = Bound j then
blanchet@33192
  1873
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  1874
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  1875
                else
blanchet@33192
  1876
                  t
blanchet@33192
  1877
              end
blanchet@33192
  1878
          val (nonrecs, recs) =
blanchet@34121
  1879
            List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
blanchet@33192
  1880
                           (disjuncts body)
blanchet@33192
  1881
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  1882
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  1883
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  1884
        in
blanchet@33192
  1885
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  1886
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  1887
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  1888
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  1889
        end
blanchet@33192
  1890
      | aux t =
blanchet@33232
  1891
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  1892
  in aux end
blanchet@33192
  1893
blanchet@33192
  1894
(* extended_context -> styp -> term -> term *)
blanchet@33851
  1895
fun starred_linear_pred_const (ext_ctxt as {simp_table, ...}) (x as (s, T))
blanchet@33851
  1896
                              def =
blanchet@33192
  1897
  let
blanchet@33192
  1898
    val j = maxidx_of_term def + 1
blanchet@33192
  1899
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1900
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1901
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  1902
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  1903
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  1904
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  1905
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  1906
    val set_T = tuple_T --> bool_T
blanchet@33192
  1907
    val curried_T = tuple_T --> set_T
blanchet@33192
  1908
    val uncurried_T = Type ("*", [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  1909
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  1910
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  1911
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  1912
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1913
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  1914
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  1915
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  1916
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1917
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  1918
  in
blanchet@33192
  1919
    list_abs (outer,
blanchet@33192
  1920
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  1921
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  1922
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  1923
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  1924
              $ list_comb (Const base_x, outer_bounds)
blanchet@33192
  1925
              |> ap_curry tuple_arg_Ts tuple_T bool_T)
blanchet@33192
  1926
    |> unfold_defs_in_term ext_ctxt
blanchet@33192
  1927
  end
blanchet@33192
  1928
blanchet@33192
  1929
(* extended_context -> bool -> styp -> term *)
blanchet@33192
  1930
fun unrolled_inductive_pred_const (ext_ctxt as {thy, star_linear_preds,
blanchet@33192
  1931
                                                def_table, simp_table, ...})
blanchet@33192
  1932
                                  gfp (x as (s, T)) =
blanchet@33192
  1933
  let
blanchet@33192
  1934
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  1935
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  1936
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  1937
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1938
  in
blanchet@33192
  1939
    if is_equational_fun ext_ctxt x' then
blanchet@33192
  1940
      unrolled_const (* already done *)
blanchet@34936
  1941
    else if not gfp andalso is_linear_inductive_pred_def def andalso
blanchet@34936
  1942
         star_linear_preds then
blanchet@33851
  1943
      starred_linear_pred_const ext_ctxt x def
blanchet@33192
  1944
    else
blanchet@33192
  1945
      let
blanchet@33192
  1946
        val j = maxidx_of_term def + 1
blanchet@33192
  1947
        val (outer, fp_app) = strip_abs def
blanchet@33192
  1948
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1949
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  1950
        val next = suc_const iter_T $ cur
blanchet@33192
  1951
        val rhs = case fp_app of
blanchet@33192
  1952
                    Const _ $ t =>
blanchet@33192
  1953
                    betapply (t, list_comb (Const x', next :: outer_bounds))
blanchet@33232
  1954
                  | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_\
blanchet@33232
  1955
                                     \const", [fp_app])
blanchet@33192
  1956
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  1957
        val all = outer @ inner
blanchet@33192
  1958
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  1959
        val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  1960
        val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
blanchet@33192
  1961
                 |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  1962
        val _ = add_simps simp_table s' [eq]
blanchet@33192
  1963
      in unrolled_const end
blanchet@33192
  1964
  end
blanchet@33192
  1965
blanchet@33192
  1966
(* extended_context -> styp -> term *)
blanchet@33192
  1967
fun raw_inductive_pred_axiom ({thy, def_table, ...} : extended_context) x =
blanchet@33192
  1968
  let
blanchet@33192
  1969
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1970
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1971
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1972
    val rhs = case fp_app of
blanchet@33192
  1973
                Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
blanchet@33232
  1974
              | _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom",
blanchet@33192
  1975
                                 [fp_app])
blanchet@33192
  1976
    val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  1977
    val all = outer @ inner
blanchet@33192
  1978
    val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  1979
    val j = maxidx_of_term def + 1
blanchet@33192
  1980
    val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  1981
  in
blanchet@33192
  1982
    HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
blanchet@33192
  1983
    |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  1984
  end
blanchet@33192
  1985
fun inductive_pred_axiom ext_ctxt (x as (s, T)) =
blanchet@33192
  1986
  if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
blanchet@33192
  1987
    let val x' = (after_name_sep s, T) in
blanchet@33192
  1988
      raw_inductive_pred_axiom ext_ctxt x' |> subst_atomic [(Const x', Const x)]
blanchet@33192
  1989
    end
blanchet@33192
  1990
  else
blanchet@33192
  1991
    raw_inductive_pred_axiom ext_ctxt x
blanchet@33192
  1992
blanchet@33192
  1993
(* extended_context -> styp -> term list *)
blanchet@33192
  1994
fun raw_equational_fun_axioms (ext_ctxt as {thy, fast_descrs, simp_table,
blanchet@33192
  1995
                                            psimp_table, ...}) (x as (s, _)) =
blanchet@33556
  1996
  case def_props_for_const thy fast_descrs (!simp_table) x of
blanchet@33192
  1997
    [] => (case def_props_for_const thy fast_descrs psimp_table x of
blanchet@33192
  1998
             [] => [inductive_pred_axiom ext_ctxt x]
blanchet@33192
  1999
           | psimps => psimps)
blanchet@33192
  2000
  | simps => simps
blanchet@33192
  2001
blanchet@33192
  2002
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
blanchet@33192
  2003
blanchet@33192
  2004
(* term list -> term list *)
blanchet@33556
  2005
fun merge_type_vars_in_terms ts =
blanchet@33192
  2006
  let
blanchet@33192
  2007
    (* typ -> (sort * string) list -> (sort * string) list *)
blanchet@33192
  2008
    fun add_type (TFree (s, S)) table =
blanchet@33192
  2009
        (case AList.lookup (op =) table S of
blanchet@33192
  2010
           SOME s' =>
blanchet@33192
  2011
           if string_ord (s', s) = LESS then AList.update (op =) (S, s') table
blanchet@33192
  2012
           else table
blanchet@33192
  2013
         | NONE => (S, s) :: table)
blanchet@33192
  2014
      | add_type _ table = table
blanchet@33192
  2015
    val table = fold (fold_types (fold_atyps add_type)) ts []
blanchet@33192
  2016
    (* typ -> typ *)
blanchet@33192
  2017
    fun coalesce (TFree (s, S)) = TFree (AList.lookup (op =) table S |> the, S)
blanchet@33192
  2018
      | coalesce T = T
blanchet@33192
  2019
  in map (map_types (map_atyps coalesce)) ts end
blanchet@33192
  2020
blanchet@33192
  2021
(* extended_context -> typ -> typ list -> typ list *)
blanchet@33192
  2022
fun add_ground_types ext_ctxt T accum =
blanchet@33192
  2023
  case T of
blanchet@33192
  2024
    Type ("fun", Ts) => fold (add_ground_types ext_ctxt) Ts accum
blanchet@33192
  2025
  | Type ("*", Ts) => fold (add_ground_types ext_ctxt) Ts accum
blanchet@33192
  2026
  | Type (@{type_name itself}, [T1]) => add_ground_types ext_ctxt T1 accum
blanchet@33192
  2027
  | Type (_, Ts) =>
blanchet@34121
  2028
    if member (op =) (@{typ prop} :: @{typ bool} :: @{typ unit} :: accum) T then
blanchet@33192
  2029
      accum
blanchet@33192
  2030
    else
blanchet@33192
  2031
      T :: accum
blanchet@33192
  2032
      |> fold (add_ground_types ext_ctxt)
blanchet@33192
  2033
              (case boxed_datatype_constrs ext_ctxt T of
blanchet@33192
  2034
                 [] => Ts
blanchet@33192
  2035
               | xs => map snd xs)
blanchet@33192
  2036
  | _ => insert (op =) T accum
blanchet@33192
  2037
(* extended_context -> typ -> typ list *)
blanchet@33192
  2038
fun ground_types_in_type ext_ctxt T = add_ground_types ext_ctxt T []
blanchet@33192
  2039
(* extended_context -> term list -> typ list *)
blanchet@33192
  2040
fun ground_types_in_terms ext_ctxt ts =
blanchet@33192
  2041
  fold (fold_types (add_ground_types ext_ctxt)) ts []
blanchet@33192
  2042
blanchet@33192
  2043
(* typ list -> int -> term -> bool *)
blanchet@33192
  2044
fun has_heavy_bounds_or_vars Ts level t =
blanchet@33192
  2045
  let
blanchet@33192
  2046
    (* typ list -> bool *)
blanchet@33192
  2047
    fun aux [] = false
blanchet@33192
  2048
      | aux [T] = is_fun_type T orelse is_pair_type T
blanchet@33192
  2049
      | aux _ = true
blanchet@33192
  2050
  in aux (map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t)) end
blanchet@33192
  2051
blanchet@33192
  2052
(* typ list -> int -> int -> int -> term -> term *)
blanchet@33192
  2053
fun fresh_value_var Ts k n j t =
blanchet@33192
  2054
  Var ((val_var_prefix ^ nat_subscript (n - j), k), fastype_of1 (Ts, t))
blanchet@33192
  2055
blanchet@33192
  2056
(* theory -> typ list -> bool -> int -> int -> term -> term list -> term list
blanchet@33192
  2057
   -> term * term list *)
blanchet@33192
  2058
fun pull_out_constr_comb thy Ts relax k level t args seen =
blanchet@33192
  2059
  let val t_comb = list_comb (t, args) in
blanchet@33192
  2060
    case t of
blanchet@33192
  2061
      Const x =>
blanchet@34936
  2062
      if not relax andalso is_constr thy x andalso
blanchet@34936
  2063
         not (is_fun_type (fastype_of1 (Ts, t_comb))) andalso
blanchet@34936
  2064
         has_heavy_bounds_or_vars Ts level t_comb andalso
blanchet@34936
  2065
         not (loose_bvar (t_comb, level)) then
blanchet@33192
  2066
        let
blanchet@34121
  2067
          val (j, seen) = case find_index (curry (op =) t_comb) seen of
blanchet@33192
  2068
                            ~1 => (0, t_comb :: seen)
blanchet@33192
  2069
                          | j => (j, seen)
blanchet@33192
  2070
        in (fresh_value_var Ts k (length seen) j t_comb, seen) end
blanchet@33192
  2071
      else
blanchet@33192
  2072
        (t_comb, seen)
blanchet@33192
  2073
    | _ => (t_comb, seen)
blanchet@33192
  2074
  end
blanchet@33192
  2075
blanchet@33192
  2076
(* (term -> term) -> typ list -> int -> term list -> term list *)
blanchet@33192
  2077
fun equations_for_pulled_out_constrs mk_eq Ts k seen =
blanchet@33192
  2078
  let val n = length seen in
blanchet@33192
  2079
    map2 (fn j => fn t => mk_eq (fresh_value_var Ts k n j t, t))
blanchet@33192
  2080
         (index_seq 0 n) seen
blanchet@33192
  2081
  end
blanchet@33192
  2082
blanchet@33192
  2083
(* theory -> bool -> term -> term *)
blanchet@33192
  2084
fun pull_out_universal_constrs thy def t =
blanchet@33192
  2085
  let
blanchet@33192
  2086
    val k = maxidx_of_term t + 1
blanchet@33192
  2087
    (* typ list -> bool -> term -> term list -> term list -> term * term list *)
blanchet@33192
  2088
    fun do_term Ts def t args seen =
blanchet@33192
  2089
      case t of
blanchet@33192
  2090
        (t0 as Const (@{const_name "=="}, _)) $ t1 $ t2 =>
blanchet@33978
  2091
        do_eq_or_imp Ts true def t0 t1 t2 seen
blanchet@33978
  2092
      | (t0 as @{const "==>"}) $ t1 $ t2 =>
blanchet@34982
  2093
        if def then (t, []) else do_eq_or_imp Ts false def t0 t1 t2 seen
blanchet@33192
  2094
      | (t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2 =>
blanchet@33978
  2095
        do_eq_or_imp Ts true def t0 t1 t2 seen
blanchet@33978
  2096
      | (t0 as @{const "op -->"}) $ t1 $ t2 =>
blanchet@33978
  2097
        do_eq_or_imp Ts false def t0 t1 t2 seen
blanchet@33192
  2098
      | Abs (s, T, t') =>
blanchet@33192
  2099
        let val (t', seen) = do_term (T :: Ts) def t' [] seen in
blanchet@33192
  2100
          (list_comb (Abs (s, T, t'), args), seen)
blanchet@33192
  2101
        end
blanchet@33192
  2102
      | t1 $ t2 =>
blanchet@33192
  2103
        let val (t2, seen) = do_term Ts def t2 [] seen in
blanchet@33192
  2104
          do_term Ts def t1 (t2 :: args) seen
blanchet@33192
  2105
        end
blanchet@33192
  2106
      | _ => pull_out_constr_comb thy Ts def k 0 t args seen
blanchet@33978
  2107
    (* typ list -> bool -> bool -> term -> term -> term -> term list
blanchet@33192
  2108
       -> term * term list *)
blanchet@33978
  2109
    and do_eq_or_imp Ts eq def t0 t1 t2 seen =
blanchet@33192
  2110
      let
blanchet@33978
  2111
        val (t2, seen) = if eq andalso def then (t2, seen)
blanchet@33978
  2112
                         else do_term Ts false t2 [] seen
blanchet@33192
  2113
        val (t1, seen) = do_term Ts false t1 [] seen
blanchet@33192
  2114
      in (t0 $ t1 $ t2, seen) end
blanchet@33192
  2115
    val (concl, seen) = do_term [] def t [] []
blanchet@33192
  2116
  in
blanchet@33192
  2117
    Logic.list_implies (equations_for_pulled_out_constrs Logic.mk_equals [] k
blanchet@33192
  2118
                                                         seen, concl)
blanchet@33192
  2119
  end
blanchet@33192
  2120
blanchet@33580
  2121
(* extended_context -> bool -> term -> term *)
blanchet@33580
  2122
fun destroy_pulled_out_constrs (ext_ctxt as {thy, ...}) axiom t =
blanchet@33192
  2123
  let
blanchet@33192
  2124
    (* styp -> int *)
blanchet@33192
  2125
    val num_occs_of_var =
blanchet@33192
  2126
      fold_aterms (fn Var z => (fn f => fn z' => f z' |> z = z' ? Integer.add 1)
blanchet@33192
  2127
                    | _ => I) t (K 0)
blanchet@33192
  2128
    (* bool -> term -> term *)
blanchet@33192
  2129
    fun aux careful ((t0 as Const (@{const_name "=="}, _)) $ t1 $ t2) =
blanchet@33192
  2130
        aux_eq careful true t0 t1 t2
blanchet@33192
  2131
      | aux careful ((t0 as @{const "==>"}) $ t1 $ t2) =
blanchet@33192
  2132
        t0 $ aux false t1 $ aux careful t2
blanchet@33192
  2133
      | aux careful ((t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2) =
blanchet@33192
  2134
        aux_eq careful true t0 t1 t2
blanchet@33192
  2135
      | aux careful ((t0 as @{const "op -->"}) $ t1 $ t2) =
blanchet@33192
  2136
        t0 $ aux false t1 $ aux careful t2
blanchet@33192
  2137
      | aux careful (Abs (s, T, t')) = Abs (s, T, aux careful t')
blanchet@33192
  2138
      | aux careful (t1 $ t2) = aux careful t1 $ aux careful t2
blanchet@33192
  2139
      | aux _ t = t
blanchet@33192
  2140
    (* bool -> bool -> term -> term -> term -> term *)
blanchet@33192
  2141
    and aux_eq careful pass1 t0 t1 t2 =
blanchet@34982
  2142
      ((if careful then