src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Mon Nov 23 17:26:32 2009 +0100 (2009-11-23)
changeset 33864 232daf7eafaf
parent 33851 ab6ecae44033
child 33876 62bcf6a52493
permissions -rw-r--r--
fix Nitpick soundness bugs related to integration (in particular, "code_numeral")
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(*  Title:      HOL/Nitpick/Tools/nitpick_hol.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2008, 2009
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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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    wfs: (styp option * bool option) list,
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    user_axioms: bool option,
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    debug: bool,
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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 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 short_name : string -> string
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  val short_const_name : string -> string
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  val shorten_const_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_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_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_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 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_precise_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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  wfs: (styp option * bool option) list,
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  user_axioms: bool option,
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  debug: bool,
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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) = if @{const False} mem [t1, t2] 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) = if @{const True} mem [t1, t2] 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 mem [@{const "op &"}, @{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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   (@{const_name fst}, 1),
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   (@{const_name snd}, 1),
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   (@{const_name Id}, 0),
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   (@{const_name insert}, 2),
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   (@{const_name converse}, 1),
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   (@{const_name trancl}, 1),
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   (@{const_name rel_comp}, 2),
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   (@{const_name image}, 2),
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   (@{const_name Suc}, 0),
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   (@{const_name finite}, 1),
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   (@{const_name nat}, 0),
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   (@{const_name zero_nat_inst.zero_nat}, 0),
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   (@{const_name one_nat_inst.one_nat}, 0),
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   (@{const_name plus_nat_inst.plus_nat}, 0),
blanchet@33192
   304
   (@{const_name minus_nat_inst.minus_nat}, 0),
blanchet@33192
   305
   (@{const_name times_nat_inst.times_nat}, 0),
blanchet@33192
   306
   (@{const_name div_nat_inst.div_nat}, 0),
blanchet@33192
   307
   (@{const_name div_nat_inst.mod_nat}, 0),
blanchet@33192
   308
   (@{const_name ord_nat_inst.less_nat}, 2),
blanchet@33192
   309
   (@{const_name ord_nat_inst.less_eq_nat}, 2),
blanchet@33192
   310
   (@{const_name nat_gcd}, 0),
blanchet@33192
   311
   (@{const_name nat_lcm}, 0),
blanchet@33192
   312
   (@{const_name zero_int_inst.zero_int}, 0),
blanchet@33192
   313
   (@{const_name one_int_inst.one_int}, 0),
blanchet@33192
   314
   (@{const_name plus_int_inst.plus_int}, 0),
blanchet@33192
   315
   (@{const_name minus_int_inst.minus_int}, 0),
blanchet@33192
   316
   (@{const_name times_int_inst.times_int}, 0),
blanchet@33192
   317
   (@{const_name div_int_inst.div_int}, 0),
blanchet@33192
   318
   (@{const_name div_int_inst.mod_int}, 0),
blanchet@33571
   319
   (@{const_name uminus_int_inst.uminus_int}, 0),
blanchet@33192
   320
   (@{const_name ord_int_inst.less_int}, 2),
blanchet@33192
   321
   (@{const_name ord_int_inst.less_eq_int}, 2),
blanchet@33192
   322
   (@{const_name Tha}, 1),
blanchet@33192
   323
   (@{const_name Frac}, 0),
blanchet@33192
   324
   (@{const_name norm_frac}, 0)]
blanchet@33192
   325
val built_in_descr_consts =
blanchet@33192
   326
  [(@{const_name The}, 1),
blanchet@33192
   327
   (@{const_name Eps}, 1)]
blanchet@33192
   328
val built_in_typed_consts =
blanchet@33192
   329
  [((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   330
val built_in_set_consts =
blanchet@33192
   331
  [(@{const_name lower_semilattice_fun_inst.inf_fun}, 2),
blanchet@33192
   332
   (@{const_name upper_semilattice_fun_inst.sup_fun}, 2),
blanchet@33192
   333
   (@{const_name minus_fun_inst.minus_fun}, 2),
blanchet@33192
   334
   (@{const_name ord_fun_inst.less_eq_fun}, 2)]
blanchet@33192
   335
blanchet@33192
   336
(* typ -> typ *)
blanchet@33192
   337
fun unbox_type (Type (@{type_name fun_box}, Ts)) =
blanchet@33192
   338
    Type ("fun", map unbox_type Ts)
blanchet@33192
   339
  | unbox_type (Type (@{type_name pair_box}, Ts)) =
blanchet@33192
   340
    Type ("*", map unbox_type Ts)
blanchet@33192
   341
  | unbox_type (Type (s, Ts)) = Type (s, map unbox_type Ts)
blanchet@33192
   342
  | unbox_type T = T
blanchet@33192
   343
(* Proof.context -> typ -> string *)
blanchet@33192
   344
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unbox_type
blanchet@33192
   345
blanchet@33192
   346
(* string -> string -> string *)
blanchet@33192
   347
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@33192
   348
(* string -> string *)
blanchet@33192
   349
fun short_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   350
(* string -> term -> term *)
blanchet@33192
   351
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@33192
   352
(* term -> term *)
blanchet@33192
   353
val shorten_abs_vars = Term.map_abs_vars short_name
blanchet@33192
   354
(* string -> string *)
blanchet@33192
   355
fun short_const_name s =
blanchet@33192
   356
  case space_explode name_sep s of
blanchet@33192
   357
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@33192
   358
  | ss => map short_name ss |> space_implode "_"
blanchet@33192
   359
(* term -> term *)
blanchet@33192
   360
val shorten_const_names_in_term =
blanchet@33192
   361
  map_aterms (fn Const (s, T) => Const (short_const_name s, T) | t => t)
blanchet@33192
   362
blanchet@33192
   363
(* theory -> typ * typ -> bool *)
blanchet@33192
   364
fun type_match thy (T1, T2) =
blanchet@33192
   365
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   366
  handle Type.TYPE_MATCH => false
blanchet@33192
   367
(* theory -> styp * styp -> bool *)
blanchet@33192
   368
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   369
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   370
(* theory -> term * term -> bool *)
blanchet@33192
   371
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   372
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@33192
   373
    const_match thy ((short_name s1, T1), (short_name s2, T2))
blanchet@33192
   374
  | term_match thy (t1, t2) = t1 aconv t2
blanchet@33192
   375
blanchet@33192
   376
(* typ -> bool *)
blanchet@33192
   377
fun is_TFree (TFree _) = true
blanchet@33192
   378
  | is_TFree _ = false
blanchet@33192
   379
fun is_higher_order_type (Type ("fun", _)) = true
blanchet@33192
   380
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   381
  | is_higher_order_type _ = false
blanchet@33192
   382
fun is_fun_type (Type ("fun", _)) = true
blanchet@33192
   383
  | is_fun_type _ = false
blanchet@33192
   384
fun is_set_type (Type ("fun", [_, @{typ bool}])) = true
blanchet@33192
   385
  | is_set_type _ = false
blanchet@33192
   386
fun is_pair_type (Type ("*", _)) = true
blanchet@33192
   387
  | is_pair_type _ = false
blanchet@33192
   388
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   389
  | is_lfp_iterator_type _ = false
blanchet@33192
   390
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   391
  | is_gfp_iterator_type _ = false
blanchet@33192
   392
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@33192
   393
val is_boolean_type = equal prop_T orf equal bool_T
blanchet@33192
   394
val is_integer_type =
blanchet@33192
   395
  member (op =) [nat_T, int_T, @{typ bisim_iterator}] orf is_fp_iterator_type
blanchet@33192
   396
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   397
(* theory -> typ -> bool *)
blanchet@33192
   398
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   399
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   400
  | is_frac_type _ _ = false
blanchet@33192
   401
fun is_number_type thy = is_integer_type orf is_frac_type thy
blanchet@33192
   402
blanchet@33192
   403
(* bool -> styp -> typ *)
blanchet@33192
   404
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   405
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   406
        binder_types T)
blanchet@33192
   407
(* typ -> styp *)
blanchet@33192
   408
fun const_for_iterator_type (Type (s, Ts)) = (after_name_sep s, Ts ---> bool_T)
blanchet@33192
   409
  | const_for_iterator_type T =
blanchet@33232
   410
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   411
blanchet@33192
   412
(* int -> typ -> typ * typ *)
blanchet@33192
   413
fun strip_n_binders 0 T = ([], T)
blanchet@33192
   414
  | strip_n_binders n (Type ("fun", [T1, T2])) =
blanchet@33192
   415
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   416
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@33192
   417
    strip_n_binders n (Type ("fun", Ts))
blanchet@33232
   418
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   419
(* typ -> typ *)
blanchet@33192
   420
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   421
blanchet@33192
   422
(* typ -> int *)
blanchet@33192
   423
fun num_factors_in_type (Type ("*", [T1, T2])) =
blanchet@33192
   424
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   425
  | num_factors_in_type _ = 1
blanchet@33192
   426
fun num_binder_types (Type ("fun", [_, T2])) = 1 + num_binder_types T2
blanchet@33192
   427
  | num_binder_types _ = 0
blanchet@33192
   428
(* typ -> typ list *)
blanchet@33192
   429
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   430
fun maybe_curried_binder_types T =
blanchet@33192
   431
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   432
blanchet@33192
   433
(* typ -> term list -> term *)
blanchet@33192
   434
fun mk_flat_tuple _ [t] = t
blanchet@33192
   435
  | mk_flat_tuple (Type ("*", [T1, T2])) (t :: ts) =
blanchet@33192
   436
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   437
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   438
(* int -> term -> term list *)
blanchet@33192
   439
fun dest_n_tuple 1 t = [t]
blanchet@33192
   440
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   441
blanchet@33192
   442
(* int -> typ -> typ list *)
blanchet@33192
   443
fun dest_n_tuple_type 1 T = [T]
blanchet@33192
   444
  | dest_n_tuple_type n (Type (_, [T1, T2])) =
blanchet@33192
   445
    T1 :: dest_n_tuple_type (n - 1) T2
blanchet@33232
   446
  | dest_n_tuple_type _ T =
blanchet@33232
   447
    raise TYPE ("Nitpick_HOL.dest_n_tuple_type", [T], [])
blanchet@33192
   448
blanchet@33192
   449
(* (typ * typ) list -> typ -> typ *)
blanchet@33192
   450
fun typ_subst [] T = T
blanchet@33192
   451
  | typ_subst ps T =
blanchet@33192
   452
    let
blanchet@33192
   453
      (* typ -> typ *)
blanchet@33192
   454
      fun subst T =
blanchet@33192
   455
        case AList.lookup (op =) ps T of
blanchet@33192
   456
          SOME T' => T'
blanchet@33192
   457
        | NONE => case T of Type (s, Ts) => Type (s, map subst Ts) | _ => T
blanchet@33192
   458
    in subst T end
blanchet@33192
   459
blanchet@33192
   460
(* theory -> typ -> typ -> typ -> typ *)
blanchet@33192
   461
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   462
  Same.commit (Envir.subst_type_same
blanchet@33192
   463
                   (Sign.typ_match thy (Logic.varifyT T1, T1') Vartab.empty))
blanchet@33192
   464
              (Logic.varifyT T2)
blanchet@33192
   465
  handle Type.TYPE_MATCH =>
blanchet@33232
   466
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@33192
   467
blanchet@33192
   468
(* theory -> typ -> typ -> styp *)
blanchet@33192
   469
fun repair_constr_type thy body_T' T =
blanchet@33192
   470
  instantiate_type thy (body_type T) body_T' T
blanchet@33192
   471
blanchet@33192
   472
(* string -> (string * string) list -> theory -> theory *)
blanchet@33192
   473
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   474
  let
blanchet@33583
   475
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   476
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   477
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   478
(* string -> theory -> theory *)
blanchet@33192
   479
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   480
blanchet@33192
   481
(* typ -> string -> styp list -> theory -> theory *)
blanchet@33192
   482
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   483
  let
blanchet@33583
   484
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   485
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   486
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   487
    val _ =
blanchet@33192
   488
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) then ()
blanchet@33232
   489
      else raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   490
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   491
                                   codatatypes
blanchet@33583
   492
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   493
(* typ -> theory -> theory *)
blanchet@33192
   494
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   495
blanchet@33192
   496
type typedef_info =
blanchet@33192
   497
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@33192
   498
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@33192
   499
   Rep_inverse: thm option}
blanchet@33192
   500
blanchet@33192
   501
(* theory -> string -> typedef_info *)
blanchet@33192
   502
fun typedef_info thy s =
blanchet@33192
   503
  if is_frac_type thy (Type (s, [])) then
blanchet@33192
   504
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@33192
   505
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@33192
   506
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@33192
   507
                          |> Logic.varify,
blanchet@33192
   508
          set_name = @{const_name Frac}, Rep_inverse = NONE}
blanchet@33192
   509
  else case Typedef.get_info thy s of
blanchet@33192
   510
    SOME {abs_type, rep_type, Abs_name, Rep_name, set_def, Rep, Rep_inverse,
blanchet@33192
   511
          ...} =>
blanchet@33192
   512
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@33192
   513
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@33192
   514
          set_name = set_prefix ^ s, Rep_inverse = SOME Rep_inverse}
blanchet@33192
   515
  | NONE => NONE
blanchet@33192
   516
blanchet@33864
   517
(* FIXME: use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@33864
   518
   e.g., by adding a field to "DatatypeAux.info". *)
blanchet@33192
   519
(* string -> bool *)
blanchet@33192
   520
fun is_basic_datatype s =
blanchet@33192
   521
    s mem [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@33864
   522
           @{type_name nat}, @{type_name int}, "Code_Numeral.code_numeral"]
blanchet@33192
   523
(* theory -> string -> bool *)
blanchet@33192
   524
val is_typedef = is_some oo typedef_info
blanchet@33192
   525
val is_real_datatype = is_some oo Datatype.get_info
blanchet@33192
   526
(* theory -> typ -> bool *)
blanchet@33192
   527
fun is_codatatype thy (T as Type (s, _)) =
blanchet@33583
   528
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   529
               |> Option.map snd |> these))
blanchet@33192
   530
  | is_codatatype _ _ = false
blanchet@33192
   531
fun is_pure_typedef thy (T as Type (s, _)) =
blanchet@33192
   532
    is_typedef thy s andalso
blanchet@33192
   533
    not (is_real_datatype thy s orelse is_codatatype thy T
blanchet@33192
   534
         orelse is_record_type T orelse is_integer_type T)
blanchet@33192
   535
  | is_pure_typedef _ _ = false
blanchet@33192
   536
fun is_univ_typedef thy (Type (s, _)) =
blanchet@33192
   537
    (case typedef_info thy s of
blanchet@33192
   538
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@33192
   539
       (case set_def of
blanchet@33192
   540
          SOME thm =>
blanchet@33192
   541
          try (fst o dest_Const o snd o Logic.dest_equals o prop_of) thm
blanchet@33192
   542
        | NONE =>
blanchet@33192
   543
          try (fst o dest_Const o snd o HOLogic.dest_mem
blanchet@33864
   544
               o HOLogic.dest_Trueprop) prop_of_Rep) = SOME @{const_name top}
blanchet@33192
   545
     | NONE => false)
blanchet@33192
   546
  | is_univ_typedef _ _ = false
blanchet@33192
   547
fun is_datatype thy (T as Type (s, _)) =
blanchet@33192
   548
    (is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind})
blanchet@33192
   549
    andalso not (is_basic_datatype s)
blanchet@33192
   550
  | is_datatype _ _ = false
blanchet@33192
   551
blanchet@33192
   552
(* theory -> typ -> (string * typ) list * (string * typ) *)
blanchet@33192
   553
fun all_record_fields thy T =
blanchet@33192
   554
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   555
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   556
  end
blanchet@33192
   557
  handle TYPE _ => []
blanchet@33192
   558
(* styp -> bool *)
blanchet@33192
   559
fun is_record_constr (x as (s, T)) =
blanchet@33192
   560
  String.isSuffix Record.extN s andalso
blanchet@33192
   561
  let val dataT = body_type T in
blanchet@33192
   562
    is_record_type dataT andalso
blanchet@33192
   563
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   564
  end
blanchet@33192
   565
(* theory -> typ -> int *)
blanchet@33192
   566
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   567
(* theory -> string -> typ -> int *)
blanchet@33192
   568
fun no_of_record_field thy s T1 =
blanchet@33192
   569
  find_index (equal s o fst) (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@33192
   570
(* theory -> styp -> bool *)
blanchet@33192
   571
fun is_record_get thy (s, Type ("fun", [T1, _])) =
blanchet@33192
   572
    exists (equal s o fst) (all_record_fields thy T1)
blanchet@33192
   573
  | is_record_get _ _ = false
blanchet@33192
   574
fun is_record_update thy (s, T) =
blanchet@33192
   575
  String.isSuffix Record.updateN s andalso
blanchet@33192
   576
  exists (equal (unsuffix Record.updateN s) o fst)
blanchet@33192
   577
         (all_record_fields thy (body_type T))
blanchet@33192
   578
  handle TYPE _ => false
blanchet@33192
   579
fun is_abs_fun thy (s, Type ("fun", [_, Type (s', _)])) =
blanchet@33192
   580
    (case typedef_info thy s' of
blanchet@33192
   581
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   582
     | NONE => false)
blanchet@33192
   583
  | is_abs_fun _ _ = false
blanchet@33192
   584
fun is_rep_fun thy (s, Type ("fun", [Type (s', _), _])) =
blanchet@33192
   585
    (case typedef_info thy s' of
blanchet@33192
   586
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   587
     | NONE => false)
blanchet@33192
   588
  | is_rep_fun _ _ = false
blanchet@33192
   589
blanchet@33192
   590
(* theory -> styp -> styp *)
blanchet@33192
   591
fun mate_of_rep_fun thy (x as (_, Type ("fun", [T1 as Type (s', _), T2]))) =
blanchet@33192
   592
    (case typedef_info thy s' of
blanchet@33192
   593
       SOME {Abs_name, ...} => (Abs_name, Type ("fun", [T2, T1]))
blanchet@33232
   594
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   595
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@33192
   596
blanchet@33192
   597
(* theory -> styp -> bool *)
blanchet@33192
   598
fun is_coconstr thy (s, T) =
blanchet@33192
   599
  let
blanchet@33583
   600
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   601
    val co_T = body_type T
blanchet@33192
   602
    val co_s = dest_Type co_T |> fst
blanchet@33192
   603
  in
blanchet@33192
   604
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   605
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   606
  end
blanchet@33192
   607
  handle TYPE ("dest_Type", _, _) => false
blanchet@33192
   608
fun is_constr_like thy (s, T) =
blanchet@33192
   609
  s mem [@{const_name FunBox}, @{const_name PairBox}] orelse
blanchet@33192
   610
  let val (x as (s, T)) = (s, unbox_type T) in
blanchet@33192
   611
    Refute.is_IDT_constructor thy x orelse is_record_constr x
blanchet@33192
   612
    orelse (is_abs_fun thy x andalso is_pure_typedef thy (range_type T))
blanchet@33192
   613
    orelse s mem [@{const_name Zero_Rep}, @{const_name Suc_Rep}]
blanchet@33192
   614
    orelse x = (@{const_name zero_nat_inst.zero_nat}, nat_T)
blanchet@33192
   615
    orelse is_coconstr thy x
blanchet@33192
   616
  end
blanchet@33581
   617
fun is_stale_constr thy (x as (_, T)) =
blanchet@33581
   618
  is_codatatype thy (body_type T) andalso is_constr_like thy x
blanchet@33581
   619
  andalso not (is_coconstr thy x)
blanchet@33192
   620
fun is_constr thy (x as (_, T)) =
blanchet@33192
   621
  is_constr_like thy x
blanchet@33192
   622
  andalso not (is_basic_datatype (fst (dest_Type (body_type T))))
blanchet@33581
   623
  andalso not (is_stale_constr thy x)
blanchet@33192
   624
(* string -> bool *)
blanchet@33192
   625
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   626
val is_sel_like_and_no_discr =
blanchet@33192
   627
  String.isPrefix sel_prefix
blanchet@33192
   628
  orf (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   629
blanchet@33192
   630
datatype boxability =
blanchet@33192
   631
  InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
blanchet@33192
   632
blanchet@33192
   633
(* boxability -> boxability *)
blanchet@33192
   634
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   635
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   636
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   637
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   638
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   639
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   640
blanchet@33192
   641
(* extended_context -> boxability -> typ -> bool *)
blanchet@33192
   642
fun is_boxing_worth_it (ext_ctxt : extended_context) boxy T =
blanchet@33192
   643
  case T of
blanchet@33192
   644
    Type ("fun", _) =>
blanchet@33192
   645
    boxy mem [InPair, InFunLHS] andalso not (is_boolean_type (body_type T))
blanchet@33192
   646
  | Type ("*", Ts) =>
blanchet@33192
   647
    boxy mem [InPair, InFunRHS1, InFunRHS2]
blanchet@33192
   648
    orelse (boxy mem [InExpr, InFunLHS]
blanchet@33192
   649
            andalso exists (is_boxing_worth_it ext_ctxt InPair)
blanchet@33192
   650
                           (map (box_type ext_ctxt InPair) Ts))
blanchet@33192
   651
  | _ => false
blanchet@33192
   652
(* extended_context -> boxability -> string * typ list -> string *)
blanchet@33192
   653
and should_box_type (ext_ctxt as {thy, boxes, ...}) boxy (z as (s, Ts)) =
blanchet@33192
   654
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   655
    SOME (SOME box_me) => box_me
blanchet@33192
   656
  | _ => is_boxing_worth_it ext_ctxt boxy (Type z)
blanchet@33192
   657
(* extended_context -> boxability -> typ -> typ *)
blanchet@33192
   658
and box_type ext_ctxt boxy T =
blanchet@33192
   659
  case T of
blanchet@33192
   660
    Type (z as ("fun", [T1, T2])) =>
blanchet@33192
   661
    if not (boxy mem [InConstr, InSel])
blanchet@33192
   662
       andalso should_box_type ext_ctxt boxy z then
blanchet@33192
   663
      Type (@{type_name fun_box},
blanchet@33192
   664
            [box_type ext_ctxt InFunLHS T1, box_type ext_ctxt InFunRHS1 T2])
blanchet@33192
   665
    else
blanchet@33192
   666
      box_type ext_ctxt (in_fun_lhs_for boxy) T1
blanchet@33192
   667
      --> box_type ext_ctxt (in_fun_rhs_for boxy) T2
blanchet@33192
   668
  | Type (z as ("*", Ts)) =>
blanchet@33192
   669
    if should_box_type ext_ctxt boxy z then
blanchet@33192
   670
      Type (@{type_name pair_box}, map (box_type ext_ctxt InSel) Ts)
blanchet@33192
   671
    else
blanchet@33192
   672
      Type ("*", map (box_type ext_ctxt
blanchet@33192
   673
                               (if boxy mem [InConstr, InSel] then boxy
blanchet@33192
   674
                                else InPair)) Ts)
blanchet@33192
   675
  | _ => T
blanchet@33192
   676
blanchet@33192
   677
(* styp -> styp *)
blanchet@33192
   678
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   679
blanchet@33192
   680
(* typ -> int *)
blanchet@33192
   681
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   682
(* string -> int -> string *)
blanchet@33192
   683
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   684
  if s = @{const_name Pair} then
blanchet@33192
   685
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   686
  else
blanchet@33192
   687
    sel_prefix_for n ^ s
blanchet@33192
   688
(* styp -> int -> styp *)
blanchet@33192
   689
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   690
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   691
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   692
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@33192
   693
(* extended_context -> styp -> int -> styp *)
blanchet@33192
   694
fun boxed_nth_sel_for_constr ext_ctxt =
blanchet@33192
   695
  apsnd (box_type ext_ctxt InSel) oo nth_sel_for_constr
blanchet@33192
   696
blanchet@33192
   697
(* string -> int *)
blanchet@33192
   698
fun sel_no_from_name s =
blanchet@33192
   699
  if String.isPrefix discr_prefix s then
blanchet@33192
   700
    ~1
blanchet@33192
   701
  else if String.isPrefix sel_prefix s then
blanchet@33192
   702
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   703
  else if s = @{const_name snd} then
blanchet@33192
   704
    1
blanchet@33192
   705
  else
blanchet@33192
   706
    0
blanchet@33192
   707
blanchet@33192
   708
(* typ list -> term -> int -> term *)
blanchet@33192
   709
fun eta_expand _ t 0 = t
blanchet@33192
   710
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   711
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   712
  | eta_expand Ts t n =
blanchet@33192
   713
    fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
blanchet@33192
   714
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   715
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   716
blanchet@33192
   717
(* term -> term *)
blanchet@33192
   718
fun extensionalize t =
blanchet@33192
   719
  case t of
blanchet@33192
   720
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   721
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   722
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   723
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   724
    end
blanchet@33192
   725
  | _ => t
blanchet@33192
   726
blanchet@33192
   727
(* typ -> term list -> term *)
blanchet@33192
   728
fun distinctness_formula T =
blanchet@33192
   729
  all_distinct_unordered_pairs_of
blanchet@33192
   730
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   731
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   732
blanchet@33192
   733
(* typ -> term *)
blanchet@33192
   734
fun zero_const T = Const (@{const_name zero_nat_inst.zero_nat}, T)
blanchet@33192
   735
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   736
blanchet@33192
   737
(* theory -> typ -> styp list *)
blanchet@33580
   738
fun uncached_datatype_constrs thy (T as Type (s, Ts)) =
blanchet@33583
   739
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@33581
   740
       SOME (_, xs' as (_ :: _)) =>
blanchet@33581
   741
       map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   742
     | _ =>
blanchet@33581
   743
       if is_datatype thy T then
blanchet@33581
   744
         case Datatype.get_info thy s of
blanchet@33581
   745
           SOME {index, descr, ...} =>
blanchet@33581
   746
           let
blanchet@33581
   747
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   748
           in
blanchet@33581
   749
             map (fn (s', Us) =>
blanchet@33581
   750
                     (s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us
blanchet@33581
   751
                          ---> T)) constrs
blanchet@33581
   752
           end
blanchet@33581
   753
         | NONE =>
blanchet@33581
   754
           if is_record_type T then
blanchet@33581
   755
             let
blanchet@33581
   756
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   757
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   758
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   759
             in [(s', T')] end
blanchet@33581
   760
           else case typedef_info thy s of
blanchet@33581
   761
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@33581
   762
             [(Abs_name, instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   763
           | NONE =>
blanchet@33581
   764
             if T = @{typ ind} then
blanchet@33581
   765
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   766
             else
blanchet@33581
   767
               []
blanchet@33581
   768
       else
blanchet@33581
   769
         [])
blanchet@33580
   770
  | uncached_datatype_constrs _ _ = []
blanchet@33192
   771
(* extended_context -> typ -> styp list *)
blanchet@33580
   772
fun datatype_constrs (ext_ctxt as {thy, constr_cache, ...} : extended_context)
blanchet@33580
   773
                     T =
blanchet@33580
   774
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   775
    SOME xs => xs
blanchet@33580
   776
  | NONE =>
blanchet@33580
   777
    let val xs = uncached_datatype_constrs thy T in
blanchet@33580
   778
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   779
    end
blanchet@33580
   780
fun boxed_datatype_constrs ext_ctxt =
blanchet@33580
   781
  map (apsnd (box_type ext_ctxt InConstr)) o datatype_constrs ext_ctxt
blanchet@33580
   782
(* extended_context -> typ -> int *)
blanchet@33192
   783
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   784
blanchet@33192
   785
(* string -> string *)
blanchet@33192
   786
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   787
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   788
  | constr_name_for_sel_like s' = original_name s'
blanchet@33192
   789
(* extended_context -> styp -> styp *)
blanchet@33192
   790
fun boxed_constr_for_sel ext_ctxt (s', T') =
blanchet@33192
   791
  let val s = constr_name_for_sel_like s' in
blanchet@33192
   792
    AList.lookup (op =) (boxed_datatype_constrs ext_ctxt (domain_type T')) s
blanchet@33192
   793
    |> the |> pair s
blanchet@33192
   794
  end
blanchet@33580
   795
(* extended_context -> styp -> term *)
blanchet@33580
   796
fun discr_term_for_constr ext_ctxt (x as (s, T)) =
blanchet@33192
   797
  let val dataT = body_type T in
blanchet@33192
   798
    if s = @{const_name Suc} then
blanchet@33192
   799
      Abs (Name.uu, dataT,
blanchet@33192
   800
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@33580
   801
    else if num_datatype_constrs ext_ctxt dataT >= 2 then
blanchet@33192
   802
      Const (discr_for_constr x)
blanchet@33192
   803
    else
blanchet@33192
   804
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   805
  end
blanchet@33192
   806
blanchet@33580
   807
(* extended_context -> styp -> term -> term *)
blanchet@33580
   808
fun discriminate_value (ext_ctxt as {thy, ...}) (x as (_, T)) t =
blanchet@33192
   809
  case strip_comb t of
blanchet@33192
   810
    (Const x', args) =>
blanchet@33192
   811
    if x = x' then @{const True}
blanchet@33192
   812
    else if is_constr_like thy x' then @{const False}
blanchet@33580
   813
    else betapply (discr_term_for_constr ext_ctxt x, t)
blanchet@33580
   814
  | _ => betapply (discr_term_for_constr ext_ctxt x, t)
blanchet@33192
   815
blanchet@33192
   816
(* styp -> term -> term *)
blanchet@33192
   817
fun nth_arg_sel_term_for_constr (x as (s, T)) n =
blanchet@33192
   818
  let val (arg_Ts, dataT) = strip_type T in
blanchet@33192
   819
    if dataT = nat_T then
blanchet@33192
   820
      @{term "%n::nat. minus_nat_inst.minus_nat n one_nat_inst.one_nat"}
blanchet@33192
   821
    else if is_pair_type dataT then
blanchet@33192
   822
      Const (nth_sel_for_constr x n)
blanchet@33192
   823
    else
blanchet@33192
   824
      let
blanchet@33192
   825
        (* int -> typ -> int * term *)
blanchet@33192
   826
        fun aux m (Type ("*", [T1, T2])) =
blanchet@33192
   827
            let
blanchet@33192
   828
              val (m, t1) = aux m T1
blanchet@33192
   829
              val (m, t2) = aux m T2
blanchet@33192
   830
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   831
          | aux m T =
blanchet@33192
   832
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
   833
                    $ Bound 0)
blanchet@33192
   834
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
   835
                     (List.take (arg_Ts, n)) 0
blanchet@33192
   836
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
   837
  end
blanchet@33192
   838
(* theory -> styp -> term -> int -> typ -> term *)
blanchet@33192
   839
fun select_nth_constr_arg thy x t n res_T =
blanchet@33192
   840
  case strip_comb t of
blanchet@33192
   841
    (Const x', args) =>
blanchet@33192
   842
    if x = x' then nth args n
blanchet@33192
   843
    else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
blanchet@33192
   844
    else betapply (nth_arg_sel_term_for_constr x n, t)
blanchet@33192
   845
  | _ => betapply (nth_arg_sel_term_for_constr x n, t)
blanchet@33192
   846
blanchet@33192
   847
(* theory -> styp -> term list -> term *)
blanchet@33192
   848
fun construct_value _ x [] = Const x
blanchet@33192
   849
  | construct_value thy (x as (s, _)) args =
blanchet@33192
   850
    let val args = map Envir.eta_contract args in
blanchet@33192
   851
      case hd args of
blanchet@33192
   852
        Const (x' as (s', _)) $ t =>
blanchet@33192
   853
        if is_sel_like_and_no_discr s' andalso constr_name_for_sel_like s' = s
blanchet@33192
   854
           andalso forall (fn (n, t') =>
blanchet@33192
   855
                              select_nth_constr_arg thy x t n dummyT = t')
blanchet@33192
   856
                          (index_seq 0 (length args) ~~ args) then
blanchet@33192
   857
          t
blanchet@33192
   858
        else
blanchet@33192
   859
          list_comb (Const x, args)
blanchet@33192
   860
      | _ => list_comb (Const x, args)
blanchet@33192
   861
    end
blanchet@33192
   862
blanchet@33580
   863
(* extended_context -> typ -> term -> term *)
blanchet@33580
   864
fun constr_expand (ext_ctxt as {thy, ...}) T t =
blanchet@33192
   865
  (case head_of t of
blanchet@33192
   866
     Const x => if is_constr_like thy x then t else raise SAME ()
blanchet@33192
   867
   | _ => raise SAME ())
blanchet@33192
   868
  handle SAME () =>
blanchet@33192
   869
         let
blanchet@33192
   870
           val x' as (_, T') =
blanchet@33192
   871
             if is_pair_type T then
blanchet@33192
   872
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@33192
   873
                 (@{const_name Pair}, [T1, T2] ---> T)
blanchet@33192
   874
               end
blanchet@33192
   875
             else
blanchet@33580
   876
               datatype_constrs ext_ctxt T |> the_single
blanchet@33192
   877
           val arg_Ts = binder_types T'
blanchet@33192
   878
         in
blanchet@33192
   879
           list_comb (Const x', map2 (select_nth_constr_arg thy x' t)
blanchet@33192
   880
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
   881
         end
blanchet@33192
   882
blanchet@33192
   883
(* (typ * int) list -> typ -> int *)
blanchet@33192
   884
fun card_of_type asgns (Type ("fun", [T1, T2])) =
blanchet@33192
   885
    reasonable_power (card_of_type asgns T2) (card_of_type asgns T1)
blanchet@33192
   886
  | card_of_type asgns (Type ("*", [T1, T2])) =
blanchet@33192
   887
    card_of_type asgns T1 * card_of_type asgns T2
blanchet@33192
   888
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
   889
  | card_of_type _ @{typ prop} = 2
blanchet@33192
   890
  | card_of_type _ @{typ bool} = 2
blanchet@33192
   891
  | card_of_type _ @{typ unit} = 1
blanchet@33192
   892
  | card_of_type asgns T =
blanchet@33192
   893
    case AList.lookup (op =) asgns T of
blanchet@33192
   894
      SOME k => k
blanchet@33192
   895
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
   896
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@33192
   897
(* int -> (typ * int) list -> typ -> int *)
blanchet@33192
   898
fun bounded_card_of_type max default_card asgns (Type ("fun", [T1, T2])) =
blanchet@33192
   899
    let
blanchet@33192
   900
      val k1 = bounded_card_of_type max default_card asgns T1
blanchet@33192
   901
      val k2 = bounded_card_of_type max default_card asgns T2
blanchet@33192
   902
    in
blanchet@33192
   903
      if k1 = max orelse k2 = max then max
blanchet@33192
   904
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
   905
    end
blanchet@33192
   906
  | bounded_card_of_type max default_card asgns (Type ("*", [T1, T2])) =
blanchet@33192
   907
    let
blanchet@33192
   908
      val k1 = bounded_card_of_type max default_card asgns T1
blanchet@33192
   909
      val k2 = bounded_card_of_type max default_card asgns T2
blanchet@33192
   910
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@33192
   911
  | bounded_card_of_type max default_card asgns T =
blanchet@33192
   912
    Int.min (max, if default_card = ~1 then
blanchet@33192
   913
                    card_of_type asgns T
blanchet@33192
   914
                  else
blanchet@33192
   915
                    card_of_type asgns T
blanchet@33232
   916
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
   917
                           default_card)
blanchet@33580
   918
(* extended_context -> int -> (typ * int) list -> typ -> int *)
blanchet@33580
   919
fun bounded_precise_card_of_type ext_ctxt max default_card asgns T =
blanchet@33192
   920
  let
blanchet@33192
   921
    (* typ list -> typ -> int *)
blanchet@33192
   922
    fun aux avoid T =
blanchet@33192
   923
      (if T mem avoid then
blanchet@33192
   924
         0
blanchet@33192
   925
       else case T of
blanchet@33192
   926
         Type ("fun", [T1, T2]) =>
blanchet@33192
   927
         let
blanchet@33192
   928
           val k1 = aux avoid T1
blanchet@33192
   929
           val k2 = aux avoid T2
blanchet@33192
   930
         in
blanchet@33192
   931
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
   932
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
   933
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
   934
         end
blanchet@33192
   935
       | Type ("*", [T1, T2]) =>
blanchet@33192
   936
         let
blanchet@33192
   937
           val k1 = aux avoid T1
blanchet@33192
   938
           val k2 = aux avoid T2
blanchet@33192
   939
         in
blanchet@33192
   940
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
   941
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
   942
           else Int.min (max, k1 * k2)
blanchet@33192
   943
         end
blanchet@33192
   944
       | Type (@{type_name itself}, _) => 1
blanchet@33192
   945
       | @{typ prop} => 2
blanchet@33192
   946
       | @{typ bool} => 2
blanchet@33192
   947
       | @{typ unit} => 1
blanchet@33192
   948
       | Type _ =>
blanchet@33580
   949
         (case datatype_constrs ext_ctxt T of
blanchet@33192
   950
            [] => if is_integer_type T then 0 else raise SAME ()
blanchet@33192
   951
          | constrs =>
blanchet@33192
   952
            let
blanchet@33192
   953
              val constr_cards =
blanchet@33580
   954
                datatype_constrs ext_ctxt T
blanchet@33192
   955
                |> map (Integer.prod o map (aux (T :: avoid)) o binder_types
blanchet@33192
   956
                        o snd)
blanchet@33192
   957
            in
blanchet@33192
   958
              if exists (equal 0) constr_cards then 0
blanchet@33192
   959
              else Integer.sum constr_cards
blanchet@33192
   960
            end)
blanchet@33192
   961
       | _ => raise SAME ())
blanchet@33192
   962
      handle SAME () => AList.lookup (op =) asgns T |> the_default default_card
blanchet@33192
   963
  in Int.min (max, aux [] T) end
blanchet@33192
   964
blanchet@33580
   965
(* extended_context -> typ -> bool *)
blanchet@33580
   966
fun is_finite_type ext_ctxt =
blanchet@33580
   967
  not_equal 0 o bounded_precise_card_of_type ext_ctxt 1 2 []
blanchet@33192
   968
blanchet@33192
   969
(* term -> bool *)
blanchet@33192
   970
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
   971
  | is_ground_term (Const _) = true
blanchet@33192
   972
  | is_ground_term _ = false
blanchet@33192
   973
blanchet@33192
   974
(* term -> word -> word *)
blanchet@33192
   975
fun hashw_term (t1 $ t2) = Polyhash.hashw (hashw_term t1, hashw_term t2)
blanchet@33192
   976
  | hashw_term (Const (s, _)) = Polyhash.hashw_string (s, 0w0)
blanchet@33192
   977
  | hashw_term _ = 0w0
blanchet@33192
   978
(* term -> int *)
blanchet@33192
   979
val hash_term = Word.toInt o hashw_term
blanchet@33192
   980
blanchet@33192
   981
(* term list -> (indexname * typ) list *)
blanchet@33192
   982
fun special_bounds ts =
blanchet@33192
   983
  fold Term.add_vars ts [] |> sort (TermOrd.fast_indexname_ord o pairself fst)
blanchet@33192
   984
blanchet@33192
   985
(* indexname * typ -> term -> term *)
blanchet@33192
   986
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
   987
blanchet@33571
   988
(* theory -> string -> bool *)
blanchet@33571
   989
fun is_funky_typedef_name thy s =
blanchet@33571
   990
  s mem [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@33571
   991
         @{type_name int}]
blanchet@33571
   992
  orelse is_frac_type thy (Type (s, []))
blanchet@33571
   993
(* theory -> term -> bool *)
blanchet@33571
   994
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
   995
  | is_funky_typedef _ _ = false
blanchet@33192
   996
(* term -> bool *)
blanchet@33192
   997
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
   998
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
   999
  | is_arity_type_axiom _ = false
blanchet@33192
  1000
(* theory -> bool -> term -> bool *)
blanchet@33197
  1001
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
blanchet@33197
  1002
    is_typedef_axiom thy boring t2
blanchet@33197
  1003
  | is_typedef_axiom thy boring
blanchet@33192
  1004
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@33197
  1005
         $ Const (_, Type ("fun", [Type (s, _), _])) $ Const _ $ _)) =
blanchet@33571
  1006
    boring <> is_funky_typedef_name thy s andalso is_typedef thy s
blanchet@33192
  1007
  | is_typedef_axiom _ _ _ = false
blanchet@33192
  1008
blanchet@33192
  1009
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1010
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1011
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1012
   using "typedef_info". *)
blanchet@33192
  1013
(* theory -> (string * term) list -> string list -> term list * term list *)
blanchet@33192
  1014
fun partition_axioms_by_definitionality thy axioms def_names =
blanchet@33192
  1015
  let
blanchet@33192
  1016
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1017
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1018
    val nondefs =
blanchet@33192
  1019
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1020
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
blanchet@33192
  1021
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1022
blanchet@33197
  1023
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1024
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1025
   commands. *)
blanchet@33192
  1026
(* theory -> bool *)
blanchet@33192
  1027
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1028
blanchet@33192
  1029
(* term -> bool *)
blanchet@33192
  1030
val is_plain_definition =
blanchet@33192
  1031
  let
blanchet@33192
  1032
    (* term -> bool *)
blanchet@33192
  1033
    fun do_lhs t1 =
blanchet@33192
  1034
      case strip_comb t1 of
blanchet@33192
  1035
        (Const _, args) => forall is_Var args
blanchet@33192
  1036
                           andalso not (has_duplicates (op =) args)
blanchet@33192
  1037
      | _ => false
blanchet@33192
  1038
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1039
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1040
        do_lhs t1
blanchet@33192
  1041
      | do_eq _ = false
blanchet@33192
  1042
  in do_eq end
blanchet@33192
  1043
blanchet@33192
  1044
(* theory -> term list * term list * term list *)
blanchet@33192
  1045
fun all_axioms_of thy =
blanchet@33192
  1046
  let
blanchet@33192
  1047
    (* theory list -> term list *)
blanchet@33192
  1048
    val axioms_of_thys = maps Thm.axioms_of #> map (apsnd prop_of)
blanchet@33192
  1049
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1050
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1051
                    |> OrdList.make fast_string_ord
blanchet@33192
  1052
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1053
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1054
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1055
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1056
    val (built_in_defs, built_in_nondefs) =
blanchet@33192
  1057
      partition_axioms_by_definitionality thy built_in_axioms def_names
blanchet@33197
  1058
      ||> filter (is_typedef_axiom thy false)
blanchet@33192
  1059
    val (user_defs, user_nondefs) =
blanchet@33192
  1060
      partition_axioms_by_definitionality thy user_axioms def_names
blanchet@33197
  1061
    val (built_in_nondefs, user_nondefs) =
blanchet@33197
  1062
      List.partition (is_typedef_axiom thy false) user_nondefs
blanchet@33197
  1063
      |>> append built_in_nondefs
blanchet@33556
  1064
    val defs = (thy |> PureThy.all_thms_of
blanchet@33192
  1065
                    |> filter (equal Thm.definitionK o Thm.get_kind o snd)
blanchet@33192
  1066
                    |> map (prop_of o snd) |> filter is_plain_definition) @
blanchet@33192
  1067
               user_defs @ built_in_defs
blanchet@33192
  1068
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1069
blanchet@33192
  1070
(* bool -> styp -> int option *)
blanchet@33192
  1071
fun arity_of_built_in_const fast_descrs (s, T) =
blanchet@33192
  1072
  if s = @{const_name If} then
blanchet@33192
  1073
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@33192
  1074
  else case AList.lookup (op =)
blanchet@33192
  1075
                (built_in_consts
blanchet@33192
  1076
                 |> fast_descrs ? append built_in_descr_consts) s of
blanchet@33192
  1077
    SOME n => SOME n
blanchet@33192
  1078
  | NONE =>
blanchet@33192
  1079
    case AList.lookup (op =) built_in_typed_consts (s, T) of
blanchet@33192
  1080
      SOME n => SOME n
blanchet@33192
  1081
    | NONE =>
blanchet@33192
  1082
      if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@33192
  1083
        AList.lookup (op =) built_in_set_consts s
blanchet@33192
  1084
      else
blanchet@33192
  1085
        NONE
blanchet@33192
  1086
(* bool -> styp -> bool *)
blanchet@33192
  1087
val is_built_in_const = is_some oo arity_of_built_in_const
blanchet@33192
  1088
blanchet@33192
  1089
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1090
   simplification rules (equational specifications). *)
blanchet@33192
  1091
(* term -> term *)
blanchet@33192
  1092
fun term_under_def t =
blanchet@33192
  1093
  case t of
blanchet@33192
  1094
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1095
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1096
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1097
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1098
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1099
  | t1 $ _ => term_under_def t1
blanchet@33192
  1100
  | _ => t
blanchet@33192
  1101
blanchet@33192
  1102
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
blanchet@33192
  1103
   traversal of the term, without which the wrong occurrence of a constant could
blanchet@33192
  1104
   be matched in the face of overloading. *)
blanchet@33192
  1105
(* theory -> bool -> const_table -> styp -> term list *)
blanchet@33192
  1106
fun def_props_for_const thy fast_descrs table (x as (s, _)) =
blanchet@33192
  1107
  if is_built_in_const fast_descrs x then
blanchet@33192
  1108
    []
blanchet@33192
  1109
  else
blanchet@33192
  1110
    these (Symtab.lookup table s)
blanchet@33192
  1111
    |> map_filter (try (Refute.specialize_type thy x))
blanchet@33192
  1112
    |> filter (equal (Const x) o term_under_def)
blanchet@33192
  1113
blanchet@33743
  1114
(* theory -> term -> term option *)
blanchet@33192
  1115
fun normalized_rhs_of thy t =
blanchet@33192
  1116
  let
blanchet@33743
  1117
    (* term option -> term option *)
blanchet@33743
  1118
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@33743
  1119
      | aux (c as Const (@{const_name TYPE}, T)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1120
      | aux _ _ = NONE
blanchet@33192
  1121
    val (lhs, rhs) =
blanchet@33192
  1122
      case t of
blanchet@33192
  1123
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1124
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1125
        (t1, t2)
blanchet@33232
  1126
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1127
    val args = strip_comb lhs |> snd
blanchet@33743
  1128
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1129
blanchet@33192
  1130
(* theory -> const_table -> styp -> term option *)
blanchet@33192
  1131
fun def_of_const thy table (x as (s, _)) =
blanchet@33192
  1132
  if is_built_in_const false x orelse original_name s <> s then
blanchet@33192
  1133
    NONE
blanchet@33192
  1134
  else
blanchet@33192
  1135
    x |> def_props_for_const thy false table |> List.last
blanchet@33743
  1136
      |> normalized_rhs_of thy |> Option.map (prefix_abs_vars s)
blanchet@33192
  1137
    handle List.Empty => NONE
blanchet@33192
  1138
blanchet@33192
  1139
datatype fixpoint_kind = Lfp | Gfp | NoFp
blanchet@33192
  1140
blanchet@33192
  1141
(* term -> fixpoint_kind *)
blanchet@33192
  1142
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1143
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1144
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1145
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1146
blanchet@33192
  1147
(* theory -> const_table -> term -> bool *)
blanchet@33192
  1148
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1149
  let
blanchet@33192
  1150
    (* term -> bool *)
blanchet@33192
  1151
    fun is_good_arg (Bound _) = true
blanchet@33192
  1152
      | is_good_arg (Const (s, _)) =
blanchet@33192
  1153
        s mem [@{const_name True}, @{const_name False}, @{const_name undefined}]
blanchet@33192
  1154
      | is_good_arg _ = false
blanchet@33192
  1155
  in
blanchet@33192
  1156
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1157
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1158
      (case def_of_const thy table x of
blanchet@33192
  1159
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1160
       | NONE => false)
blanchet@33192
  1161
    | _ => false
blanchet@33192
  1162
  end
blanchet@33192
  1163
(* theory -> const_table -> term -> term *)
blanchet@33192
  1164
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1165
  map_aterms (fn t as Const x =>
blanchet@33192
  1166
                 (case def_of_const thy table x of
blanchet@33192
  1167
                    SOME t' =>
blanchet@33192
  1168
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1169
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1170
                      else t
blanchet@33192
  1171
                    end
blanchet@33192
  1172
                 | NONE => t)
blanchet@33192
  1173
               | t => t)
blanchet@33192
  1174
blanchet@33192
  1175
(* term -> string * term *)
blanchet@33192
  1176
fun pair_for_prop t =
blanchet@33192
  1177
  case term_under_def t of
blanchet@33192
  1178
    Const (s, _) => (s, t)
blanchet@33192
  1179
  | Free _ => raise NOT_SUPPORTED "local definitions"
blanchet@33232
  1180
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@33192
  1181
blanchet@33192
  1182
(* (Proof.context -> term list) -> Proof.context -> const_table *)
blanchet@33192
  1183
fun table_for get ctxt =
blanchet@33192
  1184
  get ctxt |> map pair_for_prop |> AList.group (op =) |> Symtab.make
blanchet@33192
  1185
blanchet@33192
  1186
(* theory -> (string * int) list *)
blanchet@33192
  1187
fun case_const_names thy =
blanchet@33192
  1188
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@33192
  1189
                  if is_basic_datatype dtype_s then
blanchet@33192
  1190
                    I
blanchet@33192
  1191
                  else
blanchet@33192
  1192
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1193
                                     |> the |> #3 |> length))
blanchet@33192
  1194
              (Datatype.get_all thy) [] @
blanchet@33583
  1195
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1196
blanchet@33192
  1197
(* Proof.context -> term list -> const_table *)
blanchet@33192
  1198
fun const_def_table ctxt ts =
blanchet@33192
  1199
  table_for (map prop_of o Nitpick_Defs.get) ctxt
blanchet@33192
  1200
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@33192
  1201
          (map pair_for_prop ts)
blanchet@33192
  1202
(* term list -> const_table *)
blanchet@33192
  1203
fun const_nondef_table ts =
blanchet@33192
  1204
  fold (fn t => append (map (fn s => (s, t)) (Term.add_const_names t []))) ts []
blanchet@33192
  1205
  |> AList.group (op =) |> Symtab.make
blanchet@33192
  1206
(* Proof.context -> const_table *)
blanchet@33192
  1207
val const_simp_table = table_for (map prop_of o Nitpick_Simps.get)
blanchet@33192
  1208
val const_psimp_table = table_for (map prop_of o Nitpick_Psimps.get)
blanchet@33192
  1209
(* Proof.context -> const_table -> const_table *)
blanchet@33192
  1210
fun inductive_intro_table ctxt def_table =
blanchet@33192
  1211
  table_for (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
blanchet@33192
  1212
                                                  def_table o prop_of)
blanchet@33192
  1213
             o Nitpick_Intros.get) ctxt
blanchet@33192
  1214
(* theory -> term list Inttab.table *)
blanchet@33192
  1215
fun ground_theorem_table thy =
blanchet@33192
  1216
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@33192
  1217
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@33192
  1218
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@33192
  1219
blanchet@33192
  1220
val basic_ersatz_table =
blanchet@33192
  1221
  [(@{const_name prod_case}, @{const_name split}),
blanchet@33192
  1222
   (@{const_name card}, @{const_name card'}),
blanchet@33192
  1223
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@33192
  1224
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@33192
  1225
   (@{const_name wf}, @{const_name wf'}),
blanchet@33192
  1226
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@33192
  1227
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@33192
  1228
blanchet@33192
  1229
(* theory -> (string * string) list *)
blanchet@33192
  1230
fun ersatz_table thy =
blanchet@33583
  1231
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@33192
  1232
blanchet@33192
  1233
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
blanchet@33192
  1234
fun add_simps simp_table s eqs =
blanchet@33192
  1235
  Unsynchronized.change simp_table
blanchet@33192
  1236
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@33192
  1237
blanchet@33192
  1238
(* Similar to "Refute.specialize_type" but returns all matches rather than only
blanchet@33192
  1239
   the first (preorder) match. *)
blanchet@33192
  1240
(* theory -> styp -> term -> term list *)
blanchet@33197
  1241
fun multi_specialize_type thy slack (x as (s, T)) t =
blanchet@33192
  1242
  let
blanchet@33192
  1243
    (* term -> (typ * term) list -> (typ * term) list *)
blanchet@33192
  1244
    fun aux (Const (s', T')) ys =
blanchet@33192
  1245
        if s = s' then
blanchet@33197
  1246
          ys |> (if AList.defined (op =) ys T' then
blanchet@33197
  1247
                   I
blanchet@33583
  1248
                 else
blanchet@33197
  1249
                  cons (T', Refute.monomorphic_term
blanchet@33197
  1250
                                (Sign.typ_match thy (T', T) Vartab.empty) t)
blanchet@33197
  1251
                  handle Type.TYPE_MATCH => I
blanchet@33197
  1252
                       | Refute.REFUTE _ =>
blanchet@33197
  1253
                         if slack then
blanchet@33197
  1254
                           I
blanchet@33197
  1255
                         else
blanchet@33197
  1256
                           raise NOT_SUPPORTED ("too much polymorphism in \
blanchet@33197
  1257
                                                \axiom involving " ^ quote s))
blanchet@33192
  1258
        else
blanchet@33192
  1259
          ys
blanchet@33192
  1260
      | aux _ ys = ys
blanchet@33192
  1261
  in map snd (fold_aterms aux t []) end
blanchet@33192
  1262
blanchet@33197
  1263
(* theory -> bool -> const_table -> styp -> term list *)
blanchet@33197
  1264
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@33197
  1265
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@33192
  1266
blanchet@33192
  1267
(* theory -> styp list -> term list *)
blanchet@33192
  1268
fun optimized_typedef_axioms thy (abs_s, abs_Ts) =
blanchet@33192
  1269
  let val abs_T = Type (abs_s, abs_Ts) in
blanchet@33192
  1270
    if is_univ_typedef thy abs_T then
blanchet@33192
  1271
      []
blanchet@33192
  1272
    else case typedef_info thy abs_s of
blanchet@33192
  1273
      SOME {abs_type, rep_type, Abs_name, Rep_name, prop_of_Rep, set_name,
blanchet@33192
  1274
            ...} =>
blanchet@33192
  1275
      let
blanchet@33192
  1276
        val rep_T = instantiate_type thy abs_type abs_T rep_type
blanchet@33192
  1277
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@33192
  1278
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@33192
  1279
        val set_t' =
blanchet@33192
  1280
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@33192
  1281
                      |> Refute.specialize_type thy (dest_Const rep_t)
blanchet@33192
  1282
                      |> HOLogic.dest_mem |> snd
blanchet@33192
  1283
      in
blanchet@33192
  1284
        [HOLogic.all_const abs_T
blanchet@33192
  1285
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@33192
  1286
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@33192
  1287
        |> map HOLogic.mk_Trueprop
blanchet@33192
  1288
      end
blanchet@33192
  1289
    | NONE => []
blanchet@33192
  1290
  end
blanchet@33192
  1291
(* theory -> styp -> term *)
blanchet@33192
  1292
fun inverse_axiom_for_rep_fun thy (x as (_, T)) =
blanchet@33864
  1293
  let val abs_T = domain_type T in
blanchet@33864
  1294
    typedef_info thy (fst (dest_Type abs_T)) |> the |> #Rep_inverse |> the
blanchet@33864
  1295
    |> prop_of |> Refute.specialize_type thy x
blanchet@33864
  1296
  end
blanchet@33192
  1297
blanchet@33192
  1298
(* theory -> int * styp -> term *)
blanchet@33192
  1299
fun constr_case_body thy (j, (x as (_, T))) =
blanchet@33192
  1300
  let val arg_Ts = binder_types T in
blanchet@33192
  1301
    list_comb (Bound j, map2 (select_nth_constr_arg thy x (Bound 0))
blanchet@33192
  1302
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1303
  end
blanchet@33580
  1304
(* extended_context -> typ -> int * styp -> term -> term *)
blanchet@33580
  1305
fun add_constr_case (ext_ctxt as {thy, ...}) res_T (j, x) res_t =
blanchet@33192
  1306
  Const (@{const_name If}, [bool_T, res_T, res_T] ---> res_T)
blanchet@33580
  1307
  $ discriminate_value ext_ctxt x (Bound 0) $ constr_case_body thy (j, x)
blanchet@33580
  1308
  $ res_t
blanchet@33580
  1309
(* extended_context -> typ -> typ -> term *)
blanchet@33580
  1310
fun optimized_case_def (ext_ctxt as {thy, ...}) dataT res_T =
blanchet@33192
  1311
  let
blanchet@33580
  1312
    val xs = datatype_constrs ext_ctxt dataT
blanchet@33192
  1313
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs
blanchet@33192
  1314
    val (xs', x) = split_last xs
blanchet@33192
  1315
  in
blanchet@33192
  1316
    constr_case_body thy (1, x)
blanchet@33580
  1317
    |> fold_rev (add_constr_case ext_ctxt res_T) (length xs downto 2 ~~ xs')
blanchet@33192
  1318
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1319
  end
blanchet@33192
  1320
blanchet@33580
  1321
(* extended_context -> string -> typ -> typ -> term -> term *)
blanchet@33580
  1322
fun optimized_record_get (ext_ctxt as {thy, ...}) s rec_T res_T t =
blanchet@33580
  1323
  let val constr_x = the_single (datatype_constrs ext_ctxt rec_T) in
blanchet@33192
  1324
    case no_of_record_field thy s rec_T of
blanchet@33192
  1325
      ~1 => (case rec_T of
blanchet@33192
  1326
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1327
               let
blanchet@33192
  1328
                 val rec_T' = List.last Ts
blanchet@33192
  1329
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1330
               in
blanchet@33192
  1331
                 select_nth_constr_arg thy constr_x t j res_T
blanchet@33580
  1332
                 |> optimized_record_get ext_ctxt s rec_T' res_T
blanchet@33192
  1333
               end
blanchet@33232
  1334
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1335
                                []))
blanchet@33192
  1336
    | j => select_nth_constr_arg thy constr_x t j res_T
blanchet@33192
  1337
  end
blanchet@33580
  1338
(* extended_context -> string -> typ -> term -> term -> term *)
blanchet@33580
  1339
fun optimized_record_update (ext_ctxt as {thy, ...}) s rec_T fun_t rec_t =
blanchet@33192
  1340
  let
blanchet@33580
  1341
    val constr_x as (_, constr_T) = the_single (datatype_constrs ext_ctxt rec_T)
blanchet@33192
  1342
    val Ts = binder_types constr_T
blanchet@33192
  1343
    val n = length Ts
blanchet@33192
  1344
    val special_j = no_of_record_field thy s rec_T
blanchet@33192
  1345
    val ts = map2 (fn j => fn T =>
blanchet@33192
  1346
                      let
blanchet@33192
  1347
                        val t = select_nth_constr_arg thy constr_x rec_t j T
blanchet@33192
  1348
                      in
blanchet@33192
  1349
                        if j = special_j then
blanchet@33192
  1350
                          betapply (fun_t, t)
blanchet@33192
  1351
                        else if j = n - 1 andalso special_j = ~1 then
blanchet@33580
  1352
                          optimized_record_update ext_ctxt s
blanchet@33192
  1353
                              (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@33192
  1354
                        else
blanchet@33192
  1355
                          t
blanchet@33192
  1356
                      end) (index_seq 0 n) Ts
blanchet@33192
  1357
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1358
blanchet@33192
  1359
(* Constants "c" whose definition is of the form "c == c'", where "c'" is also a
blanchet@33192
  1360
   constant, are said to be trivial. For those, we ignore the simplification
blanchet@33192
  1361
   rules and use the definition instead, to ensure that built-in symbols like
blanchet@33192
  1362
   "ord_nat_inst.less_eq_nat" are picked up correctly. *)
blanchet@33192
  1363
(* theory -> const_table -> styp -> bool *)
blanchet@33192
  1364
fun has_trivial_definition thy table x =
blanchet@33192
  1365
  case def_of_const thy table x of SOME (Const _) => true | _ => false
blanchet@33192
  1366
blanchet@33192
  1367
(* theory -> const_table -> string * typ -> fixpoint_kind *)
blanchet@33192
  1368
fun fixpoint_kind_of_const thy table x =
blanchet@33192
  1369
  if is_built_in_const false x then
blanchet@33192
  1370
    NoFp
blanchet@33192
  1371
  else
blanchet@33192
  1372
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@33192
  1373
    handle Option.Option => NoFp
blanchet@33192
  1374
blanchet@33192
  1375
(* extended_context -> styp -> bool *)
blanchet@33192
  1376
fun is_real_inductive_pred ({thy, fast_descrs, def_table, intro_table, ...}
blanchet@33192
  1377
                            : extended_context) x =
blanchet@33192
  1378
  not (null (def_props_for_const thy fast_descrs intro_table x))
blanchet@33192
  1379
  andalso fixpoint_kind_of_const thy def_table x <> NoFp
blanchet@33192
  1380
fun is_real_equational_fun ({thy, fast_descrs, simp_table, psimp_table, ...}
blanchet@33192
  1381
                            : extended_context) x =
blanchet@33192
  1382
  exists (fn table => not (null (def_props_for_const thy fast_descrs table x)))
blanchet@33192
  1383
         [!simp_table, psimp_table]
blanchet@33192
  1384
fun is_inductive_pred ext_ctxt =
blanchet@33192
  1385
  is_real_inductive_pred ext_ctxt andf (not o is_real_equational_fun ext_ctxt)
blanchet@33192
  1386
fun is_equational_fun (ext_ctxt as {thy, def_table, ...}) =
blanchet@33192
  1387
  (is_real_equational_fun ext_ctxt orf is_real_inductive_pred ext_ctxt
blanchet@33192
  1388
   orf (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1389
  andf (not o has_trivial_definition thy def_table)
blanchet@33192
  1390
blanchet@33192
  1391
(* term * term -> term *)
blanchet@33192
  1392
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
blanchet@33192
  1393
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
blanchet@33192
  1394
  | s_betapply p = betapply p
blanchet@33192
  1395
(* term * term list -> term *)
blanchet@33192
  1396
val s_betapplys = Library.foldl s_betapply
blanchet@33192
  1397
blanchet@33192
  1398
(* term -> term *)
blanchet@33192
  1399
fun lhs_of_equation t =
blanchet@33192
  1400
  case t of
blanchet@33192
  1401
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1402
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1403
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1404
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@33192
  1405
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1406
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1407
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1408
  | _ => NONE
blanchet@33192
  1409
(* theory -> term -> bool *)
blanchet@33192
  1410
fun is_constr_pattern _ (Bound _) = true
blanchet@33864
  1411
  | is_constr_pattern _ (Var _) = true
blanchet@33192
  1412
  | is_constr_pattern thy t =
blanchet@33192
  1413
    case strip_comb t of
blanchet@33192
  1414
      (Const (x as (s, _)), args) =>
blanchet@33192
  1415
      is_constr_like thy x andalso forall (is_constr_pattern thy) args
blanchet@33192
  1416
    | _ => false
blanchet@33192
  1417
fun is_constr_pattern_lhs thy t =
blanchet@33192
  1418
  forall (is_constr_pattern thy) (snd (strip_comb t))
blanchet@33192
  1419
fun is_constr_pattern_formula thy t =
blanchet@33192
  1420
  case lhs_of_equation t of
blanchet@33192
  1421
    SOME t' => is_constr_pattern_lhs thy t'
blanchet@33192
  1422
  | NONE => false
blanchet@33192
  1423
blanchet@33747
  1424
val unfold_max_depth = 255
blanchet@33747
  1425
val axioms_max_depth = 255
blanchet@33192
  1426
blanchet@33192
  1427
(* extended_context -> term -> term *)
blanchet@33192
  1428
fun unfold_defs_in_term (ext_ctxt as {thy, destroy_constrs, fast_descrs,
blanchet@33192
  1429
                                      case_names, def_table, ground_thm_table,
blanchet@33192
  1430
                                      ersatz_table, ...}) =
blanchet@33192
  1431
  let
blanchet@33192
  1432
    (* int -> typ list -> term -> term *)
blanchet@33192
  1433
    fun do_term depth Ts t =
blanchet@33192
  1434
      case t of
blanchet@33192
  1435
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@33192
  1436
                      Type ("fun", [_, ran_T]))) $ t1 =>
blanchet@33192
  1437
        ((if is_number_type thy ran_T then
blanchet@33192
  1438
            let
blanchet@33192
  1439
              val j = t1 |> HOLogic.dest_numeral
blanchet@33192
  1440
                         |> ran_T <> int_T ? curry Int.max 0
blanchet@33192
  1441
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1442
            in
blanchet@33192
  1443
              if is_integer_type ran_T then
blanchet@33192
  1444
                Const (s, ran_T)
blanchet@33192
  1445
              else
blanchet@33192
  1446
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1447
                                  $ Const (s, int_T))
blanchet@33192
  1448
            end
blanchet@33192
  1449
            handle TERM _ => raise SAME ()
blanchet@33192
  1450
          else
blanchet@33192
  1451
            raise SAME ())
blanchet@33192
  1452
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1453
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1454
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@33192
  1455
      | (t0 as Const (x as (@{const_name Sigma}, T))) $ t1
blanchet@33192
  1456
        $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1457
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1458
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1459
      | Const (x as (@{const_name distinct},
blanchet@33192
  1460
               Type ("fun", [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1461
        $ (t1 as _ $ _) =>
blanchet@33192
  1462
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1463
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@33192
  1464
      | (t0 as Const (x as (@{const_name If}, _))) $ t1 $ t2 $ t3 =>
blanchet@33192
  1465
        if is_ground_term t1
blanchet@33192
  1466
           andalso exists (Pattern.matches thy o rpair t1)
blanchet@33192
  1467
                          (Inttab.lookup_list ground_thm_table
blanchet@33192
  1468
                                              (hash_term t1)) then
blanchet@33192
  1469
          do_term depth Ts t2
blanchet@33192
  1470
        else
blanchet@33192
  1471
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1472
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1473
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1474
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1475
      | Const x => do_const depth Ts t x []
blanchet@33192
  1476
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1477
      | Free _ => t
blanchet@33192
  1478
      | Var _ => t
blanchet@33192
  1479
      | Bound _ => t
blanchet@33192
  1480
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1481
    (* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
blanchet@33192
  1482
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1483
        (Abs (Name.uu, body_type T,
blanchet@33192
  1484
              select_nth_constr_arg thy x (Bound 0) n res_T), [])
blanchet@33192
  1485
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@33192
  1486
        (select_nth_constr_arg thy x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1487
    (* int -> typ list -> term -> styp -> term list -> term *)
blanchet@33192
  1488
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1489
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1490
        SOME s' =>
blanchet@33192
  1491
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1492
      | NONE =>
blanchet@33192
  1493
        let
blanchet@33192
  1494
          val (const, ts) =
blanchet@33192
  1495
            if is_built_in_const fast_descrs x then
blanchet@33192
  1496
              if s = @{const_name finite} then
blanchet@33580
  1497
                if is_finite_type ext_ctxt (domain_type T) then
blanchet@33192
  1498
                  (Abs ("A", domain_type T, @{const True}), ts)
blanchet@33192
  1499
                else case ts of
blanchet@33864
  1500
                  [Const (@{const_name top}, _)] => (@{const False}, [])
blanchet@33192
  1501
                | _ => (Const x, ts)
blanchet@33192
  1502
              else
blanchet@33192
  1503
                (Const x, ts)
blanchet@33192
  1504
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1505
              SOME n =>
blanchet@33192
  1506
              let
blanchet@33192
  1507
                val (dataT, res_T) = nth_range_type n T
blanchet@33705
  1508
                                     |> pairf domain_type range_type
blanchet@33192
  1509
              in
blanchet@33580
  1510
                (optimized_case_def ext_ctxt dataT res_T
blanchet@33192
  1511
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1512
              end
blanchet@33192
  1513
            | _ =>
blanchet@33192
  1514
              if is_constr thy x then
blanchet@33192
  1515
                (Const x, ts)
blanchet@33581
  1516
              else if is_stale_constr thy x then
blanchet@33581
  1517
                raise NOT_SUPPORTED ("(non-co-)constructors of codatatypes \
blanchet@33581
  1518
                                     \(\"" ^ s ^ "\")")
blanchet@33192
  1519
              else if is_record_get thy x then
blanchet@33192
  1520
                case length ts of
blanchet@33192
  1521
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@33580
  1522
                | _ => (optimized_record_get ext_ctxt s (domain_type T)
blanchet@33192
  1523
                                             (range_type T) (hd ts), tl ts)
blanchet@33192
  1524
              else if is_record_update thy x then
blanchet@33192
  1525
                case length ts of
blanchet@33580
  1526
                  2 => (optimized_record_update ext_ctxt
blanchet@33580
  1527
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1528
                            (do_term depth Ts (hd ts))
blanchet@33580
  1529
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1530
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@33192
  1531
              else if is_rep_fun thy x then
blanchet@33192
  1532
                let val x' = mate_of_rep_fun thy x in
blanchet@33192
  1533
                  if is_constr thy x' then
blanchet@33192
  1534
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1535
                                                    (range_type T)
blanchet@33192
  1536
                  else
blanchet@33192
  1537
                    (Const x, ts)
blanchet@33192
  1538
                end
blanchet@33192
  1539
              else if is_equational_fun ext_ctxt x then
blanchet@33192
  1540
                (Const x, ts)
blanchet@33192
  1541
              else case def_of_const thy def_table x of
blanchet@33192
  1542
                SOME def =>
blanchet@33192
  1543
                if depth > unfold_max_depth then
blanchet@33232
  1544
                  raise LIMIT ("Nitpick_HOL.unfold_defs_in_term",
blanchet@33192
  1545
                               "too many nested definitions (" ^
blanchet@33192
  1546
                               string_of_int depth ^ ") while expanding " ^
blanchet@33192
  1547
                               quote s)
blanchet@33192
  1548
                else if s = @{const_name wfrec'} then
blanchet@33192
  1549
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1550
                else
blanchet@33192
  1551
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1552
              | NONE => (Const x, ts)
blanchet@33192
  1553
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1554
  in do_term 0 [] end
blanchet@33192
  1555
blanchet@33580
  1556
(* extended_context -> typ -> term list *)
blanchet@33580
  1557
fun codatatype_bisim_axioms (ext_ctxt as {thy, ...}) T =
blanchet@33192
  1558
  let
blanchet@33580
  1559
    val xs = datatype_constrs ext_ctxt T
blanchet@33192
  1560
    val set_T = T --> bool_T
blanchet@33192
  1561
    val iter_T = @{typ bisim_iterator}
blanchet@33192
  1562
    val bisim_const = Const (@{const_name bisim}, [iter_T, T, T] ---> bool_T)
blanchet@33192
  1563
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1564
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1565
    val n_var_minus_1 =
blanchet@33192
  1566
      Const (@{const_name Tha}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1567
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1568
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1569
    val x_var = Var (("x", 0), T)
blanchet@33192
  1570
    val y_var = Var (("y", 0), T)
blanchet@33192
  1571
    (* styp -> int -> typ -> term *)
blanchet@33192
  1572
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1573
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1574
       else HOLogic.eq_const nth_T)
blanchet@33192
  1575
      $ select_nth_constr_arg thy x x_var n nth_T
blanchet@33192
  1576
      $ select_nth_constr_arg thy x y_var n nth_T
blanchet@33192
  1577
    (* styp -> term *)
blanchet@33192
  1578
    fun case_func (x as (_, T)) =
blanchet@33192
  1579
      let
blanchet@33192
  1580
        val arg_Ts = binder_types T
blanchet@33192
  1581
        val core_t =
blanchet@33580
  1582
          discriminate_value ext_ctxt x y_var ::
blanchet@33192
  1583
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1584
          |> foldr1 s_conj
blanchet@33192
  1585
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1586
  in
blanchet@33192
  1587
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1588
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@33580
  1589
        $ (betapplys (optimized_case_def ext_ctxt T bool_T,
blanchet@33192
  1590
                      map case_func xs @ [x_var]))),
blanchet@33192
  1591
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@33192
  1592
     $ (Const (@{const_name insert}, [T, set_T] ---> set_T)
blanchet@33192
  1593
        $ x_var $ Const (@{const_name bot_fun_inst.bot_fun}, set_T))]
blanchet@33192
  1594
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1595
  end
blanchet@33192
  1596
blanchet@33192
  1597
exception NO_TRIPLE of unit
blanchet@33192
  1598
blanchet@33192
  1599
(* theory -> styp -> term -> term list * term list * term *)
blanchet@33192
  1600
fun triple_for_intro_rule thy x t =
blanchet@33192
  1601
  let
blanchet@33192
  1602
    val prems = Logic.strip_imp_prems t |> map (ObjectLogic.atomize_term thy)
blanchet@33192
  1603
    val concl = Logic.strip_imp_concl t |> ObjectLogic.atomize_term thy
blanchet@33192
  1604
    val (main, side) = List.partition (exists_Const (equal x)) prems
blanchet@33192
  1605
    (* term -> bool *)
blanchet@33192
  1606
     val is_good_head = equal (Const x) o head_of
blanchet@33192
  1607
  in
blanchet@33192
  1608
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1609
  end
blanchet@33192
  1610
blanchet@33192
  1611
(* term -> term *)
blanchet@33192
  1612
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1613
blanchet@33192
  1614
(* indexname * typ -> term list -> term -> term -> term *)
blanchet@33192
  1615
fun wf_constraint_for rel side concl main =
blanchet@33192
  1616
  let
blanchet@33192
  1617
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1618
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1619
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1620
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1621
  in
blanchet@33192
  1622
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1623
                      HOLogic.all_const T
blanchet@33192
  1624
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1625
                  (t, vars)
blanchet@33192
  1626
  end
blanchet@33192
  1627
blanchet@33192
  1628
(* indexname * typ -> term list * term list * term -> term *)
blanchet@33192
  1629
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1630
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1631
blanchet@33192
  1632
(* Proof.context -> Time.time option -> thm
blanchet@33192
  1633
   -> (Proof.context -> tactic -> tactic) -> bool *)
blanchet@33192
  1634
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1635
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1636
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1637
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1638
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1639
blanchet@33557
  1640
val max_cached_wfs = 100
blanchet@33192
  1641
val cached_timeout = Unsynchronized.ref (SOME Time.zeroTime)
blanchet@33192
  1642
val cached_wf_props : (term * bool) list Unsynchronized.ref =
blanchet@33192
  1643
  Unsynchronized.ref []
blanchet@33192
  1644
krauss@33351
  1645
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1646
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1647
blanchet@33192
  1648
(* extended_context -> const_table -> styp -> bool *)
blanchet@33580
  1649
fun uncached_is_well_founded_inductive_pred
blanchet@33192
  1650
        ({thy, ctxt, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@33192
  1651
         : extended_context) (x as (_, T)) =
blanchet@33192
  1652
  case def_props_for_const thy fast_descrs intro_table x of
blanchet@33580
  1653
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  1654
                      [Const x])
blanchet@33192
  1655
  | intro_ts =>
blanchet@33192
  1656
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1657
          |> filter_out (null o #2) of
blanchet@33192
  1658
       [] => true
blanchet@33192
  1659
     | triples =>
blanchet@33192
  1660
       let
blanchet@33192
  1661
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1662
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33192
  1663
         val j = List.foldl Int.max 0 (map maxidx_of_term intro_ts) + 1
blanchet@33192
  1664
         val rel = (("R", j), rel_T)
blanchet@33192
  1665
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1666
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1667
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1668
         val _ = if debug then
blanchet@33192
  1669
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1670
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1671
                 else
blanchet@33192
  1672
                   ()
blanchet@33192
  1673
       in
blanchet@33557
  1674
         if tac_timeout = (!cached_timeout)
blanchet@33557
  1675
            andalso length (!cached_wf_props) < max_cached_wfs then
blanchet@33557
  1676
           ()
blanchet@33557
  1677
         else
blanchet@33557
  1678
           (cached_wf_props := []; cached_timeout := tac_timeout);
blanchet@33192
  1679
         case AList.lookup (op =) (!cached_wf_props) prop of
blanchet@33192
  1680
           SOME wf => wf
blanchet@33192
  1681
         | NONE =>
blanchet@33192
  1682
           let
blanchet@33192
  1683
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  1684
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  1685
                             termination_tacs
blanchet@33192
  1686
           in Unsynchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1687
       end)
blanchet@33192
  1688
    handle List.Empty => false
blanchet@33192
  1689
         | NO_TRIPLE () => false
blanchet@33192
  1690
blanchet@33192
  1691
(* The type constraint below is a workaround for a Poly/ML bug. *)
blanchet@33192
  1692
blanchet@33192
  1693
(* extended_context -> styp -> bool *)
blanchet@33192
  1694
fun is_well_founded_inductive_pred
blanchet@33192
  1695
        (ext_ctxt as {thy, wfs, def_table, wf_cache, ...} : extended_context)
blanchet@33192
  1696
        (x as (s, _)) =
blanchet@33192
  1697
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1698
    SOME (SOME b) => b
blanchet@33197
  1699
  | _ => s mem [@{const_name Nats}, @{const_name fold_graph'}]
blanchet@33192
  1700
         orelse case AList.lookup (op =) (!wf_cache) x of
blanchet@33192
  1701
                  SOME (_, wf) => wf
blanchet@33192
  1702
                | NONE =>
blanchet@33192
  1703
                  let
blanchet@33192
  1704
                    val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@33580
  1705
                    val wf = uncached_is_well_founded_inductive_pred ext_ctxt x
blanchet@33192
  1706
                  in
blanchet@33192
  1707
                    Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@33192
  1708
                  end
blanchet@33192
  1709
blanchet@33192
  1710
(* typ list -> typ -> typ -> term -> term *)
blanchet@33192
  1711
fun ap_curry [_] _ _ t = t
blanchet@33192
  1712
  | ap_curry arg_Ts tuple_T body_T t =
blanchet@33192
  1713
    let val n = length arg_Ts in
blanchet@33192
  1714
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1715
                incr_boundvars n t
blanchet@33192
  1716
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1717
    end
blanchet@33192
  1718
blanchet@33192
  1719
(* int -> term -> int *)
blanchet@33192
  1720
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1721
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@33192
  1722
  | num_occs_of_bound_in_term j (Abs (s, T, t')) =
blanchet@33192
  1723
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1724
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1725
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1726
blanchet@33192
  1727
(* term -> bool *)
blanchet@33192
  1728
val is_linear_inductive_pred_def =
blanchet@33192
  1729
  let
blanchet@33192
  1730
    (* int -> term -> bool *)
blanchet@33192
  1731
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  1732
        do_disjunct (j + 1) t2
blanchet@33192
  1733
      | do_disjunct j t =
blanchet@33192
  1734
        case num_occs_of_bound_in_term j t of
blanchet@33192
  1735
          0 => true
blanchet@33192
  1736
        | 1 => exists (equal (Bound j) o head_of) (conjuncts t)
blanchet@33192
  1737
        | _ => false
blanchet@33192
  1738
    (* term -> bool *)
blanchet@33192
  1739
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1740
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  1741
          case length xs of
blanchet@33192
  1742
            1 => false
blanchet@33192
  1743
          | n => forall (do_disjunct (n - 1)) (disjuncts body)
blanchet@33192
  1744
        end
blanchet@33192
  1745
      | do_lfp_def _ = false
blanchet@33192
  1746
  in do_lfp_def o strip_abs_body end
blanchet@33192
  1747
blanchet@33851
  1748
(* int -> int list list *)
blanchet@33851
  1749
fun n_ptuple_paths 0 = []
blanchet@33851
  1750
  | n_ptuple_paths 1 = []
blanchet@33851
  1751
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  1752
(* int -> typ -> typ -> term -> term *)
blanchet@33851
  1753
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  1754
blanchet@33192
  1755
(* term -> term * term *)
blanchet@33192
  1756
val linear_pred_base_and_step_rhss =
blanchet@33192
  1757
  let
blanchet@33192
  1758
    (* term -> term *)
blanchet@33192
  1759
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1760
        let
blanchet@33192
  1761
          val (xs, body) = strip_abs t2
blanchet@33192
  1762
          val arg_Ts = map snd (tl xs)
blanchet@33192
  1763
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  1764
          val j = length arg_Ts
blanchet@33192
  1765
          (* int -> term -> term *)
blanchet@33192
  1766
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  1767
              Const (@{const_name Ex}, T1)
blanchet@33192
  1768
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  1769
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  1770
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  1771
            | repair_rec j t =
blanchet@33192
  1772
              let val (head, args) = strip_comb t in
blanchet@33192
  1773
                if head = Bound j then
blanchet@33192
  1774
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  1775
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  1776
                else
blanchet@33192
  1777
                  t
blanchet@33192
  1778
              end
blanchet@33192
  1779
          val (nonrecs, recs) =
blanchet@33192
  1780
            List.partition (equal 0 o num_occs_of_bound_in_term j)
blanchet@33192
  1781
                           (disjuncts body)
blanchet@33192
  1782
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  1783
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  1784
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  1785
        in
blanchet@33192
  1786
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  1787
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  1788
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  1789
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  1790
        end
blanchet@33192
  1791
      | aux t =
blanchet@33232
  1792
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  1793
  in aux end
blanchet@33192
  1794
blanchet@33192
  1795
(* extended_context -> styp -> term -> term *)
blanchet@33851
  1796
fun starred_linear_pred_const (ext_ctxt as {simp_table, ...}) (x as (s, T))
blanchet@33851
  1797
                              def =
blanchet@33192
  1798
  let
blanchet@33192
  1799
    val j = maxidx_of_term def + 1
blanchet@33192
  1800
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1801
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1802
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  1803
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  1804
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  1805
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  1806
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  1807
    val set_T = tuple_T --> bool_T
blanchet@33192
  1808
    val curried_T = tuple_T --> set_T
blanchet@33192
  1809
    val uncurried_T = Type ("*", [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  1810
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  1811
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  1812
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  1813
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1814
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  1815
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  1816
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  1817
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1818
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  1819
  in
blanchet@33192
  1820
    list_abs (outer,
blanchet@33192
  1821
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  1822
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  1823
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  1824
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  1825
              $ list_comb (Const base_x, outer_bounds)
blanchet@33192
  1826
              |> ap_curry tuple_arg_Ts tuple_T bool_T)
blanchet@33192
  1827
    |> unfold_defs_in_term ext_ctxt
blanchet@33192
  1828
  end
blanchet@33192
  1829
blanchet@33192
  1830
(* extended_context -> bool -> styp -> term *)
blanchet@33192
  1831
fun unrolled_inductive_pred_const (ext_ctxt as {thy, star_linear_preds,
blanchet@33192
  1832
                                                def_table, simp_table, ...})
blanchet@33192
  1833
                                  gfp (x as (s, T)) =
blanchet@33192
  1834
  let
blanchet@33192
  1835
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  1836
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  1837
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  1838
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1839
  in
blanchet@33192
  1840
    if is_equational_fun ext_ctxt x' then
blanchet@33192
  1841
      unrolled_const (* already done *)
blanchet@33192
  1842
    else if not gfp andalso is_linear_inductive_pred_def def
blanchet@33192
  1843
         andalso star_linear_preds then
blanchet@33851
  1844
      starred_linear_pred_const ext_ctxt x def
blanchet@33192
  1845
    else
blanchet@33192
  1846
      let
blanchet@33192
  1847
        val j = maxidx_of_term def + 1
blanchet@33192
  1848
        val (outer, fp_app) = strip_abs def
blanchet@33192
  1849
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1850
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  1851
        val next = suc_const iter_T $ cur
blanchet@33192
  1852
        val rhs = case fp_app of
blanchet@33192
  1853
                    Const _ $ t =>
blanchet@33192
  1854
                    betapply (t, list_comb (Const x', next :: outer_bounds))
blanchet@33232
  1855
                  | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_\
blanchet@33232
  1856
                                     \const", [fp_app])
blanchet@33192
  1857
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  1858
        val all = outer @ inner
blanchet@33192
  1859
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  1860
        val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  1861
        val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
blanchet@33192
  1862
                 |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  1863
        val _ = add_simps simp_table s' [eq]
blanchet@33192
  1864
      in unrolled_const end
blanchet@33192
  1865
  end
blanchet@33192
  1866
blanchet@33192
  1867
(* extended_context -> styp -> term *)
blanchet@33192
  1868
fun raw_inductive_pred_axiom ({thy, def_table, ...} : extended_context) x =
blanchet@33192
  1869
  let
blanchet@33192
  1870
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1871
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1872
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1873
    val rhs = case fp_app of
blanchet@33192
  1874
                Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
blanchet@33232
  1875
              | _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom",
blanchet@33192
  1876
                                 [fp_app])
blanchet@33192
  1877
    val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  1878
    val all = outer @ inner
blanchet@33192
  1879
    val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  1880
    val j = maxidx_of_term def + 1
blanchet@33192
  1881
    val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  1882
  in
blanchet@33192
  1883
    HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
blanchet@33192
  1884
    |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  1885
  end
blanchet@33192
  1886
fun inductive_pred_axiom ext_ctxt (x as (s, T)) =
blanchet@33192
  1887
  if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
blanchet@33192
  1888
    let val x' = (after_name_sep s, T) in
blanchet@33192
  1889
      raw_inductive_pred_axiom ext_ctxt x' |> subst_atomic [(Const x', Const x)]
blanchet@33192
  1890
    end
blanchet@33192
  1891
  else
blanchet@33192
  1892
    raw_inductive_pred_axiom ext_ctxt x
blanchet@33192
  1893
blanchet@33192
  1894
(* extended_context -> styp -> term list *)
blanchet@33192
  1895
fun raw_equational_fun_axioms (ext_ctxt as {thy, fast_descrs, simp_table,
blanchet@33192
  1896
                                            psimp_table, ...}) (x as (s, _)) =
blanchet@33556
  1897
  case def_props_for_const thy fast_descrs (!simp_table) x of
blanchet@33192
  1898
    [] => (case def_props_for_const thy fast_descrs psimp_table x of
blanchet@33192
  1899
             [] => [inductive_pred_axiom ext_ctxt x]
blanchet@33192
  1900
           | psimps => psimps)
blanchet@33192
  1901
  | simps => simps
blanchet@33192
  1902
blanchet@33192
  1903
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
blanchet@33192
  1904
blanchet@33192
  1905
(* term list -> term list *)
blanchet@33556
  1906
fun merge_type_vars_in_terms ts =
blanchet@33192
  1907
  let
blanchet@33192
  1908
    (* typ -> (sort * string) list -> (sort * string) list *)
blanchet@33192
  1909
    fun add_type (TFree (s, S)) table =
blanchet@33192
  1910
        (case AList.lookup (op =) table S of
blanchet@33192
  1911
           SOME s' =>
blanchet@33192
  1912
           if string_ord (s', s) = LESS then AList.update (op =) (S, s') table
blanchet@33192
  1913
           else table
blanchet@33192
  1914
         | NONE => (S, s) :: table)
blanchet@33192
  1915
      | add_type _ table = table
blanchet@33192
  1916
    val table = fold (fold_types (fold_atyps add_type)) ts []
blanchet@33192
  1917
    (* typ -> typ *)
blanchet@33192
  1918
    fun coalesce (TFree (s, S)) = TFree (AList.lookup (op =) table S |> the, S)
blanchet@33192
  1919
      | coalesce T = T
blanchet@33192
  1920
  in map (map_types (map_atyps coalesce)) ts end
blanchet@33192
  1921
blanchet@33192
  1922
(* extended_context -> typ -> typ list -> typ list *)
blanchet@33192
  1923
fun add_ground_types ext_ctxt T accum =
blanchet@33192
  1924
  case T of
blanchet@33192
  1925
    Type ("fun", Ts) => fold (add_ground_types ext_ctxt) Ts accum
blanchet@33192
  1926
  | Type ("*", Ts) => fold (add_ground_types ext_ctxt) Ts accum
blanchet@33192
  1927
  | Type (@{type_name itself}, [T1]) => add_ground_types ext_ctxt T1 accum
blanchet@33192
  1928
  | Type (_, Ts) =>
blanchet@33192
  1929
    if T mem @{typ prop} :: @{typ bool} :: @{typ unit} :: accum then
blanchet@33192
  1930
      accum
blanchet@33192
  1931
    else
blanchet@33192
  1932
      T :: accum
blanchet@33192
  1933
      |> fold (add_ground_types ext_ctxt)
blanchet@33192
  1934
              (case boxed_datatype_constrs ext_ctxt T of
blanchet@33192
  1935
                 [] => Ts
blanchet@33192
  1936
               | xs => map snd xs)
blanchet@33192
  1937
  | _ => insert (op =) T accum
blanchet@33192
  1938
(* extended_context -> typ -> typ list *)
blanchet@33192
  1939
fun ground_types_in_type ext_ctxt T = add_ground_types ext_ctxt T []
blanchet@33192
  1940
(* extended_context -> term list -> typ list *)
blanchet@33192
  1941
fun ground_types_in_terms ext_ctxt ts =
blanchet@33192
  1942
  fold (fold_types (add_ground_types ext_ctxt)) ts []
blanchet@33192
  1943
blanchet@33192
  1944
(* typ list -> int -> term -> bool *)
blanchet@33192
  1945
fun has_heavy_bounds_or_vars Ts level t =
blanchet@33192
  1946
  let
blanchet@33192
  1947
    (* typ list -> bool *)
blanchet@33192
  1948
    fun aux [] = false
blanchet@33192
  1949
      | aux [T] = is_fun_type T orelse is_pair_type T
blanchet@33192
  1950
      | aux _ = true
blanchet@33192
  1951
  in aux (map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t)) end
blanchet@33192
  1952
blanchet@33192
  1953
(* typ list -> int -> int -> int -> term -> term *)
blanchet@33192
  1954
fun fresh_value_var Ts k n j t =
blanchet@33192
  1955
  Var ((val_var_prefix ^ nat_subscript (n - j), k), fastype_of1 (Ts, t))
blanchet@33192
  1956
blanchet@33192
  1957
(* theory -> typ list -> bool -> int -> int -> term -> term list -> term list
blanchet@33192
  1958
   -> term * term list *)
blanchet@33192
  1959
fun pull_out_constr_comb thy Ts relax k level t args seen =
blanchet@33192
  1960
  let val t_comb = list_comb (t, args) in
blanchet@33192
  1961
    case t of
blanchet@33192
  1962
      Const x =>
blanchet@33192
  1963
      if not relax andalso is_constr thy x
blanchet@33192
  1964
         andalso not (is_fun_type (fastype_of1 (Ts, t_comb)))
blanchet@33192
  1965
         andalso has_heavy_bounds_or_vars Ts level t_comb
blanchet@33192
  1966
         andalso not (loose_bvar (t_comb, level)) then
blanchet@33192
  1967
        let
blanchet@33192
  1968
          val (j, seen) = case find_index (equal t_comb) seen of
blanchet@33192
  1969
                            ~1 => (0, t_comb :: seen)
blanchet@33192
  1970
                          | j => (j, seen)
blanchet@33192
  1971
        in (fresh_value_var Ts k (length seen) j t_comb, seen) end
blanchet@33192
  1972
      else
blanchet@33192
  1973
        (t_comb, seen)
blanchet@33192
  1974
    | _ => (t_comb, seen)
blanchet@33192
  1975
  end
blanchet@33192
  1976
blanchet@33192
  1977
(* (term -> term) -> typ list -> int -> term list -> term list *)
blanchet@33192
  1978
fun equations_for_pulled_out_constrs mk_eq Ts k seen =
blanchet@33192
  1979
  let val n = length seen in
blanchet@33192
  1980
    map2 (fn j => fn t => mk_eq (fresh_value_var Ts k n j t, t))
blanchet@33192
  1981
         (index_seq 0 n) seen
blanchet@33192
  1982
  end
blanchet@33192
  1983
blanchet@33192
  1984
(* theory -> bool -> term -> term *)
blanchet@33192
  1985
fun pull_out_universal_constrs thy def t =
blanchet@33192
  1986
  let
blanchet@33192
  1987
    val k = maxidx_of_term t + 1
blanchet@33192
  1988
    (* typ list -> bool -> term -> term list -> term list -> term * term list *)
blanchet@33192
  1989
    fun do_term Ts def t args seen =
blanchet@33192
  1990
      case t of
blanchet@33192
  1991
        (t0 as Const (@{const_name "=="}, _)) $ t1 $ t2 =>
blanchet@33192
  1992
        do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1993
      | (t0 as @{const "==>"}) $ t1 $ t2 => do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1994
      | (t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2 =>
blanchet@33192
  1995
        do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1996
      | (t0 as @{const "op -->"}) $ t1 $ t2 => do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1997
      | Abs (s, T, t') =>
blanchet@33192
  1998
        let val (t', seen) = do_term (T :: Ts) def t' [] seen in
blanchet@33192
  1999
          (list_comb (Abs (s, T, t'), args), seen)
blanchet@33192
  2000
        end
blanchet@33192
  2001
      | t1 $ t2 =>
blanchet@33192
  2002
        let val (t2, seen) = do_term Ts def t2 [] seen in
blanchet@33192
  2003
          do_term Ts def t1 (t2 :: args) seen
blanchet@33192
  2004
        end
blanchet@33192
  2005
      | _ => pull_out_constr_comb thy Ts def k 0 t args seen
blanchet@33192
  2006
    (* typ list -> bool -> term -> term -> term -> term list
blanchet@33192
  2007
       -> term * term list *)
blanchet@33192
  2008
    and do_eq_or_imp Ts def t0 t1 t2 seen =
blanchet@33192
  2009
      let
blanchet@33192
  2010
        val (t2, seen) = do_term Ts def t2 [] seen
blanchet@33192
  2011
        val (t1, seen) = do_term Ts false t1 [] seen
blanchet@33192
  2012
      in (t0 $ t1 $ t2, seen) end
blanchet@33192
  2013
    val (concl, seen) = do_term [] def t [] []
blanchet@33192
  2014
  in
blanchet@33192
  2015
    Logic.list_implies (equations_for_pulled_out_constrs Logic.mk_equals [] k
blanchet@33192
  2016
                                                         seen, concl)
blanchet@33192
  2017
  end
blanchet@33192
  2018
blanchet@33580
  2019
(* extended_context -> bool -> term -> term *)
blanchet@33580
  2020
fun destroy_pulled_out_constrs (ext_ctxt as {thy, ...}) axiom t =
blanchet@33192
  2021
  let
blanchet@33192
  2022
    (* styp -> int *)
blanchet@33192
  2023
    val num_occs_of_var =
blanchet@33192
  2024
      fold_aterms (fn Var z => (fn f => fn z' => f z' |> z = z' ? Integer.add 1)
blanchet@33192
  2025
                    | _ => I) t (K 0)
blanchet@33192
  2026
    (* bool -> term -> term *)
blanchet@33192
  2027
    fun aux careful ((t0 as Const (@{const_name "=="}, _)) $ t1 $ t2) =
blanchet@33192
  2028
        aux_eq careful true t0 t1 t2
blanchet@33192
  2029
      | aux careful ((t0 as @{const "==>"}) $ t1 $ t2) =
blanchet@33192
  2030
        t0 $ aux false t1 $ aux careful t2
blanchet@33192
  2031
      | aux careful ((t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2) =
blanchet@33192
  2032
        aux_eq careful true t0 t1 t2
blanchet@33192
  2033
      | aux careful ((t0 as @{const "op -->"}) $ t1 $ t2) =
blanchet@33192
  2034
        t0 $ aux false t1 $ aux careful t2
blanchet@33192
  2035
      | aux careful (Abs (s, T, t')) = Abs (s, T, aux careful t')
blanchet@33192
  2036
      | aux careful (t1 $ t2) = aux careful t1 $ aux careful t2
blanchet@33192
  2037
      | aux _ t = t
blanchet@33192
  2038
    (* bool -> bool -> term -> term -> term -> term *)
blanchet@33192
  2039
    and aux_eq careful pass1 t0 t1 t2 =
blanchet@33192
  2040
      (if careful then
blanchet@33192
  2041
         raise SAME ()
blanchet@33192
  2042
       else if axiom andalso is_Var t2
blanchet@33192
  2043
               andalso num_occs_of_var (dest_Var t2) = 1 then
blanchet@33192
  2044
         @{const True}
blanchet@33192
  2045
       else case strip_comb t2 of
blanchet@33192
  2046
         (Const (x as (s, T)), args) =>
blanchet@33192
  2047
         let val arg_Ts = binder_types T in
blanchet@33192
  2048
           if length arg_Ts = length args
blanchet@33192
  2049
              andalso (is_constr thy x orelse s mem [@{const_name Pair}]
blanchet@33192
  2050
                       orelse x = dest_Const @{const Suc})
blanchet@33192
  2051
              andalso (not careful orelse not (is_Var t1)
blanchet@33192
  2052
                       orelse String.isPrefix val_var_prefix
blanchet@33192
  2053
                                              (fst (fst (dest_Var t1)))) then
blanchet@33580
  2054
             discriminate_value ext_ctxt x t1 ::
blanchet@33192
  2055
             map3 (sel_eq x t1) (index_seq 0 (length args)) arg_Ts args
blanchet@33192
  2056
             |> foldr1 s_conj
blanchet@33192
  2057
             |> body_type (type_of t0) = prop_T ? HOLogic.mk_Trueprop
blanchet@33192
  2058
           else
blanchet@33192
  2059
             raise SAME ()
blanchet@33192
  2060
         end
blanchet@33192
  2061
       | _ => raise SAME ())
blanchet@33192
  2062
      handle SAME () => if pass1 then aux_eq careful false t0 t2 t1
blanchet@33192
  2063
                        else t0 $ aux false t2 $ aux false t1
blanchet@33192
  2064
    (* styp -> term -> int -> typ -> term -> term *)
blanchet@33192
  2065
    and sel_eq x t n nth_T nth_t =
blanchet@33192
  2066
      HOLogic.eq_const nth_T $ nth_t $ select_nth_constr_arg thy x t n nth_T
blanchet@33192
  2067
      |> aux false
blanchet@33192
  2068
  in aux axiom t end
blanchet@33192
  2069
blanchet@33192
  2070
(* theory -> term -> term *)
blanchet@33192
  2071
fun simplify_constrs_and_sels thy t =
blanchet@33192
  2072
  let
blanchet@33192
  2073
    (* term -> int -> term *)
blanchet@33192
  2074
    fun is_nth_sel_on t' n (Const (s, _) $ t) =
blanchet@33192
  2075
        (t = t' andalso is_sel_like_and_no_discr s
blanchet@33192
  2076
         andalso sel_no_from_name s = n)
blanchet@33192
  2077
      | is_nth_sel_on _ _ _ = false
blanchet@33192
  2078
    (* term -> term list -> term *)
blanchet@33192
  2079
    fun do_term (Const (@{const_name Rep_Frac}, _)
blanchet@33192
  2080
                 $ (Const (@{const_name Abs_Frac}, _) $ t1)) [] = do_term t1 []
blanchet@33192
  2081
      | do_term (Const (@{const_name Abs_Frac}, _)
blanchet@33192
  2082
                 $ (Const (@{const_name Rep_Frac}, _) $ t1)) [] = do_term t1 []
blanchet@33192
  2083
      | do_term (t1 $ t2) args = do_term t1 (do_term t2 [] :: args)
blanchet@33192
  2084
      | do_term (t as Const (x as (s, T))) (args as _ :: _) =
blanchet@33192
  2085
        ((if is_constr_like thy x then
blanchet@33192
  2086
            if length args = num_binder_types T then
blanchet@33192
  2087
              case hd args of
blanchet@33192
  2088
                Const (x' as (_, T')) $ t' =>
blanchet@33192
  2089
                if domain_type T' = body_type T
blanchet@33192
  2090
                   andalso forall (uncurry (is_nth_sel_on t'))
blanchet@33192
  2091
                                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  2092
                  t'
blanchet@33192
  2093
                else
blanchet@33192
  2094
                  raise SAME ()
blanchet@33192
  2095
              | _ => raise SAME ()
blanchet@33192
  2096
            else
blanchet@33192
  2097
              raise SAME ()
blanchet@33192
  2098
          else if is_sel_like_and_no_discr s then
blanchet@33192
  2099
            case strip_comb (hd args) of
blanchet@33192
  2100
              (Const (x' as (s', T')), ts') =>
blanchet@33192
  2101
              if is_constr_like thy x'
blanchet@33192
  2102
                 andalso constr_name_for_sel_like s = s'
blanchet@33192
  2103
                 andalso not (exists is_pair_type (binder_types T')) then
blanchet@33192
  2104
                list_comb (nth ts' (sel_no_from_name s), tl args)
blanchet@33192
  2105
              else
blanchet@33192
  2106
                raise SAME ()
blanchet@33192
  2107
            | _ => raise SAME ()
blanchet@33192
  2108
          else
blanchet@33192
  2109
            raise SAME ())
blanchet@33192
  2110
         handle SAME () => betapplys (t, args))
blanchet@33192
  2111
      | do_term (Abs (s, T, t')) args =
blanchet@33192
  2112
        betapplys (Abs (s, T, do_term t' []), args)
blanchet@33192
  2113
      | do_term t args = betapplys (t, args)
blanchet@33192
  2114
  in do_term t [] end
blanchet@33192
  2115
blanchet@33192
  2116
(* term -> term *)
blanchet@33192
  2117
fun curry_assms (@{const "==>"} $ (@{const Trueprop}
blanchet@33192
  2118
                                   $ (@{const "op &"} $ t1 $ t2)) $ t3) =
blanchet@33192
  2119
    curry_assms (Logic.list_implies ([t1, t2] |> map HOLogic.mk_Trueprop, t3))
blanchet@33192
  2120
  | curry_assms (@{const "==>"} $ t1 $ t2) =
blanchet@33192
  2121
    @{const "==>"} $ curry_assms t1 $ curry_assms t2
blanchet@33192
  2122
  | curry_assms t = t
blanchet@33192
  2123
blanchet@33192
  2124
(* term -> term *)
blanchet@33192
  2125
val destroy_universal_equalities =
blanchet@33192
  2126
  let
blanchet@33192
  2127
    (* term list -> (indexname * typ) list -> term -> term *)
blanchet@33192
  2128
    fun aux prems zs t =
blanchet@33192
  2129
      case t of
blanchet@33192
  2130
        @{const "==>"} $ t1 $ t2 => aux_implies prems zs t1 t2
blanchet@33192
  2131
      | _ => Logic.list_implies (rev prems, t)
blanchet@33192
  2132
    (* term list -> (indexname * typ) list -> term -> term -> term *)
blanchet@33192
  2133
    and aux_implies prems zs t1 t2 =
blanchet@33192
  2134
      case t1 of
blanchet@33192
  2135
        Const (@{const_name "=="}, _) $ Var z $ t' => aux_eq prems zs z t' t1 t2
blanchet@33192
  2136
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ Var z $ t') =>
blanchet@33192
  2137
        aux_eq prems zs z t' t1 t2
blanchet@33192
  2138
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t' $ Var z) =>
blanchet@33192
  2139
        aux_eq prems zs z t' t1 t2
blanchet@33192
  2140
      | _ => aux (t1 :: prems) (Term.add_vars t1 zs) t2
blanchet@33192
  2141
    (* term list -> (indexname * typ) list -> indexname * typ -> term -> term
blanchet@33192
  2142
       -> term -> term *)
blanchet@33192
  2143
    and aux_eq prems zs z t' t1 t2 =
blanchet@33192
  2144
      if not (z mem zs) andalso not (exists_subterm (equal (Var z)) t') then
blanchet@33192
  2145
        aux prems zs (subst_free [(Var z, t')] t2)
blanchet@33192
  2146
      else
blanchet@33192
  2147
        aux (t1 :: prems) (Term.add_vars t1 zs) t2
blanchet@33192
  2148
  in aux [] [] end
blanchet@33192
  2149
blanchet@33192
  2150
(* theory -> term -> term *)