src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Fri Oct 23 18:59:24 2009 +0200 (2009-10-23)
changeset 33197 de6285ebcc05
parent 33192 08a39a957ed7
child 33200 c56c627dae19
permissions -rw-r--r--
continuation of Nitpick's integration into Isabelle;
added examples, and integrated non-Main theories better.
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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 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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  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_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 : theory -> typ -> styp list
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  val boxed_datatype_constrs : extended_context -> typ -> styp list
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  val num_datatype_constrs : theory -> 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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    theory -> int -> int -> (typ * int) list -> typ -> int
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  val is_finite_type : theory -> 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 coalesce_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 NitpickHOL : NITPICK_HOL =
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struct
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open NitpickUtil
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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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structure TheoryData = TheoryDataFun(
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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 copy = I
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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}) =
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    {frac_types = AList.merge (op =) (op =) (fs1, fs2),
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     codatatypes = AList.merge (op =) (op =) (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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   "NitpickNut.nut_from_term", and perhaps in "NitpickMono.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),
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   (@{const_name minus_nat_inst.minus_nat}, 0),
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   (@{const_name times_nat_inst.times_nat}, 0),
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   (@{const_name div_nat_inst.div_nat}, 0),
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   304
   (@{const_name div_nat_inst.mod_nat}, 0),
blanchet@33192
   305
   (@{const_name ord_nat_inst.less_nat}, 2),
blanchet@33192
   306
   (@{const_name ord_nat_inst.less_eq_nat}, 2),
blanchet@33192
   307
   (@{const_name nat_gcd}, 0),
blanchet@33192
   308
   (@{const_name nat_lcm}, 0),
blanchet@33192
   309
   (@{const_name zero_int_inst.zero_int}, 0),
blanchet@33192
   310
   (@{const_name one_int_inst.one_int}, 0),
blanchet@33192
   311
   (@{const_name plus_int_inst.plus_int}, 0),
blanchet@33192
   312
   (@{const_name minus_int_inst.minus_int}, 0),
blanchet@33192
   313
   (@{const_name times_int_inst.times_int}, 0),
blanchet@33192
   314
   (@{const_name div_int_inst.div_int}, 0),
blanchet@33192
   315
   (@{const_name div_int_inst.mod_int}, 0),
blanchet@33192
   316
   (@{const_name uminus_int_inst.uminus_int}, 0), (* FIXME: needed? *)
blanchet@33192
   317
   (@{const_name ord_int_inst.less_int}, 2),
blanchet@33192
   318
   (@{const_name ord_int_inst.less_eq_int}, 2),
blanchet@33192
   319
   (@{const_name Tha}, 1),
blanchet@33192
   320
   (@{const_name Frac}, 0),
blanchet@33192
   321
   (@{const_name norm_frac}, 0)]
blanchet@33192
   322
val built_in_descr_consts =
blanchet@33192
   323
  [(@{const_name The}, 1),
blanchet@33192
   324
   (@{const_name Eps}, 1)]
blanchet@33192
   325
val built_in_typed_consts =
blanchet@33192
   326
  [((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   327
val built_in_set_consts =
blanchet@33192
   328
  [(@{const_name lower_semilattice_fun_inst.inf_fun}, 2),
blanchet@33192
   329
   (@{const_name upper_semilattice_fun_inst.sup_fun}, 2),
blanchet@33192
   330
   (@{const_name minus_fun_inst.minus_fun}, 2),
blanchet@33192
   331
   (@{const_name ord_fun_inst.less_eq_fun}, 2)]
blanchet@33192
   332
blanchet@33192
   333
(* typ -> typ *)
blanchet@33192
   334
fun unbox_type (Type (@{type_name fun_box}, Ts)) =
blanchet@33192
   335
    Type ("fun", map unbox_type Ts)
blanchet@33192
   336
  | unbox_type (Type (@{type_name pair_box}, Ts)) =
blanchet@33192
   337
    Type ("*", map unbox_type Ts)
blanchet@33192
   338
  | unbox_type (Type (s, Ts)) = Type (s, map unbox_type Ts)
blanchet@33192
   339
  | unbox_type T = T
blanchet@33192
   340
(* Proof.context -> typ -> string *)
blanchet@33192
   341
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unbox_type
blanchet@33192
   342
blanchet@33192
   343
(* string -> string -> string *)
blanchet@33192
   344
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@33192
   345
(* string -> string *)
blanchet@33192
   346
fun short_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   347
(* string -> term -> term *)
blanchet@33192
   348
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@33192
   349
(* term -> term *)
blanchet@33192
   350
val shorten_abs_vars = Term.map_abs_vars short_name
blanchet@33192
   351
(* string -> string *)
blanchet@33192
   352
fun short_const_name s =
blanchet@33192
   353
  case space_explode name_sep s of
blanchet@33192
   354
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@33192
   355
  | ss => map short_name ss |> space_implode "_"
blanchet@33192
   356
(* term -> term *)
blanchet@33192
   357
val shorten_const_names_in_term =
blanchet@33192
   358
  map_aterms (fn Const (s, T) => Const (short_const_name s, T) | t => t)
blanchet@33192
   359
blanchet@33192
   360
(* theory -> typ * typ -> bool *)
blanchet@33192
   361
fun type_match thy (T1, T2) =
blanchet@33192
   362
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   363
  handle Type.TYPE_MATCH => false
blanchet@33192
   364
(* theory -> styp * styp -> bool *)
blanchet@33192
   365
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   366
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   367
(* theory -> term * term -> bool *)
blanchet@33192
   368
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   369
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@33192
   370
    const_match thy ((short_name s1, T1), (short_name s2, T2))
blanchet@33192
   371
  | term_match thy (t1, t2) = t1 aconv t2
blanchet@33192
   372
blanchet@33192
   373
(* typ -> bool *)
blanchet@33192
   374
fun is_TFree (TFree _) = true
blanchet@33192
   375
  | is_TFree _ = false
blanchet@33192
   376
fun is_higher_order_type (Type ("fun", _)) = true
blanchet@33192
   377
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   378
  | is_higher_order_type _ = false
blanchet@33192
   379
fun is_fun_type (Type ("fun", _)) = true
blanchet@33192
   380
  | is_fun_type _ = false
blanchet@33192
   381
fun is_set_type (Type ("fun", [_, @{typ bool}])) = true
blanchet@33192
   382
  | is_set_type _ = false
blanchet@33192
   383
fun is_pair_type (Type ("*", _)) = true
blanchet@33192
   384
  | is_pair_type _ = false
blanchet@33192
   385
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   386
  | is_lfp_iterator_type _ = false
blanchet@33192
   387
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   388
  | is_gfp_iterator_type _ = false
blanchet@33192
   389
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@33192
   390
val is_boolean_type = equal prop_T orf equal bool_T
blanchet@33192
   391
val is_integer_type =
blanchet@33192
   392
  member (op =) [nat_T, int_T, @{typ bisim_iterator}] orf is_fp_iterator_type
blanchet@33192
   393
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   394
(* theory -> typ -> bool *)
blanchet@33192
   395
fun is_frac_type thy (Type (s, [])) =
blanchet@33192
   396
    not (null (these (AList.lookup (op =) (#frac_types (TheoryData.get thy))
blanchet@33192
   397
                                          s)))
blanchet@33192
   398
  | is_frac_type _ _ = false
blanchet@33192
   399
fun is_number_type thy = is_integer_type orf is_frac_type thy
blanchet@33192
   400
blanchet@33192
   401
(* bool -> styp -> typ *)
blanchet@33192
   402
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   403
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   404
        binder_types T)
blanchet@33192
   405
(* typ -> styp *)
blanchet@33192
   406
fun const_for_iterator_type (Type (s, Ts)) = (after_name_sep s, Ts ---> bool_T)
blanchet@33192
   407
  | const_for_iterator_type T =
blanchet@33192
   408
    raise TYPE ("NitpickHOL.const_for_iterator_type", [T], [])
blanchet@33192
   409
blanchet@33192
   410
(* int -> typ -> typ * typ *)
blanchet@33192
   411
fun strip_n_binders 0 T = ([], T)
blanchet@33192
   412
  | strip_n_binders n (Type ("fun", [T1, T2])) =
blanchet@33192
   413
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   414
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@33192
   415
    strip_n_binders n (Type ("fun", Ts))
blanchet@33192
   416
  | strip_n_binders _ T = raise TYPE ("NitpickHOL.strip_n_binders", [T], [])
blanchet@33192
   417
(* typ -> typ *)
blanchet@33192
   418
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   419
blanchet@33192
   420
(* typ -> int *)
blanchet@33192
   421
fun num_factors_in_type (Type ("*", [T1, T2])) =
blanchet@33192
   422
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   423
  | num_factors_in_type _ = 1
blanchet@33192
   424
fun num_binder_types (Type ("fun", [_, T2])) = 1 + num_binder_types T2
blanchet@33192
   425
  | num_binder_types _ = 0
blanchet@33192
   426
(* typ -> typ list *)
blanchet@33192
   427
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   428
fun maybe_curried_binder_types T =
blanchet@33192
   429
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   430
blanchet@33192
   431
(* typ -> term list -> term *)
blanchet@33192
   432
fun mk_flat_tuple _ [t] = t
blanchet@33192
   433
  | mk_flat_tuple (Type ("*", [T1, T2])) (t :: ts) =
blanchet@33192
   434
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33192
   435
  | mk_flat_tuple T ts = raise TYPE ("NitpickHOL.mk_flat_tuple", [T], ts)
blanchet@33192
   436
(* int -> term -> term list *)
blanchet@33192
   437
fun dest_n_tuple 1 t = [t]
blanchet@33192
   438
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   439
blanchet@33192
   440
(* int -> typ -> typ list *)
blanchet@33192
   441
fun dest_n_tuple_type 1 T = [T]
blanchet@33192
   442
  | dest_n_tuple_type n (Type (_, [T1, T2])) =
blanchet@33192
   443
    T1 :: dest_n_tuple_type (n - 1) T2
blanchet@33192
   444
  | dest_n_tuple_type _ T = raise TYPE ("NitpickHOL.dest_n_tuple_type", [T], [])
blanchet@33192
   445
blanchet@33192
   446
(* (typ * typ) list -> typ -> typ *)
blanchet@33192
   447
fun typ_subst [] T = T
blanchet@33192
   448
  | typ_subst ps T =
blanchet@33192
   449
    let
blanchet@33192
   450
      (* typ -> typ *)
blanchet@33192
   451
      fun subst T =
blanchet@33192
   452
        case AList.lookup (op =) ps T of
blanchet@33192
   453
          SOME T' => T'
blanchet@33192
   454
        | NONE => case T of Type (s, Ts) => Type (s, map subst Ts) | _ => T
blanchet@33192
   455
    in subst T end
blanchet@33192
   456
blanchet@33192
   457
(* theory -> typ -> typ -> typ -> typ *)
blanchet@33192
   458
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   459
  Same.commit (Envir.subst_type_same
blanchet@33192
   460
                   (Sign.typ_match thy (Logic.varifyT T1, T1') Vartab.empty))
blanchet@33192
   461
              (Logic.varifyT T2)
blanchet@33192
   462
  handle Type.TYPE_MATCH =>
blanchet@33192
   463
         raise TYPE ("NitpickHOL.instantiate_type", [T1, T1'], [])
blanchet@33192
   464
blanchet@33192
   465
(* theory -> typ -> typ -> styp *)
blanchet@33192
   466
fun repair_constr_type thy body_T' T =
blanchet@33192
   467
  instantiate_type thy (body_type T) body_T' T
blanchet@33192
   468
blanchet@33192
   469
(* string -> (string * string) list -> theory -> theory *)
blanchet@33192
   470
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   471
  let
blanchet@33192
   472
    val {frac_types, codatatypes} = TheoryData.get thy
blanchet@33192
   473
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33192
   474
  in TheoryData.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   475
(* string -> theory -> theory *)
blanchet@33192
   476
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   477
blanchet@33192
   478
(* typ -> string -> styp list -> theory -> theory *)
blanchet@33192
   479
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   480
  let
blanchet@33192
   481
    val {frac_types, codatatypes} = TheoryData.get thy
blanchet@33192
   482
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   483
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   484
    val _ =
blanchet@33192
   485
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) then ()
blanchet@33192
   486
      else raise TYPE ("NitpickHOL.register_codatatype", [co_T], [])
blanchet@33192
   487
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   488
                                   codatatypes
blanchet@33192
   489
  in TheoryData.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   490
(* typ -> theory -> theory *)
blanchet@33192
   491
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   492
blanchet@33192
   493
type typedef_info =
blanchet@33192
   494
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@33192
   495
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@33192
   496
   Rep_inverse: thm option}
blanchet@33192
   497
blanchet@33192
   498
(* theory -> string -> typedef_info *)
blanchet@33192
   499
fun typedef_info thy s =
blanchet@33192
   500
  if is_frac_type thy (Type (s, [])) then
blanchet@33192
   501
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@33192
   502
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@33192
   503
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@33192
   504
                          |> Logic.varify,
blanchet@33192
   505
          set_name = @{const_name Frac}, Rep_inverse = NONE}
blanchet@33192
   506
  else case Typedef.get_info thy s of
blanchet@33192
   507
    SOME {abs_type, rep_type, Abs_name, Rep_name, set_def, Rep, Rep_inverse,
blanchet@33192
   508
          ...} =>
blanchet@33192
   509
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@33192
   510
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@33192
   511
          set_name = set_prefix ^ s, Rep_inverse = SOME Rep_inverse}
blanchet@33192
   512
  | NONE => NONE
blanchet@33192
   513
blanchet@33192
   514
(* string -> bool *)
blanchet@33192
   515
fun is_basic_datatype s =
blanchet@33192
   516
    s mem [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@33192
   517
           @{type_name nat}, @{type_name int}]
blanchet@33192
   518
(* theory -> string -> bool *)
blanchet@33192
   519
val is_typedef = is_some oo typedef_info
blanchet@33192
   520
val is_real_datatype = is_some oo Datatype.get_info
blanchet@33192
   521
(* theory -> typ -> bool *)
blanchet@33192
   522
fun is_codatatype thy (T as Type (s, _)) =
blanchet@33192
   523
    not (null (AList.lookup (op =) (#codatatypes (TheoryData.get thy)) s
blanchet@33192
   524
               |> Option.map snd |> these))
blanchet@33192
   525
  | is_codatatype _ _ = false
blanchet@33192
   526
fun is_pure_typedef thy (T as Type (s, _)) =
blanchet@33192
   527
    is_typedef thy s andalso
blanchet@33192
   528
    not (is_real_datatype thy s orelse is_codatatype thy T
blanchet@33192
   529
         orelse is_record_type T orelse is_integer_type T)
blanchet@33192
   530
  | is_pure_typedef _ _ = false
blanchet@33192
   531
fun is_univ_typedef thy (Type (s, _)) =
blanchet@33192
   532
    (case typedef_info thy s of
blanchet@33192
   533
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@33192
   534
       (case set_def of
blanchet@33192
   535
          SOME thm =>
blanchet@33192
   536
          try (fst o dest_Const o snd o Logic.dest_equals o prop_of) thm
blanchet@33192
   537
        | NONE =>
blanchet@33192
   538
          try (fst o dest_Const o snd o HOLogic.dest_mem
blanchet@33192
   539
               o HOLogic.dest_Trueprop) prop_of_Rep) = SOME @{const_name UNIV}
blanchet@33192
   540
     | NONE => false)
blanchet@33192
   541
  | is_univ_typedef _ _ = false
blanchet@33192
   542
fun is_datatype thy (T as Type (s, _)) =
blanchet@33192
   543
    (is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind})
blanchet@33192
   544
    andalso not (is_basic_datatype s)
blanchet@33192
   545
  | is_datatype _ _ = false
blanchet@33192
   546
blanchet@33192
   547
(* theory -> typ -> (string * typ) list * (string * typ) *)
blanchet@33192
   548
fun all_record_fields thy T =
blanchet@33192
   549
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   550
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   551
  end
blanchet@33192
   552
  handle TYPE _ => []
blanchet@33192
   553
(* styp -> bool *)
blanchet@33192
   554
fun is_record_constr (x as (s, T)) =
blanchet@33192
   555
  String.isSuffix Record.extN s andalso
blanchet@33192
   556
  let val dataT = body_type T in
blanchet@33192
   557
    is_record_type dataT andalso
blanchet@33192
   558
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   559
  end
blanchet@33192
   560
(* theory -> typ -> int *)
blanchet@33192
   561
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   562
(* theory -> string -> typ -> int *)
blanchet@33192
   563
fun no_of_record_field thy s T1 =
blanchet@33192
   564
  find_index (equal s o fst) (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@33192
   565
(* theory -> styp -> bool *)
blanchet@33192
   566
fun is_record_get thy (s, Type ("fun", [T1, _])) =
blanchet@33192
   567
    exists (equal s o fst) (all_record_fields thy T1)
blanchet@33192
   568
  | is_record_get _ _ = false
blanchet@33192
   569
fun is_record_update thy (s, T) =
blanchet@33192
   570
  String.isSuffix Record.updateN s andalso
blanchet@33192
   571
  exists (equal (unsuffix Record.updateN s) o fst)
blanchet@33192
   572
         (all_record_fields thy (body_type T))
blanchet@33192
   573
  handle TYPE _ => false
blanchet@33192
   574
fun is_abs_fun thy (s, Type ("fun", [_, Type (s', _)])) =
blanchet@33192
   575
    (case typedef_info thy s' of
blanchet@33192
   576
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   577
     | NONE => false)
blanchet@33192
   578
  | is_abs_fun _ _ = false
blanchet@33192
   579
fun is_rep_fun thy (s, Type ("fun", [Type (s', _), _])) =
blanchet@33192
   580
    (case typedef_info thy s' of
blanchet@33192
   581
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   582
     | NONE => false)
blanchet@33192
   583
  | is_rep_fun _ _ = false
blanchet@33192
   584
blanchet@33192
   585
(* theory -> styp -> styp *)
blanchet@33192
   586
fun mate_of_rep_fun thy (x as (_, Type ("fun", [T1 as Type (s', _), T2]))) =
blanchet@33192
   587
    (case typedef_info thy s' of
blanchet@33192
   588
       SOME {Abs_name, ...} => (Abs_name, Type ("fun", [T2, T1]))
blanchet@33192
   589
     | NONE => raise TERM ("NitpickHOL.mate_of_rep_fun", [Const x]))
blanchet@33192
   590
  | mate_of_rep_fun _ x = raise TERM ("NitpickHOL.mate_of_rep_fun", [Const x])
blanchet@33192
   591
blanchet@33192
   592
(* theory -> styp -> bool *)
blanchet@33192
   593
fun is_coconstr thy (s, T) =
blanchet@33192
   594
  let
blanchet@33192
   595
    val {codatatypes, ...} = TheoryData.get thy
blanchet@33192
   596
    val co_T = body_type T
blanchet@33192
   597
    val co_s = dest_Type co_T |> fst
blanchet@33192
   598
  in
blanchet@33192
   599
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   600
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   601
  end
blanchet@33192
   602
  handle TYPE ("dest_Type", _, _) => false
blanchet@33192
   603
fun is_constr_like thy (s, T) =
blanchet@33192
   604
  s mem [@{const_name FunBox}, @{const_name PairBox}] orelse
blanchet@33192
   605
  let val (x as (s, T)) = (s, unbox_type T) in
blanchet@33192
   606
    Refute.is_IDT_constructor thy x orelse is_record_constr x
blanchet@33192
   607
    orelse (is_abs_fun thy x andalso is_pure_typedef thy (range_type T))
blanchet@33192
   608
    orelse s mem [@{const_name Zero_Rep}, @{const_name Suc_Rep}]
blanchet@33192
   609
    orelse x = (@{const_name zero_nat_inst.zero_nat}, nat_T)
blanchet@33192
   610
    orelse is_coconstr thy x
blanchet@33192
   611
  end
blanchet@33192
   612
fun is_constr thy (x as (_, T)) =
blanchet@33192
   613
  is_constr_like thy x
blanchet@33192
   614
  andalso not (is_basic_datatype (fst (dest_Type (body_type T))))
blanchet@33192
   615
(* string -> bool *)
blanchet@33192
   616
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   617
val is_sel_like_and_no_discr =
blanchet@33192
   618
  String.isPrefix sel_prefix
blanchet@33192
   619
  orf (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   620
blanchet@33192
   621
datatype boxability =
blanchet@33192
   622
  InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
blanchet@33192
   623
blanchet@33192
   624
(* boxability -> boxability *)
blanchet@33192
   625
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   626
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   627
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   628
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   629
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   630
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   631
blanchet@33192
   632
(* extended_context -> boxability -> typ -> bool *)
blanchet@33192
   633
fun is_boxing_worth_it (ext_ctxt : extended_context) boxy T =
blanchet@33192
   634
  case T of
blanchet@33192
   635
    Type ("fun", _) =>
blanchet@33192
   636
    boxy mem [InPair, InFunLHS] andalso not (is_boolean_type (body_type T))
blanchet@33192
   637
  | Type ("*", Ts) =>
blanchet@33192
   638
    boxy mem [InPair, InFunRHS1, InFunRHS2]
blanchet@33192
   639
    orelse (boxy mem [InExpr, InFunLHS]
blanchet@33192
   640
            andalso exists (is_boxing_worth_it ext_ctxt InPair)
blanchet@33192
   641
                           (map (box_type ext_ctxt InPair) Ts))
blanchet@33192
   642
  | _ => false
blanchet@33192
   643
(* extended_context -> boxability -> string * typ list -> string *)
blanchet@33192
   644
and should_box_type (ext_ctxt as {thy, boxes, ...}) boxy (z as (s, Ts)) =
blanchet@33192
   645
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   646
    SOME (SOME box_me) => box_me
blanchet@33192
   647
  | _ => is_boxing_worth_it ext_ctxt boxy (Type z)
blanchet@33192
   648
(* extended_context -> boxability -> typ -> typ *)
blanchet@33192
   649
and box_type ext_ctxt boxy T =
blanchet@33192
   650
  case T of
blanchet@33192
   651
    Type (z as ("fun", [T1, T2])) =>
blanchet@33192
   652
    if not (boxy mem [InConstr, InSel])
blanchet@33192
   653
       andalso should_box_type ext_ctxt boxy z then
blanchet@33192
   654
      Type (@{type_name fun_box},
blanchet@33192
   655
            [box_type ext_ctxt InFunLHS T1, box_type ext_ctxt InFunRHS1 T2])
blanchet@33192
   656
    else
blanchet@33192
   657
      box_type ext_ctxt (in_fun_lhs_for boxy) T1
blanchet@33192
   658
      --> box_type ext_ctxt (in_fun_rhs_for boxy) T2
blanchet@33192
   659
  | Type (z as ("*", Ts)) =>
blanchet@33192
   660
    if should_box_type ext_ctxt boxy z then
blanchet@33192
   661
      Type (@{type_name pair_box}, map (box_type ext_ctxt InSel) Ts)
blanchet@33192
   662
    else
blanchet@33192
   663
      Type ("*", map (box_type ext_ctxt
blanchet@33192
   664
                               (if boxy mem [InConstr, InSel] then boxy
blanchet@33192
   665
                                else InPair)) Ts)
blanchet@33192
   666
  | _ => T
blanchet@33192
   667
blanchet@33192
   668
(* styp -> styp *)
blanchet@33192
   669
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   670
blanchet@33192
   671
(* typ -> int *)
blanchet@33192
   672
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   673
(* string -> int -> string *)
blanchet@33192
   674
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   675
  if s = @{const_name Pair} then
blanchet@33192
   676
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   677
  else
blanchet@33192
   678
    sel_prefix_for n ^ s
blanchet@33192
   679
(* styp -> int -> styp *)
blanchet@33192
   680
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   681
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   682
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   683
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@33192
   684
(* extended_context -> styp -> int -> styp *)
blanchet@33192
   685
fun boxed_nth_sel_for_constr ext_ctxt =
blanchet@33192
   686
  apsnd (box_type ext_ctxt InSel) oo nth_sel_for_constr
blanchet@33192
   687
blanchet@33192
   688
(* string -> int *)
blanchet@33192
   689
fun sel_no_from_name s =
blanchet@33192
   690
  if String.isPrefix discr_prefix s then
blanchet@33192
   691
    ~1
blanchet@33192
   692
  else if String.isPrefix sel_prefix s then
blanchet@33192
   693
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   694
  else if s = @{const_name snd} then
blanchet@33192
   695
    1
blanchet@33192
   696
  else
blanchet@33192
   697
    0
blanchet@33192
   698
blanchet@33192
   699
(* typ list -> term -> int -> term *)
blanchet@33192
   700
fun eta_expand _ t 0 = t
blanchet@33192
   701
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   702
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   703
  | eta_expand Ts t n =
blanchet@33192
   704
    fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
blanchet@33192
   705
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   706
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   707
blanchet@33192
   708
(* term -> term *)
blanchet@33192
   709
fun extensionalize t =
blanchet@33192
   710
  case t of
blanchet@33192
   711
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   712
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   713
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   714
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   715
    end
blanchet@33192
   716
  | _ => t
blanchet@33192
   717
blanchet@33192
   718
(* typ -> term list -> term *)
blanchet@33192
   719
fun distinctness_formula T =
blanchet@33192
   720
  all_distinct_unordered_pairs_of
blanchet@33192
   721
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   722
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   723
blanchet@33192
   724
(* typ -> term *)
blanchet@33192
   725
fun zero_const T = Const (@{const_name zero_nat_inst.zero_nat}, T)
blanchet@33192
   726
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   727
blanchet@33192
   728
(* theory -> typ -> styp list *)
blanchet@33192
   729
fun datatype_constrs thy (T as Type (s, Ts)) =
blanchet@33192
   730
    if is_datatype thy T then
blanchet@33192
   731
      case Datatype.get_info thy s of
blanchet@33192
   732
        SOME {index, descr, ...} =>
blanchet@33192
   733
        let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in
blanchet@33192
   734
          map (fn (s', Us) =>
blanchet@33192
   735
                  (s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@33192
   736
              constrs
blanchet@33192
   737
         end
blanchet@33192
   738
      | NONE =>
blanchet@33192
   739
        case AList.lookup (op =) (#codatatypes (TheoryData.get thy)) s of
blanchet@33192
   740
          SOME (_, xs' as (_ :: _)) =>
blanchet@33192
   741
          map (apsnd (repair_constr_type thy T)) xs'
blanchet@33192
   742
        | _ =>
blanchet@33192
   743
          if is_record_type T then
blanchet@33192
   744
            let
blanchet@33192
   745
              val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33192
   746
              val T' = (Record.get_extT_fields thy T
blanchet@33192
   747
                       |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33192
   748
            in [(s', T')] end
blanchet@33192
   749
          else case typedef_info thy s of
blanchet@33192
   750
            SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@33192
   751
            [(Abs_name, instantiate_type thy abs_type T rep_type --> T)]
blanchet@33192
   752
          | NONE =>
blanchet@33192
   753
            if T = @{typ ind} then
blanchet@33192
   754
              [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33192
   755
            else
blanchet@33192
   756
              []
blanchet@33192
   757
    else
blanchet@33192
   758
      []
blanchet@33192
   759
  | datatype_constrs _ _ = []
blanchet@33192
   760
(* extended_context -> typ -> styp list *)
blanchet@33192
   761
fun boxed_datatype_constrs (ext_ctxt as {thy, ...}) =
blanchet@33192
   762
  map (apsnd (box_type ext_ctxt InConstr)) o datatype_constrs thy
blanchet@33192
   763
(* theory -> typ -> int *)
blanchet@33192
   764
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   765
blanchet@33192
   766
(* string -> string *)
blanchet@33192
   767
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   768
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   769
  | constr_name_for_sel_like s' = original_name s'
blanchet@33192
   770
(* extended_context -> styp -> styp *)
blanchet@33192
   771
fun boxed_constr_for_sel ext_ctxt (s', T') =
blanchet@33192
   772
  let val s = constr_name_for_sel_like s' in
blanchet@33192
   773
    AList.lookup (op =) (boxed_datatype_constrs ext_ctxt (domain_type T')) s
blanchet@33192
   774
    |> the |> pair s
blanchet@33192
   775
  end
blanchet@33192
   776
(* theory -> styp -> term *)
blanchet@33192
   777
fun discr_term_for_constr thy (x as (s, T)) =
blanchet@33192
   778
  let val dataT = body_type T in
blanchet@33192
   779
    if s = @{const_name Suc} then
blanchet@33192
   780
      Abs (Name.uu, dataT,
blanchet@33192
   781
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@33192
   782
    else if num_datatype_constrs thy dataT >= 2 then
blanchet@33192
   783
      Const (discr_for_constr x)
blanchet@33192
   784
    else
blanchet@33192
   785
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   786
  end
blanchet@33192
   787
blanchet@33192
   788
(* theory -> styp -> term -> term *)
blanchet@33192
   789
fun discriminate_value thy (x as (_, T)) t =
blanchet@33192
   790
  case strip_comb t of
blanchet@33192
   791
    (Const x', args) =>
blanchet@33192
   792
    if x = x' then @{const True}
blanchet@33192
   793
    else if is_constr_like thy x' then @{const False}
blanchet@33192
   794
    else betapply (discr_term_for_constr thy x, t)
blanchet@33192
   795
  | _ => betapply (discr_term_for_constr thy x, t)
blanchet@33192
   796
blanchet@33192
   797
(* styp -> term -> term *)
blanchet@33192
   798
fun nth_arg_sel_term_for_constr (x as (s, T)) n =
blanchet@33192
   799
  let val (arg_Ts, dataT) = strip_type T in
blanchet@33192
   800
    if dataT = nat_T then
blanchet@33192
   801
      @{term "%n::nat. minus_nat_inst.minus_nat n one_nat_inst.one_nat"}
blanchet@33192
   802
    else if is_pair_type dataT then
blanchet@33192
   803
      Const (nth_sel_for_constr x n)
blanchet@33192
   804
    else
blanchet@33192
   805
      let
blanchet@33192
   806
        (* int -> typ -> int * term *)
blanchet@33192
   807
        fun aux m (Type ("*", [T1, T2])) =
blanchet@33192
   808
            let
blanchet@33192
   809
              val (m, t1) = aux m T1
blanchet@33192
   810
              val (m, t2) = aux m T2
blanchet@33192
   811
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   812
          | aux m T =
blanchet@33192
   813
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
   814
                    $ Bound 0)
blanchet@33192
   815
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
   816
                     (List.take (arg_Ts, n)) 0
blanchet@33192
   817
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
   818
  end
blanchet@33192
   819
(* theory -> styp -> term -> int -> typ -> term *)
blanchet@33192
   820
fun select_nth_constr_arg thy x t n res_T =
blanchet@33192
   821
  case strip_comb t of
blanchet@33192
   822
    (Const x', args) =>
blanchet@33192
   823
    if x = x' then nth args n
blanchet@33192
   824
    else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
blanchet@33192
   825
    else betapply (nth_arg_sel_term_for_constr x n, t)
blanchet@33192
   826
  | _ => betapply (nth_arg_sel_term_for_constr x n, t)
blanchet@33192
   827
blanchet@33192
   828
(* theory -> styp -> term list -> term *)
blanchet@33192
   829
fun construct_value _ x [] = Const x
blanchet@33192
   830
  | construct_value thy (x as (s, _)) args =
blanchet@33192
   831
    let val args = map Envir.eta_contract args in
blanchet@33192
   832
      case hd args of
blanchet@33192
   833
        Const (x' as (s', _)) $ t =>
blanchet@33192
   834
        if is_sel_like_and_no_discr s' andalso constr_name_for_sel_like s' = s
blanchet@33192
   835
           andalso forall (fn (n, t') =>
blanchet@33192
   836
                              select_nth_constr_arg thy x t n dummyT = t')
blanchet@33192
   837
                          (index_seq 0 (length args) ~~ args) then
blanchet@33192
   838
          t
blanchet@33192
   839
        else
blanchet@33192
   840
          list_comb (Const x, args)
blanchet@33192
   841
      | _ => list_comb (Const x, args)
blanchet@33192
   842
    end
blanchet@33192
   843
blanchet@33192
   844
(* theory -> typ -> term -> term *)
blanchet@33192
   845
fun constr_expand thy T t =
blanchet@33192
   846
  (case head_of t of
blanchet@33192
   847
     Const x => if is_constr_like thy x then t else raise SAME ()
blanchet@33192
   848
   | _ => raise SAME ())
blanchet@33192
   849
  handle SAME () =>
blanchet@33192
   850
         let
blanchet@33192
   851
           val x' as (_, T') =
blanchet@33192
   852
             if is_pair_type T then
blanchet@33192
   853
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@33192
   854
                 (@{const_name Pair}, [T1, T2] ---> T)
blanchet@33192
   855
               end
blanchet@33192
   856
             else
blanchet@33192
   857
               datatype_constrs thy T |> the_single
blanchet@33192
   858
           val arg_Ts = binder_types T'
blanchet@33192
   859
         in
blanchet@33192
   860
           list_comb (Const x', map2 (select_nth_constr_arg thy x' t)
blanchet@33192
   861
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
   862
         end
blanchet@33192
   863
blanchet@33192
   864
(* (typ * int) list -> typ -> int *)
blanchet@33192
   865
fun card_of_type asgns (Type ("fun", [T1, T2])) =
blanchet@33192
   866
    reasonable_power (card_of_type asgns T2) (card_of_type asgns T1)
blanchet@33192
   867
  | card_of_type asgns (Type ("*", [T1, T2])) =
blanchet@33192
   868
    card_of_type asgns T1 * card_of_type asgns T2
blanchet@33192
   869
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
   870
  | card_of_type _ @{typ prop} = 2
blanchet@33192
   871
  | card_of_type _ @{typ bool} = 2
blanchet@33192
   872
  | card_of_type _ @{typ unit} = 1
blanchet@33192
   873
  | card_of_type asgns T =
blanchet@33192
   874
    case AList.lookup (op =) asgns T of
blanchet@33192
   875
      SOME k => k
blanchet@33192
   876
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33192
   877
              else raise TYPE ("NitpickHOL.card_of_type", [T], [])
blanchet@33192
   878
(* int -> (typ * int) list -> typ -> int *)
blanchet@33192
   879
fun bounded_card_of_type max default_card asgns (Type ("fun", [T1, T2])) =
blanchet@33192
   880
    let
blanchet@33192
   881
      val k1 = bounded_card_of_type max default_card asgns T1
blanchet@33192
   882
      val k2 = bounded_card_of_type max default_card asgns T2
blanchet@33192
   883
    in
blanchet@33192
   884
      if k1 = max orelse k2 = max then max
blanchet@33192
   885
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
   886
    end
blanchet@33192
   887
  | bounded_card_of_type max default_card asgns (Type ("*", [T1, T2])) =
blanchet@33192
   888
    let
blanchet@33192
   889
      val k1 = bounded_card_of_type max default_card asgns T1
blanchet@33192
   890
      val k2 = bounded_card_of_type max default_card asgns T2
blanchet@33192
   891
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@33192
   892
  | bounded_card_of_type max default_card asgns T =
blanchet@33192
   893
    Int.min (max, if default_card = ~1 then
blanchet@33192
   894
                    card_of_type asgns T
blanchet@33192
   895
                  else
blanchet@33192
   896
                    card_of_type asgns T
blanchet@33192
   897
                    handle TYPE ("NitpickHOL.card_of_type", _, _) =>
blanchet@33192
   898
                           default_card)
blanchet@33192
   899
(* theory -> int -> (typ * int) list -> typ -> int *)
blanchet@33192
   900
fun bounded_precise_card_of_type thy max default_card asgns T =
blanchet@33192
   901
  let
blanchet@33192
   902
    (* typ list -> typ -> int *)
blanchet@33192
   903
    fun aux avoid T =
blanchet@33192
   904
      (if T mem avoid then
blanchet@33192
   905
         0
blanchet@33192
   906
       else case T of
blanchet@33192
   907
         Type ("fun", [T1, T2]) =>
blanchet@33192
   908
         let
blanchet@33192
   909
           val k1 = aux avoid T1
blanchet@33192
   910
           val k2 = aux avoid T2
blanchet@33192
   911
         in
blanchet@33192
   912
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
   913
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
   914
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
   915
         end
blanchet@33192
   916
       | Type ("*", [T1, T2]) =>
blanchet@33192
   917
         let
blanchet@33192
   918
           val k1 = aux avoid T1
blanchet@33192
   919
           val k2 = aux avoid T2
blanchet@33192
   920
         in
blanchet@33192
   921
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
   922
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
   923
           else Int.min (max, k1 * k2)
blanchet@33192
   924
         end
blanchet@33192
   925
       | Type (@{type_name itself}, _) => 1
blanchet@33192
   926
       | @{typ prop} => 2
blanchet@33192
   927
       | @{typ bool} => 2
blanchet@33192
   928
       | @{typ unit} => 1
blanchet@33192
   929
       | Type _ =>
blanchet@33192
   930
         (case datatype_constrs thy T of
blanchet@33192
   931
            [] => if is_integer_type T then 0 else raise SAME ()
blanchet@33192
   932
          | constrs =>
blanchet@33192
   933
            let
blanchet@33192
   934
              val constr_cards =
blanchet@33192
   935
                datatype_constrs thy T
blanchet@33192
   936
                |> map (Integer.prod o map (aux (T :: avoid)) o binder_types
blanchet@33192
   937
                        o snd)
blanchet@33192
   938
            in
blanchet@33192
   939
              if exists (equal 0) constr_cards then 0
blanchet@33192
   940
              else Integer.sum constr_cards
blanchet@33192
   941
            end)
blanchet@33192
   942
       | _ => raise SAME ())
blanchet@33192
   943
      handle SAME () => AList.lookup (op =) asgns T |> the_default default_card
blanchet@33192
   944
  in Int.min (max, aux [] T) end
blanchet@33192
   945
blanchet@33192
   946
(* theory -> typ -> bool *)
blanchet@33192
   947
fun is_finite_type thy = not_equal 0 o bounded_precise_card_of_type thy 1 2 []
blanchet@33192
   948
blanchet@33192
   949
(* term -> bool *)
blanchet@33192
   950
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
   951
  | is_ground_term (Const _) = true
blanchet@33192
   952
  | is_ground_term _ = false
blanchet@33192
   953
blanchet@33192
   954
(* term -> word -> word *)
blanchet@33192
   955
fun hashw_term (t1 $ t2) = Polyhash.hashw (hashw_term t1, hashw_term t2)
blanchet@33192
   956
  | hashw_term (Const (s, _)) = Polyhash.hashw_string (s, 0w0)
blanchet@33192
   957
  | hashw_term _ = 0w0
blanchet@33192
   958
(* term -> int *)
blanchet@33192
   959
val hash_term = Word.toInt o hashw_term
blanchet@33192
   960
blanchet@33192
   961
(* term list -> (indexname * typ) list *)
blanchet@33192
   962
fun special_bounds ts =
blanchet@33192
   963
  fold Term.add_vars ts [] |> sort (TermOrd.fast_indexname_ord o pairself fst)
blanchet@33192
   964
blanchet@33192
   965
(* indexname * typ -> term -> term *)
blanchet@33192
   966
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
   967
blanchet@33192
   968
(* term -> bool *)
blanchet@33192
   969
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
   970
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
   971
  | is_arity_type_axiom _ = false
blanchet@33192
   972
(* theory -> bool -> term -> bool *)
blanchet@33197
   973
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
blanchet@33197
   974
    is_typedef_axiom thy boring t2
blanchet@33197
   975
  | is_typedef_axiom thy boring
blanchet@33192
   976
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@33197
   977
         $ Const (_, Type ("fun", [Type (s, _), _])) $ Const _ $ _)) =
blanchet@33197
   978
    boring <> (s mem [@{type_name unit}, @{type_name "*"}, @{type_name "+"}]
blanchet@33197
   979
               orelse is_frac_type thy (Type (s, [])))
blanchet@33197
   980
    andalso is_typedef thy s
blanchet@33192
   981
  | is_typedef_axiom _ _ _ = false
blanchet@33192
   982
blanchet@33192
   983
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
   984
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
   985
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
   986
   using "typedef_info". *)
blanchet@33192
   987
(* theory -> (string * term) list -> string list -> term list * term list *)
blanchet@33192
   988
fun partition_axioms_by_definitionality thy axioms def_names =
blanchet@33192
   989
  let
blanchet@33192
   990
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
   991
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
   992
    val nondefs =
blanchet@33192
   993
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
   994
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
blanchet@33192
   995
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
   996
blanchet@33197
   997
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
   998
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
   999
   commands. *)
blanchet@33192
  1000
(* theory -> bool *)
blanchet@33192
  1001
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1002
blanchet@33192
  1003
(* term -> bool *)
blanchet@33192
  1004
val is_plain_definition =
blanchet@33192
  1005
  let
blanchet@33192
  1006
    (* term -> bool *)
blanchet@33192
  1007
    fun do_lhs t1 =
blanchet@33192
  1008
      case strip_comb t1 of
blanchet@33192
  1009
        (Const _, args) => forall is_Var args
blanchet@33192
  1010
                           andalso not (has_duplicates (op =) args)
blanchet@33192
  1011
      | _ => false
blanchet@33192
  1012
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1013
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1014
        do_lhs t1
blanchet@33192
  1015
      | do_eq _ = false
blanchet@33192
  1016
  in do_eq end
blanchet@33192
  1017
blanchet@33192
  1018
(* This table is not pretty. A better approach would be to avoid expanding the
blanchet@33192
  1019
   operators to their low-level definitions, but this would require dealing with
blanchet@33192
  1020
   overloading. *)
blanchet@33192
  1021
val built_in_built_in_defs =
blanchet@33192
  1022
  [@{thm div_int_inst.div_int}, @{thm div_int_inst.mod_int},
blanchet@33192
  1023
   @{thm div_nat_inst.div_nat}, @{thm div_nat_inst.mod_nat},
blanchet@33192
  1024
   @{thm lower_semilattice_fun_inst.inf_fun}, @{thm minus_fun_inst.minus_fun},
blanchet@33192
  1025
   @{thm minus_int_inst.minus_int}, @{thm minus_nat_inst.minus_nat},
blanchet@33192
  1026
   @{thm one_int_inst.one_int}, @{thm one_nat_inst.one_nat},
blanchet@33192
  1027
   @{thm ord_fun_inst.less_eq_fun}, @{thm ord_int_inst.less_eq_int},
blanchet@33192
  1028
   @{thm ord_int_inst.less_int}, @{thm ord_nat_inst.less_eq_nat},
blanchet@33192
  1029
   @{thm ord_nat_inst.less_nat}, @{thm plus_int_inst.plus_int},
blanchet@33192
  1030
   @{thm plus_nat_inst.plus_nat}, @{thm times_int_inst.times_int},
blanchet@33192
  1031
   @{thm times_nat_inst.times_nat}, @{thm uminus_int_inst.uminus_int},
blanchet@33192
  1032
   @{thm upper_semilattice_fun_inst.sup_fun}, @{thm zero_int_inst.zero_int},
blanchet@33192
  1033
   @{thm zero_nat_inst.zero_nat}]
blanchet@33192
  1034
  |> map prop_of
blanchet@33192
  1035
blanchet@33192
  1036
(* theory -> term list * term list * term list *)
blanchet@33192
  1037
fun all_axioms_of thy =
blanchet@33192
  1038
  let
blanchet@33192
  1039
    (* theory list -> term list *)
blanchet@33192
  1040
    val axioms_of_thys = maps Thm.axioms_of #> map (apsnd prop_of)
blanchet@33192
  1041
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
blanchet@33197
  1042
    val def_names = specs |> maps snd |> filter #is_def |> map #name
blanchet@33197
  1043
                    |> OrdList.make fast_string_ord
blanchet@33192
  1044
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1045
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1046
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1047
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1048
    val (built_in_defs, built_in_nondefs) =
blanchet@33192
  1049
      partition_axioms_by_definitionality thy built_in_axioms def_names
blanchet@33197
  1050
      ||> filter (is_typedef_axiom thy false)
blanchet@33192
  1051
    val (user_defs, user_nondefs) =
blanchet@33192
  1052
      partition_axioms_by_definitionality thy user_axioms def_names
blanchet@33197
  1053
    val (built_in_nondefs, user_nondefs) =
blanchet@33197
  1054
      List.partition (is_typedef_axiom thy false) user_nondefs
blanchet@33197
  1055
      |>> append built_in_nondefs
blanchet@33192
  1056
    val defs = built_in_built_in_defs @
blanchet@33192
  1057
               (thy |> PureThy.all_thms_of
blanchet@33192
  1058
                    |> filter (equal Thm.definitionK o Thm.get_kind o snd)
blanchet@33192
  1059
                    |> map (prop_of o snd) |> filter is_plain_definition) @
blanchet@33192
  1060
               user_defs @ built_in_defs
blanchet@33192
  1061
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1062
blanchet@33192
  1063
(* bool -> styp -> int option *)
blanchet@33192
  1064
fun arity_of_built_in_const fast_descrs (s, T) =
blanchet@33192
  1065
  if s = @{const_name If} then
blanchet@33192
  1066
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@33192
  1067
  else case AList.lookup (op =)
blanchet@33192
  1068
                (built_in_consts
blanchet@33192
  1069
                 |> fast_descrs ? append built_in_descr_consts) s of
blanchet@33192
  1070
    SOME n => SOME n
blanchet@33192
  1071
  | NONE =>
blanchet@33192
  1072
    case AList.lookup (op =) built_in_typed_consts (s, T) of
blanchet@33192
  1073
      SOME n => SOME n
blanchet@33192
  1074
    | NONE =>
blanchet@33192
  1075
      if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@33192
  1076
        AList.lookup (op =) built_in_set_consts s
blanchet@33192
  1077
      else
blanchet@33192
  1078
        NONE
blanchet@33192
  1079
(* bool -> styp -> bool *)
blanchet@33192
  1080
val is_built_in_const = is_some oo arity_of_built_in_const
blanchet@33192
  1081
blanchet@33192
  1082
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1083
   simplification rules (equational specifications). *)
blanchet@33192
  1084
(* term -> term *)
blanchet@33192
  1085
fun term_under_def t =
blanchet@33192
  1086
  case t of
blanchet@33192
  1087
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1088
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1089
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1090
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1091
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1092
  | t1 $ _ => term_under_def t1
blanchet@33192
  1093
  | _ => t
blanchet@33192
  1094
blanchet@33192
  1095
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
blanchet@33192
  1096
   traversal of the term, without which the wrong occurrence of a constant could
blanchet@33192
  1097
   be matched in the face of overloading. *)
blanchet@33192
  1098
(* theory -> bool -> const_table -> styp -> term list *)
blanchet@33192
  1099
fun def_props_for_const thy fast_descrs table (x as (s, _)) =
blanchet@33192
  1100
  if is_built_in_const fast_descrs x then
blanchet@33192
  1101
    []
blanchet@33192
  1102
  else
blanchet@33192
  1103
    these (Symtab.lookup table s)
blanchet@33192
  1104
    |> map_filter (try (Refute.specialize_type thy x))
blanchet@33192
  1105
    |> filter (equal (Const x) o term_under_def)
blanchet@33192
  1106
blanchet@33192
  1107
(* term -> term *)
blanchet@33192
  1108
fun normalized_rhs_of thy t =
blanchet@33192
  1109
  let
blanchet@33192
  1110
    (* term -> term *)
blanchet@33192
  1111
    fun aux (v as Var _) t = lambda v t
blanchet@33192
  1112
      | aux (c as Const (@{const_name TYPE}, T)) t = lambda c t
blanchet@33192
  1113
      | aux _ _ = raise TERM ("NitpickHOL.normalized_rhs_of", [t])
blanchet@33192
  1114
    val (lhs, rhs) =
blanchet@33192
  1115
      case t of
blanchet@33192
  1116
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1117
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1118
        (t1, t2)
blanchet@33192
  1119
      | _ => raise TERM ("NitpickHOL.normalized_rhs_of", [t])
blanchet@33192
  1120
    val args = strip_comb lhs |> snd
blanchet@33192
  1121
  in fold_rev aux args rhs end
blanchet@33192
  1122
blanchet@33192
  1123
(* theory -> const_table -> styp -> term option *)
blanchet@33192
  1124
fun def_of_const thy table (x as (s, _)) =
blanchet@33192
  1125
  if is_built_in_const false x orelse original_name s <> s then
blanchet@33192
  1126
    NONE
blanchet@33192
  1127
  else
blanchet@33192
  1128
    x |> def_props_for_const thy false table |> List.last
blanchet@33192
  1129
      |> normalized_rhs_of thy |> prefix_abs_vars s |> SOME
blanchet@33192
  1130
    handle List.Empty => NONE
blanchet@33192
  1131
blanchet@33192
  1132
datatype fixpoint_kind = Lfp | Gfp | NoFp
blanchet@33192
  1133
blanchet@33192
  1134
(* term -> fixpoint_kind *)
blanchet@33192
  1135
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1136
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1137
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1138
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1139
blanchet@33192
  1140
(* theory -> const_table -> term -> bool *)
blanchet@33192
  1141
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1142
  let
blanchet@33192
  1143
    (* term -> bool *)
blanchet@33192
  1144
    fun is_good_arg (Bound _) = true
blanchet@33192
  1145
      | is_good_arg (Const (s, _)) =
blanchet@33192
  1146
        s mem [@{const_name True}, @{const_name False}, @{const_name undefined}]
blanchet@33192
  1147
      | is_good_arg _ = false
blanchet@33192
  1148
  in
blanchet@33192
  1149
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1150
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1151
      (case def_of_const thy table x of
blanchet@33192
  1152
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1153
       | NONE => false)
blanchet@33192
  1154
    | _ => false
blanchet@33192
  1155
  end
blanchet@33192
  1156
(* theory -> const_table -> term -> term *)
blanchet@33192
  1157
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1158
  map_aterms (fn t as Const x =>
blanchet@33192
  1159
                 (case def_of_const thy table x of
blanchet@33192
  1160
                    SOME t' =>
blanchet@33192
  1161
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1162
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1163
                      else t
blanchet@33192
  1164
                    end
blanchet@33192
  1165
                 | NONE => t)
blanchet@33192
  1166
               | t => t)
blanchet@33192
  1167
blanchet@33192
  1168
(* term -> string * term *)
blanchet@33192
  1169
fun pair_for_prop t =
blanchet@33192
  1170
  case term_under_def t of
blanchet@33192
  1171
    Const (s, _) => (s, t)
blanchet@33192
  1172
  | Free _ => raise NOT_SUPPORTED "local definitions"
blanchet@33192
  1173
  | t' => raise TERM ("NitpickHOL.pair_for_prop", [t, t'])
blanchet@33192
  1174
blanchet@33192
  1175
(* (Proof.context -> term list) -> Proof.context -> const_table *)
blanchet@33192
  1176
fun table_for get ctxt =
blanchet@33192
  1177
  get ctxt |> map pair_for_prop |> AList.group (op =) |> Symtab.make
blanchet@33192
  1178
blanchet@33192
  1179
(* theory -> (string * int) list *)
blanchet@33192
  1180
fun case_const_names thy =
blanchet@33192
  1181
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@33192
  1182
                  if is_basic_datatype dtype_s then
blanchet@33192
  1183
                    I
blanchet@33192
  1184
                  else
blanchet@33192
  1185
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1186
                                     |> the |> #3 |> length))
blanchet@33192
  1187
              (Datatype.get_all thy) [] @
blanchet@33192
  1188
  map (apsnd length o snd) (#codatatypes (TheoryData.get thy))
blanchet@33192
  1189
blanchet@33192
  1190
(* Proof.context -> term list -> const_table *)
blanchet@33192
  1191
fun const_def_table ctxt ts =
blanchet@33192
  1192
  table_for (map prop_of o Nitpick_Defs.get) ctxt
blanchet@33192
  1193
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@33192
  1194
          (map pair_for_prop ts)
blanchet@33192
  1195
(* term list -> const_table *)
blanchet@33192
  1196
fun const_nondef_table ts =
blanchet@33192
  1197
  fold (fn t => append (map (fn s => (s, t)) (Term.add_const_names t []))) ts []
blanchet@33192
  1198
  |> AList.group (op =) |> Symtab.make
blanchet@33192
  1199
(* Proof.context -> const_table *)
blanchet@33192
  1200
val const_simp_table = table_for (map prop_of o Nitpick_Simps.get)
blanchet@33192
  1201
val const_psimp_table = table_for (map prop_of o Nitpick_Psimps.get)
blanchet@33192
  1202
(* Proof.context -> const_table -> const_table *)
blanchet@33192
  1203
fun inductive_intro_table ctxt def_table =
blanchet@33192
  1204
  table_for (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
blanchet@33192
  1205
                                                  def_table o prop_of)
blanchet@33192
  1206
             o Nitpick_Intros.get) ctxt
blanchet@33192
  1207
(* theory -> term list Inttab.table *)
blanchet@33192
  1208
fun ground_theorem_table thy =
blanchet@33192
  1209
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@33192
  1210
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@33192
  1211
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@33192
  1212
blanchet@33192
  1213
val basic_ersatz_table =
blanchet@33192
  1214
  [(@{const_name prod_case}, @{const_name split}),
blanchet@33192
  1215
   (@{const_name card}, @{const_name card'}),
blanchet@33192
  1216
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@33192
  1217
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@33192
  1218
   (@{const_name wf}, @{const_name wf'}),
blanchet@33192
  1219
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@33192
  1220
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@33192
  1221
blanchet@33192
  1222
(* theory -> (string * string) list *)
blanchet@33192
  1223
fun ersatz_table thy =
blanchet@33192
  1224
  fold (append o snd) (#frac_types (TheoryData.get thy)) basic_ersatz_table
blanchet@33192
  1225
blanchet@33192
  1226
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
blanchet@33192
  1227
fun add_simps simp_table s eqs =
blanchet@33192
  1228
  Unsynchronized.change simp_table
blanchet@33192
  1229
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@33192
  1230
blanchet@33192
  1231
(* Similar to "Refute.specialize_type" but returns all matches rather than only
blanchet@33192
  1232
   the first (preorder) match. *)
blanchet@33192
  1233
(* theory -> styp -> term -> term list *)
blanchet@33197
  1234
fun multi_specialize_type thy slack (x as (s, T)) t =
blanchet@33192
  1235
  let
blanchet@33192
  1236
    (* term -> (typ * term) list -> (typ * term) list *)
blanchet@33192
  1237
    fun aux (Const (s', T')) ys =
blanchet@33192
  1238
        if s = s' then
blanchet@33197
  1239
          ys |> (if AList.defined (op =) ys T' then
blanchet@33197
  1240
                   I
blanchet@33197
  1241
                else
blanchet@33197
  1242
                  cons (T', Refute.monomorphic_term
blanchet@33197
  1243
                                (Sign.typ_match thy (T', T) Vartab.empty) t)
blanchet@33197
  1244
                  handle Type.TYPE_MATCH => I
blanchet@33197
  1245
                       | Refute.REFUTE _ =>
blanchet@33197
  1246
                         if slack then
blanchet@33197
  1247
                           I
blanchet@33197
  1248
                         else
blanchet@33197
  1249
                           raise NOT_SUPPORTED ("too much polymorphism in \
blanchet@33197
  1250
                                                \axiom involving " ^ quote s))
blanchet@33192
  1251
        else
blanchet@33192
  1252
          ys
blanchet@33192
  1253
      | aux _ ys = ys
blanchet@33192
  1254
  in map snd (fold_aterms aux t []) end
blanchet@33192
  1255
blanchet@33197
  1256
(* theory -> bool -> const_table -> styp -> term list *)
blanchet@33197
  1257
fun nondef_props_for_const thy slack table (x as (s, _)) =
blanchet@33197
  1258
  these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
blanchet@33192
  1259
blanchet@33192
  1260
(* theory -> styp list -> term list *)
blanchet@33192
  1261
fun optimized_typedef_axioms thy (abs_s, abs_Ts) =
blanchet@33192
  1262
  let val abs_T = Type (abs_s, abs_Ts) in
blanchet@33192
  1263
    if is_univ_typedef thy abs_T then
blanchet@33192
  1264
      []
blanchet@33192
  1265
    else case typedef_info thy abs_s of
blanchet@33192
  1266
      SOME {abs_type, rep_type, Abs_name, Rep_name, prop_of_Rep, set_name,
blanchet@33192
  1267
            ...} =>
blanchet@33192
  1268
      let
blanchet@33192
  1269
        val rep_T = instantiate_type thy abs_type abs_T rep_type
blanchet@33192
  1270
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@33192
  1271
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@33192
  1272
        val set_t' =
blanchet@33192
  1273
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@33192
  1274
                      |> Refute.specialize_type thy (dest_Const rep_t)
blanchet@33192
  1275
                      |> HOLogic.dest_mem |> snd
blanchet@33192
  1276
      in
blanchet@33192
  1277
        [HOLogic.all_const abs_T
blanchet@33192
  1278
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@33192
  1279
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@33192
  1280
        |> map HOLogic.mk_Trueprop
blanchet@33192
  1281
      end
blanchet@33192
  1282
    | NONE => []
blanchet@33192
  1283
  end
blanchet@33192
  1284
(* theory -> styp -> term *)
blanchet@33192
  1285
fun inverse_axiom_for_rep_fun thy (x as (_, T)) =
blanchet@33192
  1286
  typedef_info thy (fst (dest_Type (domain_type T)))
blanchet@33192
  1287
  |> the |> #Rep_inverse |> the |> prop_of |> Refute.specialize_type thy x
blanchet@33192
  1288
blanchet@33192
  1289
(* theory -> int * styp -> term *)
blanchet@33192
  1290
fun constr_case_body thy (j, (x as (_, T))) =
blanchet@33192
  1291
  let val arg_Ts = binder_types T in
blanchet@33192
  1292
    list_comb (Bound j, map2 (select_nth_constr_arg thy x (Bound 0))
blanchet@33192
  1293
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1294
  end
blanchet@33192
  1295
(* theory -> typ -> int * styp -> term -> term *)
blanchet@33192
  1296
fun add_constr_case thy res_T (j, x) res_t =
blanchet@33192
  1297
  Const (@{const_name If}, [bool_T, res_T, res_T] ---> res_T)
blanchet@33192
  1298
  $ discriminate_value thy x (Bound 0) $ constr_case_body thy (j, x) $ res_t
blanchet@33192
  1299
(* theory -> typ -> typ -> term *)
blanchet@33192
  1300
fun optimized_case_def thy dataT res_T =
blanchet@33192
  1301
  let
blanchet@33192
  1302
    val xs = datatype_constrs thy dataT
blanchet@33192
  1303
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs
blanchet@33192
  1304
    val (xs', x) = split_last xs
blanchet@33192
  1305
  in
blanchet@33192
  1306
    constr_case_body thy (1, x)
blanchet@33192
  1307
    |> fold_rev (add_constr_case thy res_T) (length xs downto 2 ~~ xs')
blanchet@33192
  1308
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1309
  end
blanchet@33192
  1310
blanchet@33192
  1311
val redefined_in_NitpickDefs_thy =
blanchet@33192
  1312
  [@{const_name option_case}, @{const_name nat_case}, @{const_name list_case},
blanchet@33192
  1313
   @{const_name list_size}]
blanchet@33192
  1314
blanchet@33192
  1315
(* theory -> string -> typ -> typ -> term -> term *)
blanchet@33192
  1316
fun optimized_record_get thy s rec_T res_T t =
blanchet@33192
  1317
  let val constr_x = the_single (datatype_constrs thy rec_T) in
blanchet@33192
  1318
    case no_of_record_field thy s rec_T of
blanchet@33192
  1319
      ~1 => (case rec_T of
blanchet@33192
  1320
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1321
               let
blanchet@33192
  1322
                 val rec_T' = List.last Ts
blanchet@33192
  1323
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1324
               in
blanchet@33192
  1325
                 select_nth_constr_arg thy constr_x t j res_T
blanchet@33192
  1326
                 |> optimized_record_get thy s rec_T' res_T
blanchet@33192
  1327
               end
blanchet@33192
  1328
             | _ => raise TYPE ("NitpickHOL.optimized_record_get", [rec_T], []))
blanchet@33192
  1329
    | j => select_nth_constr_arg thy constr_x t j res_T
blanchet@33192
  1330
  end
blanchet@33192
  1331
(* theory -> string -> typ -> term -> term -> term *)
blanchet@33192
  1332
fun optimized_record_update thy s rec_T fun_t rec_t =
blanchet@33192
  1333
  let
blanchet@33192
  1334
    val constr_x as (_, constr_T) = the_single (datatype_constrs thy rec_T)
blanchet@33192
  1335
    val Ts = binder_types constr_T
blanchet@33192
  1336
    val n = length Ts
blanchet@33192
  1337
    val special_j = no_of_record_field thy s rec_T
blanchet@33192
  1338
    val ts = map2 (fn j => fn T =>
blanchet@33192
  1339
                      let
blanchet@33192
  1340
                        val t = select_nth_constr_arg thy constr_x rec_t j T
blanchet@33192
  1341
                      in
blanchet@33192
  1342
                        if j = special_j then
blanchet@33192
  1343
                          betapply (fun_t, t)
blanchet@33192
  1344
                        else if j = n - 1 andalso special_j = ~1 then
blanchet@33192
  1345
                          optimized_record_update thy s
blanchet@33192
  1346
                              (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@33192
  1347
                        else
blanchet@33192
  1348
                          t
blanchet@33192
  1349
                      end) (index_seq 0 n) Ts
blanchet@33192
  1350
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1351
blanchet@33192
  1352
(* Constants "c" whose definition is of the form "c == c'", where "c'" is also a
blanchet@33192
  1353
   constant, are said to be trivial. For those, we ignore the simplification
blanchet@33192
  1354
   rules and use the definition instead, to ensure that built-in symbols like
blanchet@33192
  1355
   "ord_nat_inst.less_eq_nat" are picked up correctly. *)
blanchet@33192
  1356
(* theory -> const_table -> styp -> bool *)
blanchet@33192
  1357
fun has_trivial_definition thy table x =
blanchet@33192
  1358
  case def_of_const thy table x of SOME (Const _) => true | _ => false
blanchet@33192
  1359
blanchet@33192
  1360
(* theory -> const_table -> string * typ -> fixpoint_kind *)
blanchet@33192
  1361
fun fixpoint_kind_of_const thy table x =
blanchet@33192
  1362
  if is_built_in_const false x then
blanchet@33192
  1363
    NoFp
blanchet@33192
  1364
  else
blanchet@33192
  1365
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@33192
  1366
    handle Option.Option => NoFp
blanchet@33192
  1367
blanchet@33192
  1368
(* extended_context -> styp -> bool *)
blanchet@33192
  1369
fun is_real_inductive_pred ({thy, fast_descrs, def_table, intro_table, ...}
blanchet@33192
  1370
                            : extended_context) x =
blanchet@33192
  1371
  not (null (def_props_for_const thy fast_descrs intro_table x))
blanchet@33192
  1372
  andalso fixpoint_kind_of_const thy def_table x <> NoFp
blanchet@33192
  1373
fun is_real_equational_fun ({thy, fast_descrs, simp_table, psimp_table, ...}
blanchet@33192
  1374
                            : extended_context) x =
blanchet@33192
  1375
  exists (fn table => not (null (def_props_for_const thy fast_descrs table x)))
blanchet@33192
  1376
         [!simp_table, psimp_table]
blanchet@33192
  1377
fun is_inductive_pred ext_ctxt =
blanchet@33192
  1378
  is_real_inductive_pred ext_ctxt andf (not o is_real_equational_fun ext_ctxt)
blanchet@33192
  1379
fun is_equational_fun (ext_ctxt as {thy, def_table, ...}) =
blanchet@33192
  1380
  (is_real_equational_fun ext_ctxt orf is_real_inductive_pred ext_ctxt
blanchet@33192
  1381
   orf (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1382
  andf (not o has_trivial_definition thy def_table)
blanchet@33192
  1383
  andf (not o member (op =) redefined_in_NitpickDefs_thy o fst)
blanchet@33192
  1384
blanchet@33192
  1385
(* term * term -> term *)
blanchet@33192
  1386
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
blanchet@33192
  1387
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
blanchet@33192
  1388
  | s_betapply p = betapply p
blanchet@33192
  1389
(* term * term list -> term *)
blanchet@33192
  1390
val s_betapplys = Library.foldl s_betapply
blanchet@33192
  1391
blanchet@33192
  1392
(* term -> term *)
blanchet@33192
  1393
fun lhs_of_equation t =
blanchet@33192
  1394
  case t of
blanchet@33192
  1395
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1396
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1397
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1398
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@33192
  1399
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1400
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1401
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1402
  | _ => NONE
blanchet@33192
  1403
(* theory -> term -> bool *)
blanchet@33192
  1404
fun is_constr_pattern _ (Bound _) = true
blanchet@33192
  1405
  | is_constr_pattern thy t =
blanchet@33192
  1406
    case strip_comb t of
blanchet@33192
  1407
      (Const (x as (s, _)), args) =>
blanchet@33192
  1408
      is_constr_like thy x andalso forall (is_constr_pattern thy) args
blanchet@33192
  1409
    | _ => false
blanchet@33192
  1410
fun is_constr_pattern_lhs thy t =
blanchet@33192
  1411
  forall (is_constr_pattern thy) (snd (strip_comb t))
blanchet@33192
  1412
fun is_constr_pattern_formula thy t =
blanchet@33192
  1413
  case lhs_of_equation t of
blanchet@33192
  1414
    SOME t' => is_constr_pattern_lhs thy t'
blanchet@33192
  1415
  | NONE => false
blanchet@33192
  1416
blanchet@33192
  1417
val unfold_max_depth = 63
blanchet@33192
  1418
val axioms_max_depth = 63
blanchet@33192
  1419
blanchet@33192
  1420
(* extended_context -> term -> term *)
blanchet@33192
  1421
fun unfold_defs_in_term (ext_ctxt as {thy, destroy_constrs, fast_descrs,
blanchet@33192
  1422
                                      case_names, def_table, ground_thm_table,
blanchet@33192
  1423
                                      ersatz_table, ...}) =
blanchet@33192
  1424
  let
blanchet@33192
  1425
    (* int -> typ list -> term -> term *)
blanchet@33192
  1426
    fun do_term depth Ts t =
blanchet@33192
  1427
      case t of
blanchet@33192
  1428
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@33192
  1429
                      Type ("fun", [_, ran_T]))) $ t1 =>
blanchet@33192
  1430
        ((if is_number_type thy ran_T then
blanchet@33192
  1431
            let
blanchet@33192
  1432
              val j = t1 |> HOLogic.dest_numeral
blanchet@33192
  1433
                         |> ran_T <> int_T ? curry Int.max 0
blanchet@33192
  1434
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1435
            in
blanchet@33192
  1436
              if is_integer_type ran_T then
blanchet@33192
  1437
                Const (s, ran_T)
blanchet@33192
  1438
              else
blanchet@33192
  1439
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1440
                                  $ Const (s, int_T))
blanchet@33192
  1441
            end
blanchet@33192
  1442
            handle TERM _ => raise SAME ()
blanchet@33192
  1443
          else
blanchet@33192
  1444
            raise SAME ())
blanchet@33192
  1445
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33192
  1446
      | Const (@{const_name refl_on}, T) $ Const (@{const_name UNIV}, _) $ t2 =>
blanchet@33192
  1447
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@33192
  1448
      | (t0 as Const (x as (@{const_name Sigma}, T))) $ t1
blanchet@33192
  1449
        $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1450
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1451
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1452
      | Const (x as (@{const_name distinct},
blanchet@33192
  1453
               Type ("fun", [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1454
        $ (t1 as _ $ _) =>
blanchet@33192
  1455
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1456
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@33192
  1457
      | (t0 as Const (x as (@{const_name If}, _))) $ t1 $ t2 $ t3 =>
blanchet@33192
  1458
        if is_ground_term t1
blanchet@33192
  1459
           andalso exists (Pattern.matches thy o rpair t1)
blanchet@33192
  1460
                          (Inttab.lookup_list ground_thm_table
blanchet@33192
  1461
                                              (hash_term t1)) then
blanchet@33192
  1462
          do_term depth Ts t2
blanchet@33192
  1463
        else
blanchet@33192
  1464
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1465
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1466
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1467
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1468
      | Const x => do_const depth Ts t x []
blanchet@33192
  1469
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1470
      | Free _ => t
blanchet@33192
  1471
      | Var _ => t
blanchet@33192
  1472
      | Bound _ => t
blanchet@33192
  1473
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1474
    (* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
blanchet@33192
  1475
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1476
        (Abs (Name.uu, body_type T,
blanchet@33192
  1477
              select_nth_constr_arg thy x (Bound 0) n res_T), [])
blanchet@33192
  1478
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@33192
  1479
        (select_nth_constr_arg thy x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1480
    (* int -> typ list -> term -> styp -> term list -> term *)
blanchet@33192
  1481
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1482
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1483
        SOME s' =>
blanchet@33192
  1484
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1485
      | NONE =>
blanchet@33192
  1486
        let
blanchet@33192
  1487
          val (const, ts) =
blanchet@33192
  1488
            if is_built_in_const fast_descrs x then
blanchet@33192
  1489
              if s = @{const_name finite} then
blanchet@33192
  1490
                if is_finite_type thy (domain_type T) then
blanchet@33192
  1491
                  (Abs ("A", domain_type T, @{const True}), ts)
blanchet@33192
  1492
                else case ts of
blanchet@33192
  1493
                  [Const (@{const_name UNIV}, _)] => (@{const False}, [])
blanchet@33192
  1494
                | _ => (Const x, ts)
blanchet@33192
  1495
              else
blanchet@33192
  1496
                (Const x, ts)
blanchet@33192
  1497
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1498
              SOME n =>
blanchet@33192
  1499
              let
blanchet@33192
  1500
                val (dataT, res_T) = nth_range_type n T
blanchet@33192
  1501
                                     |> domain_type pairf range_type
blanchet@33192
  1502
              in
blanchet@33192
  1503
                (optimized_case_def thy dataT res_T
blanchet@33192
  1504
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1505
              end
blanchet@33192
  1506
            | _ =>
blanchet@33192
  1507
              if is_constr thy x then
blanchet@33192
  1508
                (Const x, ts)
blanchet@33192
  1509
              else if is_record_get thy x then
blanchet@33192
  1510
                case length ts of
blanchet@33192
  1511
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@33192
  1512
                | _ => (optimized_record_get thy s (domain_type T)
blanchet@33192
  1513
                                             (range_type T) (hd ts), tl ts)
blanchet@33192
  1514
              else if is_record_update thy x then
blanchet@33192
  1515
                case length ts of
blanchet@33192
  1516
                  2 => (optimized_record_update thy (unsuffix Record.updateN s)
blanchet@33192
  1517
                                                (nth_range_type 2 T)
blanchet@33192
  1518
                                                (do_term depth Ts (hd ts))
blanchet@33192
  1519
                                                (do_term depth Ts (nth ts 1)),
blanchet@33192
  1520
                        [])
blanchet@33192
  1521
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@33192
  1522
              else if is_rep_fun thy x then
blanchet@33192
  1523
                let val x' = mate_of_rep_fun thy x in
blanchet@33192
  1524
                  if is_constr thy x' then
blanchet@33192
  1525
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1526
                                                    (range_type T)
blanchet@33192
  1527
                  else
blanchet@33192
  1528
                    (Const x, ts)
blanchet@33192
  1529
                end
blanchet@33192
  1530
              else if is_equational_fun ext_ctxt x then
blanchet@33192
  1531
                (Const x, ts)
blanchet@33192
  1532
              else case def_of_const thy def_table x of
blanchet@33192
  1533
                SOME def =>
blanchet@33192
  1534
                if depth > unfold_max_depth then
blanchet@33192
  1535
                  raise LIMIT ("NitpickHOL.unfold_defs_in_term",
blanchet@33192
  1536
                               "too many nested definitions (" ^
blanchet@33192
  1537
                               string_of_int depth ^ ") while expanding " ^
blanchet@33192
  1538
                               quote s)
blanchet@33192
  1539
                else if s = @{const_name wfrec'} then
blanchet@33192
  1540
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1541
                else
blanchet@33192
  1542
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1543
              | NONE => (Const x, ts)
blanchet@33192
  1544
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1545
  in do_term 0 [] end
blanchet@33192
  1546
blanchet@33192
  1547
(* theory -> typ -> term list *)
blanchet@33192
  1548
fun codatatype_bisim_axioms thy T =
blanchet@33192
  1549
  let
blanchet@33192
  1550
    val xs = datatype_constrs thy T
blanchet@33192
  1551
    val set_T = T --> bool_T
blanchet@33192
  1552
    val iter_T = @{typ bisim_iterator}
blanchet@33192
  1553
    val bisim_const = Const (@{const_name bisim}, [iter_T, T, T] ---> bool_T)
blanchet@33192
  1554
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1555
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1556
    val n_var_minus_1 =
blanchet@33192
  1557
      Const (@{const_name Tha}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1558
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1559
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1560
    val x_var = Var (("x", 0), T)
blanchet@33192
  1561
    val y_var = Var (("y", 0), T)
blanchet@33192
  1562
    (* styp -> int -> typ -> term *)
blanchet@33192
  1563
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1564
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1565
       else HOLogic.eq_const nth_T)
blanchet@33192
  1566
      $ select_nth_constr_arg thy x x_var n nth_T
blanchet@33192
  1567
      $ select_nth_constr_arg thy x y_var n nth_T
blanchet@33192
  1568
    (* styp -> term *)
blanchet@33192
  1569
    fun case_func (x as (_, T)) =
blanchet@33192
  1570
      let
blanchet@33192
  1571
        val arg_Ts = binder_types T
blanchet@33192
  1572
        val core_t =
blanchet@33192
  1573
          discriminate_value thy x y_var ::
blanchet@33192
  1574
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1575
          |> foldr1 s_conj
blanchet@33192
  1576
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1577
  in
blanchet@33192
  1578
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1579
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@33192
  1580
        $ (betapplys (optimized_case_def thy T bool_T,
blanchet@33192
  1581
                      map case_func xs @ [x_var]))),
blanchet@33192
  1582
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@33192
  1583
     $ (Const (@{const_name insert}, [T, set_T] ---> set_T)
blanchet@33192
  1584
        $ x_var $ Const (@{const_name bot_fun_inst.bot_fun}, set_T))]
blanchet@33192
  1585
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1586
  end
blanchet@33192
  1587
blanchet@33192
  1588
exception NO_TRIPLE of unit
blanchet@33192
  1589
blanchet@33192
  1590
(* theory -> styp -> term -> term list * term list * term *)
blanchet@33192
  1591
fun triple_for_intro_rule thy x t =
blanchet@33192
  1592
  let
blanchet@33192
  1593
    val prems = Logic.strip_imp_prems t |> map (ObjectLogic.atomize_term thy)
blanchet@33192
  1594
    val concl = Logic.strip_imp_concl t |> ObjectLogic.atomize_term thy
blanchet@33192
  1595
    val (main, side) = List.partition (exists_Const (equal x)) prems
blanchet@33192
  1596
    (* term -> bool *)
blanchet@33192
  1597
     val is_good_head = equal (Const x) o head_of
blanchet@33192
  1598
  in
blanchet@33192
  1599
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1600
  end
blanchet@33192
  1601
blanchet@33192
  1602
(* term -> term *)
blanchet@33192
  1603
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1604
blanchet@33192
  1605
(* indexname * typ -> term list -> term -> term -> term *)
blanchet@33192
  1606
fun wf_constraint_for rel side concl main =
blanchet@33192
  1607
  let
blanchet@33192
  1608
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1609
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1610
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1611
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1612
  in
blanchet@33192
  1613
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1614
                      HOLogic.all_const T
blanchet@33192
  1615
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1616
                  (t, vars)
blanchet@33192
  1617
  end
blanchet@33192
  1618
blanchet@33192
  1619
(* indexname * typ -> term list * term list * term -> term *)
blanchet@33192
  1620
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1621
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1622
blanchet@33192
  1623
(* Proof.context -> Time.time option -> thm
blanchet@33192
  1624
   -> (Proof.context -> tactic -> tactic) -> bool *)
blanchet@33192
  1625
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1626
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1627
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1628
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1629
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1630
blanchet@33192
  1631
val cached_timeout = Unsynchronized.ref (SOME Time.zeroTime)
blanchet@33192
  1632
val cached_wf_props : (term * bool) list Unsynchronized.ref =
blanchet@33192
  1633
  Unsynchronized.ref []
blanchet@33192
  1634
blanchet@33192
  1635
val termination_tacs = [LexicographicOrder.lex_order_tac,
blanchet@33192
  1636
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1637
blanchet@33192
  1638
(* extended_context -> const_table -> styp -> bool *)
blanchet@33192
  1639
fun is_is_well_founded_inductive_pred
blanchet@33192
  1640
        ({thy, ctxt, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@33192
  1641
         : extended_context) (x as (_, T)) =
blanchet@33192
  1642
  case def_props_for_const thy fast_descrs intro_table x of
blanchet@33192
  1643
    [] => raise TERM ("NitpickHOL.is_is_well_founded_inductive_pred", [Const x])
blanchet@33192
  1644
  | intro_ts =>
blanchet@33192
  1645
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1646
          |> filter_out (null o #2) of
blanchet@33192
  1647
       [] => true
blanchet@33192
  1648
     | triples =>
blanchet@33192
  1649
       let
blanchet@33192
  1650
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1651
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33192
  1652
         val j = List.foldl Int.max 0 (map maxidx_of_term intro_ts) + 1
blanchet@33192
  1653
         val rel = (("R", j), rel_T)
blanchet@33192
  1654
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1655
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1656
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1657
         val _ = if debug then
blanchet@33192
  1658
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1659
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1660
                 else
blanchet@33192
  1661
                   ()
blanchet@33192
  1662
       in
blanchet@33192
  1663
         if tac_timeout = (!cached_timeout) then ()
blanchet@33192
  1664
         else (cached_wf_props := []; cached_timeout := tac_timeout);
blanchet@33192
  1665
         case AList.lookup (op =) (!cached_wf_props) prop of
blanchet@33192
  1666
           SOME wf => wf
blanchet@33192
  1667
         | NONE =>
blanchet@33192
  1668
           let
blanchet@33192
  1669
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33192
  1670
             val wf = silence (exists (terminates_by ctxt tac_timeout goal))
blanchet@33192
  1671
                              termination_tacs
blanchet@33192
  1672
           in Unsynchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1673
       end)
blanchet@33192
  1674
    handle List.Empty => false
blanchet@33192
  1675
         | NO_TRIPLE () => false
blanchet@33192
  1676
blanchet@33192
  1677
(* The type constraint below is a workaround for a Poly/ML bug. *)
blanchet@33192
  1678
blanchet@33192
  1679
(* extended_context -> styp -> bool *)
blanchet@33192
  1680
fun is_well_founded_inductive_pred
blanchet@33192
  1681
        (ext_ctxt as {thy, wfs, def_table, wf_cache, ...} : extended_context)
blanchet@33192
  1682
        (x as (s, _)) =
blanchet@33192
  1683
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1684
    SOME (SOME b) => b
blanchet@33197
  1685
  | _ => s mem [@{const_name Nats}, @{const_name fold_graph'}]
blanchet@33192
  1686
         orelse case AList.lookup (op =) (!wf_cache) x of
blanchet@33192
  1687
                  SOME (_, wf) => wf
blanchet@33192
  1688
                | NONE =>
blanchet@33192
  1689
                  let
blanchet@33192
  1690
                    val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@33192
  1691
                    val wf = is_is_well_founded_inductive_pred ext_ctxt x
blanchet@33192
  1692
                  in
blanchet@33192
  1693
                    Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@33192
  1694
                  end
blanchet@33192
  1695
blanchet@33192
  1696
(* typ list -> typ -> typ -> term -> term *)
blanchet@33192
  1697
fun ap_curry [_] _ _ t = t
blanchet@33192
  1698
  | ap_curry arg_Ts tuple_T body_T t =
blanchet@33192
  1699
    let val n = length arg_Ts in
blanchet@33192
  1700
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1701
                incr_boundvars n t
blanchet@33192
  1702
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1703
    end
blanchet@33192
  1704
blanchet@33192
  1705
(* int -> term -> int *)
blanchet@33192
  1706
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1707
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@33192
  1708
  | num_occs_of_bound_in_term j (Abs (s, T, t')) =
blanchet@33192
  1709
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1710
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1711
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1712
blanchet@33192
  1713
(* term -> bool *)
blanchet@33192
  1714
val is_linear_inductive_pred_def =
blanchet@33192
  1715
  let
blanchet@33192
  1716
    (* int -> term -> bool *)
blanchet@33192
  1717
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  1718
        do_disjunct (j + 1) t2
blanchet@33192
  1719
      | do_disjunct j t =
blanchet@33192
  1720
        case num_occs_of_bound_in_term j t of
blanchet@33192
  1721
          0 => true
blanchet@33192
  1722
        | 1 => exists (equal (Bound j) o head_of) (conjuncts t)
blanchet@33192
  1723
        | _ => false
blanchet@33192
  1724
    (* term -> bool *)
blanchet@33192
  1725
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1726
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  1727
          case length xs of
blanchet@33192
  1728
            1 => false
blanchet@33192
  1729
          | n => forall (do_disjunct (n - 1)) (disjuncts body)
blanchet@33192
  1730
        end
blanchet@33192
  1731
      | do_lfp_def _ = false
blanchet@33192
  1732
  in do_lfp_def o strip_abs_body end
blanchet@33192
  1733
blanchet@33192
  1734
(* typ -> typ -> term -> term *)
blanchet@33192
  1735
fun ap_split tuple_T =
blanchet@33192
  1736
  HOLogic.mk_psplits (HOLogic.flat_tupleT_paths tuple_T) tuple_T
blanchet@33192
  1737
blanchet@33192
  1738
(* term -> term * term *)
blanchet@33192
  1739
val linear_pred_base_and_step_rhss =
blanchet@33192
  1740
  let
blanchet@33192
  1741
    (* term -> term *)
blanchet@33192
  1742
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1743
        let
blanchet@33192
  1744
          val (xs, body) = strip_abs t2
blanchet@33192
  1745
          val arg_Ts = map snd (tl xs)
blanchet@33192
  1746
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  1747
          val j = length arg_Ts
blanchet@33192
  1748
          (* int -> term -> term *)
blanchet@33192
  1749
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  1750
              Const (@{const_name Ex}, T1)
blanchet@33192
  1751
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  1752
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  1753
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  1754
            | repair_rec j t =
blanchet@33192
  1755
              let val (head, args) = strip_comb t in
blanchet@33192
  1756
                if head = Bound j then
blanchet@33192
  1757
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  1758
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  1759
                else
blanchet@33192
  1760
                  t
blanchet@33192
  1761
              end
blanchet@33192
  1762
          val (nonrecs, recs) =
blanchet@33192
  1763
            List.partition (equal 0 o num_occs_of_bound_in_term j)
blanchet@33192
  1764
                           (disjuncts body)
blanchet@33192
  1765
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  1766
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  1767
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  1768
        in
blanchet@33192
  1769
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33192
  1770
           |> ap_split tuple_T bool_T,
blanchet@33192
  1771
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33192
  1772
                              |> ap_split tuple_T bool_T))
blanchet@33192
  1773
        end
blanchet@33192
  1774
      | aux t =
blanchet@33192
  1775
        raise TERM ("NitpickHOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  1776
  in aux end
blanchet@33192
  1777
blanchet@33192
  1778
(* extended_context -> styp -> term -> term *)
blanchet@33192
  1779
fun closed_linear_pred_const (ext_ctxt as {simp_table, ...}) (x as (s, T)) def =
blanchet@33192
  1780
  let
blanchet@33192
  1781
    val j = maxidx_of_term def + 1
blanchet@33192
  1782
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1783
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1784
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  1785
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  1786
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  1787
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  1788
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  1789
    val set_T = tuple_T --> bool_T
blanchet@33192
  1790
    val curried_T = tuple_T --> set_T
blanchet@33192
  1791
    val uncurried_T = Type ("*", [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  1792
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  1793
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  1794
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  1795
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1796
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  1797
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  1798
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  1799
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1800
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  1801
  in
blanchet@33192
  1802
    list_abs (outer,
blanchet@33192
  1803
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  1804
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  1805
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  1806
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  1807
              $ list_comb (Const base_x, outer_bounds)
blanchet@33192
  1808
              |> ap_curry tuple_arg_Ts tuple_T bool_T)
blanchet@33192
  1809
    |> unfold_defs_in_term ext_ctxt
blanchet@33192
  1810
  end
blanchet@33192
  1811
blanchet@33192
  1812
(* extended_context -> bool -> styp -> term *)
blanchet@33192
  1813
fun unrolled_inductive_pred_const (ext_ctxt as {thy, star_linear_preds,
blanchet@33192
  1814
                                                def_table, simp_table, ...})
blanchet@33192
  1815
                                  gfp (x as (s, T)) =
blanchet@33192
  1816
  let
blanchet@33192
  1817
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  1818
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  1819
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  1820
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1821
  in
blanchet@33192
  1822
    if is_equational_fun ext_ctxt x' then
blanchet@33192
  1823
      unrolled_const (* already done *)
blanchet@33192
  1824
    else if not gfp andalso is_linear_inductive_pred_def def
blanchet@33192
  1825
         andalso star_linear_preds then
blanchet@33192
  1826
      closed_linear_pred_const ext_ctxt x def
blanchet@33192
  1827
    else
blanchet@33192
  1828
      let
blanchet@33192
  1829
        val j = maxidx_of_term def + 1
blanchet@33192
  1830
        val (outer, fp_app) = strip_abs def
blanchet@33192
  1831
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1832
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  1833
        val next = suc_const iter_T $ cur
blanchet@33192
  1834
        val rhs = case fp_app of
blanchet@33192
  1835
                    Const _ $ t =>
blanchet@33192
  1836
                    betapply (t, list_comb (Const x', next :: outer_bounds))
blanchet@33192
  1837
                  | _ => raise TERM ("NitpickHOL.unrolled_inductive_pred_const",
blanchet@33192
  1838
                                     [fp_app])
blanchet@33192
  1839
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  1840
        val all = outer @ inner
blanchet@33192
  1841
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  1842
        val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  1843
        val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
blanchet@33192
  1844
                 |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  1845
        val _ = add_simps simp_table s' [eq]
blanchet@33192
  1846
      in unrolled_const end
blanchet@33192
  1847
  end
blanchet@33192
  1848
blanchet@33192
  1849
(* extended_context -> styp -> term *)
blanchet@33192
  1850
fun raw_inductive_pred_axiom ({thy, def_table, ...} : extended_context) x =
blanchet@33192
  1851
  let
blanchet@33192
  1852
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1853
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1854
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1855
    val rhs = case fp_app of
blanchet@33192
  1856
                Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
blanchet@33192
  1857
              | _ => raise TERM ("NitpickHOL.raw_inductive_pred_axiom",
blanchet@33192
  1858
                                 [fp_app])
blanchet@33192
  1859
    val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  1860
    val all = outer @ inner
blanchet@33192
  1861
    val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  1862
    val j = maxidx_of_term def + 1
blanchet@33192
  1863
    val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  1864
  in
blanchet@33192
  1865
    HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
blanchet@33192
  1866
    |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  1867
  end
blanchet@33192
  1868
fun inductive_pred_axiom ext_ctxt (x as (s, T)) =
blanchet@33192
  1869
  if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
blanchet@33192
  1870
    let val x' = (after_name_sep s, T) in
blanchet@33192
  1871
      raw_inductive_pred_axiom ext_ctxt x' |> subst_atomic [(Const x', Const x)]
blanchet@33192
  1872
    end
blanchet@33192
  1873
  else
blanchet@33192
  1874
    raw_inductive_pred_axiom ext_ctxt x
blanchet@33192
  1875
blanchet@33192
  1876
(* extended_context -> styp -> term list *)
blanchet@33192
  1877
fun raw_equational_fun_axioms (ext_ctxt as {thy, fast_descrs, simp_table,
blanchet@33192
  1878
                                            psimp_table, ...}) (x as (s, _)) =
blanchet@33192
  1879
  if s mem redefined_in_NitpickDefs_thy then
blanchet@33192
  1880
    []
blanchet@33192
  1881
  else case def_props_for_const thy fast_descrs (!simp_table) x of
blanchet@33192
  1882
    [] => (case def_props_for_const thy fast_descrs psimp_table x of
blanchet@33192
  1883
             [] => [inductive_pred_axiom ext_ctxt x]
blanchet@33192
  1884
           | psimps => psimps)
blanchet@33192
  1885
  | simps => simps
blanchet@33192
  1886
blanchet@33192
  1887
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
blanchet@33192
  1888
blanchet@33192
  1889
(* term list -> term list *)
blanchet@33192
  1890
fun coalesce_type_vars_in_terms ts =
blanchet@33192
  1891
  let
blanchet@33192
  1892
    (* typ -> (sort * string) list -> (sort * string) list *)
blanchet@33192
  1893
    fun add_type (TFree (s, S)) table =
blanchet@33192
  1894
        (case AList.lookup (op =) table S of
blanchet@33192
  1895
           SOME s' =>
blanchet@33192
  1896
           if string_ord (s', s) = LESS then AList.update (op =) (S, s') table
blanchet@33192
  1897
           else table
blanchet@33192
  1898
         | NONE => (S, s) :: table)
blanchet@33192
  1899
      | add_type _ table = table
blanchet@33192
  1900
    val table = fold (fold_types (fold_atyps add_type)) ts []
blanchet@33192
  1901
    (* typ -> typ *)
blanchet@33192
  1902
    fun coalesce (TFree (s, S)) = TFree (AList.lookup (op =) table S |> the, S)
blanchet@33192
  1903
      | coalesce T = T
blanchet@33192
  1904
  in map (map_types (map_atyps coalesce)) ts end
blanchet@33192
  1905
blanchet@33192
  1906
(* extended_context -> typ -> typ list -> typ list *)
blanchet@33192
  1907
fun add_ground_types ext_ctxt T accum =
blanchet@33192
  1908
  case T of
blanchet@33192
  1909
    Type ("fun", Ts) => fold (add_ground_types ext_ctxt) Ts accum
blanchet@33192
  1910
  | Type ("*", Ts) => fold (add_ground_types ext_ctxt) Ts accum
blanchet@33192
  1911
  | Type (@{type_name itself}, [T1]) => add_ground_types ext_ctxt T1 accum
blanchet@33192
  1912
  | Type (_, Ts) =>
blanchet@33192
  1913
    if T mem @{typ prop} :: @{typ bool} :: @{typ unit} :: accum then
blanchet@33192
  1914
      accum
blanchet@33192
  1915
    else
blanchet@33192
  1916
      T :: accum
blanchet@33192
  1917
      |> fold (add_ground_types ext_ctxt)
blanchet@33192
  1918
              (case boxed_datatype_constrs ext_ctxt T of
blanchet@33192
  1919
                 [] => Ts
blanchet@33192
  1920
               | xs => map snd xs)
blanchet@33192
  1921
  | _ => insert (op =) T accum
blanchet@33192
  1922
(* extended_context -> typ -> typ list *)
blanchet@33192
  1923
fun ground_types_in_type ext_ctxt T = add_ground_types ext_ctxt T []
blanchet@33192
  1924
(* extended_context -> term list -> typ list *)
blanchet@33192
  1925
fun ground_types_in_terms ext_ctxt ts =
blanchet@33192
  1926
  fold (fold_types (add_ground_types ext_ctxt)) ts []
blanchet@33192
  1927
blanchet@33192
  1928
(* typ list -> int -> term -> bool *)
blanchet@33192
  1929
fun has_heavy_bounds_or_vars Ts level t =
blanchet@33192
  1930
  let
blanchet@33192
  1931
    (* typ list -> bool *)
blanchet@33192
  1932
    fun aux [] = false
blanchet@33192
  1933
      | aux [T] = is_fun_type T orelse is_pair_type T
blanchet@33192
  1934
      | aux _ = true
blanchet@33192
  1935
  in aux (map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t)) end
blanchet@33192
  1936
blanchet@33192
  1937
(* typ list -> int -> int -> int -> term -> term *)
blanchet@33192
  1938
fun fresh_value_var Ts k n j t =
blanchet@33192
  1939
  Var ((val_var_prefix ^ nat_subscript (n - j), k), fastype_of1 (Ts, t))
blanchet@33192
  1940
blanchet@33192
  1941
(* theory -> typ list -> bool -> int -> int -> term -> term list -> term list
blanchet@33192
  1942
   -> term * term list *)
blanchet@33192
  1943
fun pull_out_constr_comb thy Ts relax k level t args seen =
blanchet@33192
  1944
  let val t_comb = list_comb (t, args) in
blanchet@33192
  1945
    case t of
blanchet@33192
  1946
      Const x =>
blanchet@33192
  1947
      if not relax andalso is_constr thy x
blanchet@33192
  1948
         andalso not (is_fun_type (fastype_of1 (Ts, t_comb)))
blanchet@33192
  1949
         andalso has_heavy_bounds_or_vars Ts level t_comb
blanchet@33192
  1950
         andalso not (loose_bvar (t_comb, level)) then
blanchet@33192
  1951
        let
blanchet@33192
  1952
          val (j, seen) = case find_index (equal t_comb) seen of
blanchet@33192
  1953
                            ~1 => (0, t_comb :: seen)
blanchet@33192
  1954
                          | j => (j, seen)
blanchet@33192
  1955
        in (fresh_value_var Ts k (length seen) j t_comb, seen) end
blanchet@33192
  1956
      else
blanchet@33192
  1957
        (t_comb, seen)
blanchet@33192
  1958
    | _ => (t_comb, seen)
blanchet@33192
  1959
  end
blanchet@33192
  1960
blanchet@33192
  1961
(* (term -> term) -> typ list -> int -> term list -> term list *)
blanchet@33192
  1962
fun equations_for_pulled_out_constrs mk_eq Ts k seen =
blanchet@33192
  1963
  let val n = length seen in
blanchet@33192
  1964
    map2 (fn j => fn t => mk_eq (fresh_value_var Ts k n j t, t))
blanchet@33192
  1965
         (index_seq 0 n) seen
blanchet@33192
  1966
  end
blanchet@33192
  1967
blanchet@33192
  1968
(* theory -> bool -> term -> term *)
blanchet@33192
  1969
fun pull_out_universal_constrs thy def t =
blanchet@33192
  1970
  let
blanchet@33192
  1971
    val k = maxidx_of_term t + 1
blanchet@33192
  1972
    (* typ list -> bool -> term -> term list -> term list -> term * term list *)
blanchet@33192
  1973
    fun do_term Ts def t args seen =
blanchet@33192
  1974
      case t of
blanchet@33192
  1975
        (t0 as Const (@{const_name "=="}, _)) $ t1 $ t2 =>
blanchet@33192
  1976
        do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1977
      | (t0 as @{const "==>"}) $ t1 $ t2 => do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1978
      | (t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2 =>
blanchet@33192
  1979
        do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1980
      | (t0 as @{const "op -->"}) $ t1 $ t2 => do_eq_or_imp Ts def t0 t1 t2 seen
blanchet@33192
  1981
      | Abs (s, T, t') =>
blanchet@33192
  1982
        let val (t', seen) = do_term (T :: Ts) def t' [] seen in
blanchet@33192
  1983
          (list_comb (Abs (s, T, t'), args), seen)
blanchet@33192
  1984
        end
blanchet@33192
  1985
      | t1 $ t2 =>
blanchet@33192
  1986
        let val (t2, seen) = do_term Ts def t2 [] seen in
blanchet@33192
  1987
          do_term Ts def t1 (t2 :: args) seen
blanchet@33192
  1988
        end
blanchet@33192
  1989
      | _ => pull_out_constr_comb thy Ts def k 0 t args seen
blanchet@33192
  1990
    (* typ list -> bool -> term -> term -> term -> term list
blanchet@33192
  1991
       -> term * term list *)
blanchet@33192
  1992
    and do_eq_or_imp Ts def t0 t1 t2 seen =
blanchet@33192
  1993
      let
blanchet@33192
  1994
        val (t2, seen) = do_term Ts def t2 [] seen
blanchet@33192
  1995
        val (t1, seen) = do_term Ts false t1 [] seen
blanchet@33192
  1996
      in (t0 $ t1 $ t2, seen) end
blanchet@33192
  1997
    val (concl, seen) = do_term [] def t [] []
blanchet@33192
  1998
  in
blanchet@33192
  1999
    Logic.list_implies (equations_for_pulled_out_constrs Logic.mk_equals [] k
blanchet@33192
  2000
                                                         seen, concl)
blanchet@33192
  2001
  end
blanchet@33192
  2002
blanchet@33192
  2003
(* theory -> bool -> term -> term *)
blanchet@33192
  2004
fun destroy_pulled_out_constrs thy axiom t =
blanchet@33192
  2005
  let
blanchet@33192
  2006
    (* styp -> int *)
blanchet@33192
  2007
    val num_occs_of_var =
blanchet@33192
  2008
      fold_aterms (fn Var z => (fn f => fn z' => f z' |> z = z' ? Integer.add 1)
blanchet@33192
  2009
                    | _ => I) t (K 0)
blanchet@33192
  2010
    (* bool -> term -> term *)
blanchet@33192
  2011
    fun aux careful ((t0 as Const (@{const_name "=="}, _)) $ t1 $ t2) =
blanchet@33192
  2012
        aux_eq careful true t0 t1 t2
blanchet@33192
  2013
      | aux careful ((t0 as @{const "==>"}) $ t1 $ t2) =
blanchet@33192
  2014
        t0 $ aux false t1 $ aux careful t2
blanchet@33192
  2015
      | aux careful ((t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2) =
blanchet@33192
  2016
        aux_eq careful true t0 t1 t2
blanchet@33192
  2017
      | aux careful ((t0 as @{const "op -->"}) $ t1 $ t2) =
blanchet@33192
  2018
        t0 $ aux false t1 $ aux careful t2
blanchet@33192
  2019
      | aux careful (Abs (s, T, t')) = Abs (s, T, aux careful t')
blanchet@33192
  2020
      | aux careful (t1 $ t2) = aux careful t1 $ aux careful t2
blanchet@33192
  2021
      | aux _ t = t
blanchet@33192
  2022
    (* bool -> bool -> term -> term -> term -> term *)
blanchet@33192
  2023
    and aux_eq careful pass1 t0 t1 t2 =
blanchet@33192
  2024
      (if careful then
blanchet@33192
  2025
         raise SAME ()
blanchet@33192
  2026
       else if axiom andalso is_Var t2
blanchet@33192
  2027
               andalso num_occs_of_var (dest_Var t2) = 1 then
blanchet@33192
  2028
         @{const True}
blanchet@33192
  2029
       else case strip_comb t2 of
blanchet@33192
  2030
         (Const (x as (s, T)), args) =>
blanchet@33192
  2031
         let val arg_Ts = binder_types T in
blanchet@33192
  2032
           if length arg_Ts = length args
blanchet@33192
  2033
              andalso (is_constr thy x orelse s mem [@{const_name Pair}]
blanchet@33192
  2034
                       orelse x = dest_Const @{const Suc})
blanchet@33192
  2035
              andalso (not careful orelse not (is_Var t1)
blanchet@33192
  2036
                       orelse String.isPrefix val_var_prefix
blanchet@33192
  2037
                                              (fst (fst (dest_Var t1)))) then
blanchet@33192
  2038
             discriminate_value thy x t1 ::
blanchet@33192
  2039
             map3 (sel_eq x t1) (index_seq 0 (length args)) arg_Ts args
blanchet@33192
  2040
             |> foldr1 s_conj
blanchet@33192
  2041
             |> body_type (type_of t0) = prop_T ? HOLogic.mk_Trueprop
blanchet@33192
  2042
           else
blanchet@33192
  2043
             raise SAME ()
blanchet@33192
  2044
         end
blanchet@33192
  2045
       | _ => raise SAME ())
blanchet@33192
  2046
      handle SAME () => if pass1 then aux_eq careful false t0 t2 t1
blanchet@33192
  2047
                        else t0 $ aux false t2 $ aux false t1
blanchet@33192
  2048
    (* styp -> term -> int -> typ -> term -> term *)
blanchet@33192
  2049
    and sel_eq x t n nth_T nth_t =
blanchet@33192
  2050
      HOLogic.eq_const nth_T $ nth_t $ select_nth_constr_arg thy x t n nth_T
blanchet@33192
  2051
      |> aux false
blanchet@33192
  2052
  in aux axiom t end
blanchet@33192
  2053
blanchet@33192
  2054
(* theory -> term -> term *)
blanchet@33192
  2055
fun simplify_constrs_and_sels thy t =
blanchet@33192
  2056
  let
blanchet@33192
  2057
    (* term -> int -> term *)
blanchet@33192
  2058
    fun is_nth_sel_on t' n (Const (s, _) $ t) =
blanchet@33192
  2059
        (t = t' andalso is_sel_like_and_no_discr s
blanchet@33192
  2060
         andalso sel_no_from_name s = n)
blanchet@33192
  2061
      | is_nth_sel_on _ _ _ = false
blanchet@33192
  2062
    (* term -> term list -> term *)
blanchet@33192
  2063
    fun do_term (Const (@{const_name Rep_Frac}, _)
blanchet@33192
  2064
                 $ (Const (@{const_name Abs_Frac}, _) $ t1)) [] = do_term t1 []
blanchet@33192
  2065
      | do_term (Const (@{const_name Abs_Frac}, _)
blanchet@33192
  2066
                 $ (Const (@{const_name Rep_Frac}, _) $ t1)) [] = do_term t1 []
blanchet@33192
  2067
      | do_term (t1 $ t2) args = do_term t1 (do_term t2 [] :: args)
blanchet@33192
  2068
      | do_term (t as Const (x as (s, T))) (args as _ :: _) =
blanchet@33192
  2069
        ((if is_constr_like thy x then
blanchet@33192
  2070
            if length args = num_binder_types T then
blanchet@33192
  2071
              case hd args of
blanchet@33192
  2072
                Const (x' as (_, T')) $ t' =>
blanchet@33192
  2073
                if domain_type T' = body_type T
blanchet@33192
  2074
                   andalso forall (uncurry (is_nth_sel_on t'))
blanchet@33192
  2075
                                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  2076
                  t'
blanchet@33192
  2077
                else
blanchet@33192
  2078
                  raise SAME ()
blanchet@33192
  2079
              | _ => raise SAME ()
blanchet@33192
  2080
            else
blanchet@33192
  2081
              raise SAME ()
blanchet@33192
  2082
          else if is_sel_like_and_no_discr s then
blanchet@33192
  2083
            case strip_comb (hd args) of
blanchet@33192
  2084
              (Const (x' as (s', T')), ts') =>
blanchet@33192
  2085
              if is_constr_like thy x'
blanchet@33192
  2086
                 andalso constr_name_for_sel_like s = s'
blanchet@33192
  2087
                 andalso not (exists is_pair_type (binder_types T')) then
blanchet@33192
  2088
                list_comb (nth ts' (sel_no_from_name s), tl args)
blanchet@33192
  2089
              else
blanchet@33192
  2090
                raise SAME ()
blanchet@33192
  2091
            | _ => raise SAME ()
blanchet@33192
  2092
          else
blanchet@33192
  2093
            raise SAME ())
blanchet@33192
  2094
         handle SAME () => betapplys (t, args))
blanchet@33192
  2095
      | do_term (Abs (s, T, t')) args =
blanchet@33192
  2096
        betapplys (Abs (s, T, do_term t' []), args)
blanchet@33192
  2097
      | do_term t args = betapplys (t, args)
blanchet@33192
  2098
  in do_term t [] end
blanchet@33192
  2099
blanchet@33192
  2100
(* term -> term *)
blanchet@33192
  2101
fun curry_assms (@{const "==>"} $ (@{const Trueprop}
blanchet@33192
  2102
                                   $ (@{const "op &"} $ t1 $ t2)) $ t3) =
blanchet@33192
  2103
    curry_assms (Logic.list_implies ([t1, t2] |> map HOLogic.mk_Trueprop, t3))
blanchet@33192
  2104
  | curry_assms (@{const "==>"} $ t1 $ t2) =
blanchet@33192
  2105
    @{const "==>"} $ curry_assms t1 $ curry_assms t2
blanchet@33192
  2106
  | curry_assms t = t
blanchet@33192
  2107
blanchet@33192
  2108
(* term -> term *)
blanchet@33192
  2109
val destroy_universal_equalities =
blanchet@33192
  2110
  let
blanchet@33192
  2111
    (* term list -> (indexname * typ) list -> term -> term *)
blanchet@33192
  2112
    fun aux prems zs t =
blanchet@33192
  2113
      case t of
blanchet@33192
  2114
        @{const "==>"} $ t1 $ t2 => aux_implies prems zs t1 t2
blanchet@33192
  2115
      | _ => Logic.list_implies (rev prems, t)
blanchet@33192
  2116
    (* term list -> (indexname * typ) list -> term -> term -> term *)
blanchet@33192
  2117
    and aux_implies prems zs t1 t2 =
blanchet@33192
  2118
      case t1 of
blanchet@33192
  2119
        Const (@{const_name "=="}, _) $ Var z $ t' => aux_eq prems zs z t' t1 t2
blanchet@33192
  2120
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ Var z $ t') =>
blanchet@33192
  2121
        aux_eq prems zs z t' t1 t2
blanchet@33192
  2122
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t' $ Var z) =>
blanchet@33192
  2123
        aux_eq prems zs z t' t1 t2
blanchet@33192
  2124
      | _ => aux (t1 :: prems) (Term.add_vars t1 zs) t2
blanchet@33192
  2125
    (* term list -> (indexname * typ) list -> indexname * typ -> term -> term
blanchet@33192
  2126
       -> term -> term *)
blanchet@33192
  2127
    and aux_eq prems zs z t' t1 t2 =
blanchet@33192
  2128
      if not (z mem zs) andalso not (exists_subterm (equal (Var z)) t') then
blanchet@33192
  2129
        aux prems zs (subst_free [(Var z, t')] t2)
blanchet@33192
  2130
      else
blanchet@33192
  2131
        aux (t1 :: prems) (Term.add_vars t1 zs) t2
blanchet@33192
  2132
  in aux [] [] end
blanchet@33192
  2133
blanchet@33192
  2134
(* theory -> term -> term *)
blanchet@33192
  2135
fun pull_out_existential_constrs thy t =
blanchet@33192
  2136
  let
blanchet@33192
  2137
    val k = maxidx_of_term t + 1
blanchet@33192
  2138
    (* typ list -> int -> term -> term list -> term list -> term * term list *)
blanchet@33192
  2139
    fun aux Ts num_exists t args seen =
blanchet@33192
  2140
      case t of
blanchet@33192
  2141
        (t0 as Const (@{const_name Ex}, _)) $ Abs (s1, T1, t1) =>
blanchet@33192
  2142
        let
blanchet@33192
  2143
          val (t1, seen') = aux (T1 :: Ts) (num_exists + 1) t1 [] []
blanchet@33192
  2144
          val n = length seen'
blanchet@33192
  2145
          (* unit -> term list *)
blanchet@33192
  2146
          fun vars () = map2 (fresh_value_var Ts k n) (index_seq 0 n) seen'
blanchet@33192
  2147
        in
blanchet@33192
  2148
          (equations_for_pulled_out_constrs HOLogic.mk_eq Ts k seen'
blanchet@33192
  2149
           |> List.foldl s_conj t1 |> fold mk_exists (vars ())
blanchet@33192
  2150
           |> curry3 Abs s1 T1 |> curry (op $) t0, seen)
blanchet@33192
  2151
        end
blanchet@33192
  2152
      | t1 $ t2 =>
blanchet@33192
  2153
        let val (t2, seen) = aux Ts num_exists t2 [] seen in
blanchet@33192
  2154
          aux Ts num_exists t1 (t2 :: args) seen
blanchet@33192
  2155
        end
blanchet@33192
  2156
      | Abs (s, T, t') =>
blanchet@33192
  2157
        let
blanchet@33192
  2158
          val (t', seen) = aux (T :: Ts) 0 t' [] (map (incr_boundvars 1) seen)