src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Tue Feb 23 19:10:25 2010 +0100 (2010-02-23)
changeset 35335 f715cfde056a
parent 35332 22442ab3e7a3
child 35384 88dbcfe75c45
permissions -rw-r--r--
support local definitions in Nitpick
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(*  Title:      HOL/Tools/Nitpick/nitpick_hol.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2008, 2009, 2010
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Auxiliary HOL-related functions used by Nitpick.
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*)
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signature NITPICK_HOL =
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sig
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  type styp = Nitpick_Util.styp
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  type const_table = term list Symtab.table
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  type special_fun = (styp * int list * term list) * styp
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  type unrolled = styp * styp
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  type wf_cache = (styp * (bool * bool)) list
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  type hol_context = {
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    thy: theory,
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    ctxt: Proof.context,
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    max_bisim_depth: int,
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    boxes: (typ option * bool option) list,
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    stds: (typ option * bool) list,
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    wfs: (styp option * bool option) list,
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    user_axioms: bool option,
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    debug: bool,
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    binary_ints: bool option,
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    destroy_constrs: bool,
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    specialize: bool,
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    skolemize: bool,
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    star_linear_preds: bool,
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    uncurry: bool,
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    fast_descrs: bool,
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    tac_timeout: Time.time option,
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    evals: term list,
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    case_names: (string * int) list,
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    def_table: const_table,
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    nondef_table: const_table,
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    user_nondefs: term list,
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    simp_table: const_table Unsynchronized.ref,
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    psimp_table: const_table,
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    intro_table: const_table,
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    ground_thm_table: term list Inttab.table,
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    ersatz_table: (string * string) list,
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    skolems: (string * string list) list Unsynchronized.ref,
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    special_funs: special_fun list Unsynchronized.ref,
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    unrolled_preds: unrolled list Unsynchronized.ref,
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    wf_cache: wf_cache Unsynchronized.ref,
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    constr_cache: (typ * styp list) list Unsynchronized.ref}
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  datatype fixpoint_kind = Lfp | Gfp | NoFp
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  datatype boxability =
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    InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
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  val name_sep : string
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  val numeral_prefix : string
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  val ubfp_prefix : string
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  val lbfp_prefix : string
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  val quot_normal_prefix : string
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  val skolem_prefix : string
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  val special_prefix : string
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  val uncurry_prefix : string
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  val eval_prefix : string
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  val original_name : string -> string
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  val s_conj : term * term -> term
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  val s_disj : term * term -> term
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  val strip_any_connective : term -> term list * term
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  val conjuncts_of : term -> term list
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  val disjuncts_of : term -> term list
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  val unarize_and_unbox_type : typ -> typ
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  val unarize_unbox_and_uniterize_type : typ -> typ
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  val string_for_type : Proof.context -> typ -> string
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  val prefix_name : string -> string -> string
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  val shortest_name : string -> string
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  val short_name : string -> string
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  val shorten_names_in_term : term -> term
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  val type_match : theory -> typ * typ -> bool
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  val const_match : theory -> styp * styp -> bool
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  val term_match : theory -> term * term -> bool
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  val is_TFree : typ -> bool
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  val is_higher_order_type : typ -> bool
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  val is_fun_type : typ -> bool
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  val is_set_type : typ -> bool
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  val is_pair_type : typ -> bool
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  val is_lfp_iterator_type : typ -> bool
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  val is_gfp_iterator_type : typ -> bool
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  val is_fp_iterator_type : typ -> bool
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  val is_iterator_type : typ -> bool
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  val is_boolean_type : typ -> bool
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  val is_integer_type : typ -> bool
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  val is_bit_type : typ -> bool
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  val is_word_type : typ -> bool
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  val is_integer_like_type : typ -> bool
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  val is_record_type : typ -> bool
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  val is_number_type : theory -> typ -> bool
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  val const_for_iterator_type : typ -> styp
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  val strip_n_binders : int -> typ -> typ list * typ
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  val nth_range_type : int -> typ -> typ
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  val num_factors_in_type : typ -> int
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  val num_binder_types : typ -> int
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  val curried_binder_types : typ -> typ list
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  val mk_flat_tuple : typ -> term list -> term
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  val dest_n_tuple : int -> term -> term list
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  val is_real_datatype : theory -> string -> bool
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  val is_standard_datatype : theory -> (typ option * bool) list -> typ -> bool
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  val is_quot_type : theory -> typ -> bool
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  val is_codatatype : theory -> typ -> bool
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  val is_pure_typedef : theory -> typ -> bool
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  val is_univ_typedef : theory -> typ -> bool
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  val is_datatype : theory -> (typ option * bool) list -> typ -> bool
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  val is_record_constr : styp -> bool
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  val is_record_get : theory -> styp -> bool
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  val is_record_update : theory -> styp -> bool
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  val is_abs_fun : theory -> styp -> bool
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  val is_rep_fun : theory -> styp -> bool
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  val is_quot_abs_fun : Proof.context -> styp -> bool
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  val is_quot_rep_fun : Proof.context -> styp -> bool
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  val mate_of_rep_fun : theory -> styp -> styp
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  val is_constr_like : theory -> styp -> bool
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  val is_stale_constr : theory -> styp -> bool
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  val is_constr : theory -> (typ option * bool) list -> styp -> bool
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  val is_sel : string -> bool
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  val is_sel_like_and_no_discr : string -> bool
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  val box_type : hol_context -> boxability -> typ -> typ
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  val binarize_nat_and_int_in_type : typ -> typ
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  val binarize_nat_and_int_in_term : term -> term
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  val discr_for_constr : styp -> styp
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  val num_sels_for_constr_type : typ -> int
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  val nth_sel_name_for_constr_name : string -> int -> string
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  val nth_sel_for_constr : styp -> int -> styp
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  val binarized_and_boxed_nth_sel_for_constr :
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    hol_context -> bool -> styp -> int -> styp
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  val sel_no_from_name : string -> int
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  val close_form : term -> term
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  val eta_expand : typ list -> term -> int -> term
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  val extensionalize : term -> term
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  val distinctness_formula : typ -> term list -> term
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  val register_frac_type : string -> (string * string) list -> theory -> theory
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  val unregister_frac_type : string -> theory -> theory
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  val register_codatatype : typ -> string -> styp list -> theory -> theory
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  val unregister_codatatype : typ -> theory -> theory
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  val datatype_constrs : hol_context -> typ -> styp list
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  val binarized_and_boxed_datatype_constrs :
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    hol_context -> bool -> typ -> styp list
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  val num_datatype_constrs : hol_context -> typ -> int
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  val constr_name_for_sel_like : string -> string
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  val binarized_and_boxed_constr_for_sel : hol_context -> bool -> styp -> styp
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  val discriminate_value : hol_context -> styp -> term -> term
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  val select_nth_constr_arg :
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    theory -> (typ option * bool) list -> styp -> term -> int -> typ -> term
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  val construct_value :
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    theory -> (typ option * bool) list -> styp -> term list -> term
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  val card_of_type : (typ * int) list -> typ -> int
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  val bounded_card_of_type : int -> int -> (typ * int) list -> typ -> int
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  val bounded_exact_card_of_type :
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    hol_context -> int -> int -> (typ * int) list -> typ -> int
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  val is_finite_type : hol_context -> typ -> bool
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  val special_bounds : term list -> (indexname * typ) list
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  val is_funky_typedef : theory -> typ -> bool
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  val all_axioms_of :
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    theory -> (term * term) list -> term list * term list * term list
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  val arity_of_built_in_const :
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    theory -> (typ option * bool) list -> bool -> styp -> int option
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  val is_built_in_const :
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    theory -> (typ option * bool) list -> bool -> styp -> bool
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  val term_under_def : term -> term
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  val case_const_names :
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    theory -> (typ option * bool) list -> (string * int) list
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  val const_def_table :
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    Proof.context -> (term * term) list -> term list -> const_table
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  val const_nondef_table : term list -> const_table
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  val const_simp_table : Proof.context -> (term * term) list -> const_table
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  val const_psimp_table : Proof.context -> (term * term) list -> const_table
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  val inductive_intro_table :
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    Proof.context -> (term * term) list -> const_table -> const_table
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  val ground_theorem_table : theory -> term list Inttab.table
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  val ersatz_table : theory -> (string * string) list
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  val add_simps : const_table Unsynchronized.ref -> string -> term list -> unit
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  val inverse_axioms_for_rep_fun : theory -> styp -> term list
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  val optimized_typedef_axioms : theory -> string * typ list -> term list
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  val optimized_quot_type_axioms :
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    Proof.context -> (typ option * bool) list -> string * typ list -> term list
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  val def_of_const : theory -> const_table -> styp -> term option
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  val fixpoint_kind_of_const :
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    theory -> const_table -> string * typ -> fixpoint_kind
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  val is_inductive_pred : hol_context -> styp -> bool
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  val is_equational_fun : hol_context -> styp -> bool
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  val is_constr_pattern_lhs : theory -> term -> bool
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  val is_constr_pattern_formula : theory -> term -> bool
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  val unfold_defs_in_term : hol_context -> term -> term
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  val codatatype_bisim_axioms : hol_context -> typ -> term list
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  val is_well_founded_inductive_pred : hol_context -> styp -> bool
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  val unrolled_inductive_pred_const : hol_context -> bool -> styp -> term
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  val equational_fun_axioms : hol_context -> styp -> term list
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  val is_equational_fun_surely_complete : hol_context -> styp -> bool
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  val merge_type_vars_in_terms : term list -> term list
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  val ground_types_in_type : hol_context -> bool -> typ -> typ list
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  val ground_types_in_terms : hol_context -> bool -> term list -> typ list
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  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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   hol_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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end;
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structure Nitpick_HOL : NITPICK_HOL =
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struct
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open Nitpick_Util
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type const_table = term list Symtab.table
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type special_fun = (styp * int list * term list) * styp
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type unrolled = styp * styp
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type wf_cache = (styp * (bool * bool)) list
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type hol_context = {
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  thy: theory,
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  ctxt: Proof.context,
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  max_bisim_depth: int,
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  boxes: (typ option * bool option) list,
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  stds: (typ option * bool) list,
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  wfs: (styp option * bool option) list,
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  user_axioms: bool option,
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  debug: bool,
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  binary_ints: bool option,
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  destroy_constrs: bool,
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  specialize: bool,
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  skolemize: bool,
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  star_linear_preds: bool,
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  uncurry: bool,
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  fast_descrs: bool,
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  tac_timeout: Time.time option,
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  evals: term list,
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  case_names: (string * int) list,
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  def_table: const_table,
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  nondef_table: const_table,
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  user_nondefs: term list,
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  simp_table: const_table Unsynchronized.ref,
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  psimp_table: const_table,
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  intro_table: const_table,
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  ground_thm_table: term list Inttab.table,
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  ersatz_table: (string * string) list,
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  skolems: (string * string list) list Unsynchronized.ref,
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  special_funs: special_fun list Unsynchronized.ref,
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  unrolled_preds: unrolled list Unsynchronized.ref,
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  wf_cache: wf_cache Unsynchronized.ref,
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  constr_cache: (typ * styp list) list Unsynchronized.ref}
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datatype fixpoint_kind = Lfp | Gfp | NoFp
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datatype boxability =
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  InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
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structure Data = Theory_Data(
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  type T = {frac_types: (string * (string * string) list) list,
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            codatatypes: (string * (string * styp list)) list}
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  val empty = {frac_types = [], codatatypes = []}
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  val extend = I
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  fun merge ({frac_types = fs1, codatatypes = cs1},
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               {frac_types = fs2, codatatypes = cs2}) : T =
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    {frac_types = AList.merge (op =) (K true) (fs1, fs2),
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     codatatypes = AList.merge (op =) (K true) (cs1, cs2)})
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val name_sep = "$"
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val numeral_prefix = nitpick_prefix ^ "num" ^ name_sep
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val sel_prefix = nitpick_prefix ^ "sel"
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val discr_prefix = nitpick_prefix ^ "is" ^ name_sep
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val set_prefix = nitpick_prefix ^ "set" ^ name_sep
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val lfp_iterator_prefix = nitpick_prefix ^ "lfpit" ^ name_sep
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val gfp_iterator_prefix = nitpick_prefix ^ "gfpit" ^ name_sep
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val unrolled_prefix = nitpick_prefix ^ "unroll" ^ name_sep
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val base_prefix = nitpick_prefix ^ "base" ^ name_sep
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val step_prefix = nitpick_prefix ^ "step" ^ name_sep
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val ubfp_prefix = nitpick_prefix ^ "ubfp" ^ name_sep
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val lbfp_prefix = nitpick_prefix ^ "lbfp" ^ name_sep
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val quot_normal_prefix = nitpick_prefix ^ "qn" ^ name_sep
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val skolem_prefix = nitpick_prefix ^ "sk"
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val special_prefix = nitpick_prefix ^ "sp"
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val uncurry_prefix = nitpick_prefix ^ "unc"
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val eval_prefix = nitpick_prefix ^ "eval"
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val iter_var_prefix = "i"
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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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(* Proof.context -> typ -> string *)
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fun quot_normal_name_for_type ctxt T =
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  quot_normal_prefix ^ unyxml (Syntax.string_of_typ ctxt T)
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(* 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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   301
(* term * term -> term *)
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   302
fun s_conj (t1, @{const True}) = t1
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   303
  | s_conj (@{const True}, t2) = t2
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   304
  | s_conj (t1, t2) =
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   305
    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
blanchet@34998
   306
    else HOLogic.mk_conj (t1, t2)
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   307
fun s_disj (t1, @{const False}) = t1
blanchet@34998
   308
  | s_disj (@{const False}, t2) = t2
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   309
  | s_disj (t1, t2) =
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   310
    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
blanchet@34998
   311
    else HOLogic.mk_disj (t1, t2)
blanchet@34998
   312
blanchet@34998
   313
(* term -> term -> term list *)
blanchet@34998
   314
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
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   315
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
blanchet@34998
   316
  | strip_connective _ t = [t]
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   317
(* term -> term list * term *)
blanchet@35280
   318
fun strip_any_connective (t as (t0 $ _ $ _)) =
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   319
    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
blanchet@34998
   320
      (strip_connective t0 t, t0)
blanchet@34998
   321
    else
blanchet@34998
   322
      ([t], @{const Not})
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   323
  | strip_any_connective t = ([t], @{const Not})
blanchet@34998
   324
(* term -> term list *)
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   325
val conjuncts_of = strip_connective @{const "op &"}
blanchet@35070
   326
val disjuncts_of = strip_connective @{const "op |"}
blanchet@34998
   327
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   328
(* When you add constants to these lists, make sure to handle them in
blanchet@33232
   329
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
blanchet@33192
   330
   well. *)
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   331
val built_in_consts =
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   332
  [(@{const_name all}, 1),
blanchet@33192
   333
   (@{const_name "=="}, 2),
blanchet@33192
   334
   (@{const_name "==>"}, 2),
blanchet@33192
   335
   (@{const_name Pure.conjunction}, 2),
blanchet@33192
   336
   (@{const_name Trueprop}, 1),
blanchet@33192
   337
   (@{const_name Not}, 1),
blanchet@33192
   338
   (@{const_name False}, 0),
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   339
   (@{const_name True}, 0),
blanchet@33192
   340
   (@{const_name All}, 1),
blanchet@33192
   341
   (@{const_name Ex}, 1),
blanchet@33192
   342
   (@{const_name "op ="}, 2),
blanchet@33192
   343
   (@{const_name "op &"}, 2),
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   344
   (@{const_name "op |"}, 2),
blanchet@33192
   345
   (@{const_name "op -->"}, 2),
blanchet@33192
   346
   (@{const_name If}, 3),
blanchet@33192
   347
   (@{const_name Let}, 2),
blanchet@33192
   348
   (@{const_name Unity}, 0),
blanchet@33192
   349
   (@{const_name Pair}, 2),
blanchet@33192
   350
   (@{const_name fst}, 1),
blanchet@33192
   351
   (@{const_name snd}, 1),
blanchet@33192
   352
   (@{const_name Id}, 0),
blanchet@33192
   353
   (@{const_name insert}, 2),
blanchet@33192
   354
   (@{const_name converse}, 1),
blanchet@33192
   355
   (@{const_name trancl}, 1),
blanchet@33192
   356
   (@{const_name rel_comp}, 2),
blanchet@33192
   357
   (@{const_name image}, 2),
blanchet@33192
   358
   (@{const_name finite}, 1),
blanchet@34936
   359
   (@{const_name unknown}, 0),
blanchet@34936
   360
   (@{const_name is_unknown}, 1),
blanchet@33192
   361
   (@{const_name Tha}, 1),
blanchet@33192
   362
   (@{const_name Frac}, 0),
blanchet@33192
   363
   (@{const_name norm_frac}, 0)]
blanchet@35220
   364
val built_in_nat_consts =
blanchet@35220
   365
  [(@{const_name Suc}, 0),
blanchet@35220
   366
   (@{const_name nat}, 0),
blanchet@35220
   367
   (@{const_name nat_gcd}, 0),
blanchet@35220
   368
   (@{const_name nat_lcm}, 0)]
blanchet@33192
   369
val built_in_descr_consts =
blanchet@33192
   370
  [(@{const_name The}, 1),
blanchet@33192
   371
   (@{const_name Eps}, 1)]
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   372
val built_in_typed_consts =
blanchet@35220
   373
  [((@{const_name zero_class.zero}, int_T), 0),
blanchet@35220
   374
   ((@{const_name one_class.one}, int_T), 0),
blanchet@35220
   375
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   376
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   377
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
blanchet@35220
   378
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
blanchet@35220
   379
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
blanchet@35220
   380
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
blanchet@35220
   381
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
blanchet@35220
   382
val built_in_typed_nat_consts =
blanchet@35220
   383
  [((@{const_name zero_class.zero}, nat_T), 0),
blanchet@35220
   384
   ((@{const_name one_class.one}, nat_T), 0),
blanchet@35220
   385
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   386
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   387
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   388
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   389
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   390
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   391
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   392
val built_in_set_consts =
blanchet@35220
   393
  [(@{const_name semilattice_inf_class.inf}, 2),
blanchet@35220
   394
   (@{const_name semilattice_sup_class.sup}, 2),
blanchet@35220
   395
   (@{const_name minus_class.minus}, 2),
blanchet@35220
   396
   (@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   397
blanchet@33192
   398
(* typ -> typ *)
blanchet@35190
   399
fun unarize_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   400
  | unarize_type @{typ "signed_bit word"} = int_T
blanchet@35190
   401
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
blanchet@35190
   402
  | unarize_type T = T
blanchet@35190
   403
fun unarize_and_unbox_type (Type (@{type_name fun_box}, Ts)) =
blanchet@35190
   404
    unarize_and_unbox_type (Type ("fun", Ts))
blanchet@35190
   405
  | unarize_and_unbox_type (Type (@{type_name pair_box}, Ts)) =
blanchet@35190
   406
    Type ("*", map unarize_and_unbox_type Ts)
blanchet@35190
   407
  | unarize_and_unbox_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   408
  | unarize_and_unbox_type @{typ "signed_bit word"} = int_T
blanchet@35190
   409
  | unarize_and_unbox_type (Type (s, Ts as _ :: _)) =
blanchet@35190
   410
    Type (s, map unarize_and_unbox_type Ts)
blanchet@35190
   411
  | unarize_and_unbox_type T = T
blanchet@35280
   412
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   413
  | uniterize_type @{typ bisim_iterator} = nat_T
blanchet@35280
   414
  | uniterize_type T = T
blanchet@35280
   415
val unarize_unbox_and_uniterize_type = uniterize_type o unarize_and_unbox_type
blanchet@35280
   416
blanchet@33192
   417
(* Proof.context -> typ -> string *)
blanchet@35190
   418
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_and_unbox_type
blanchet@33192
   419
blanchet@33192
   420
(* string -> string -> string *)
blanchet@33192
   421
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@33192
   422
(* string -> string *)
blanchet@34121
   423
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   424
(* string -> term -> term *)
blanchet@33192
   425
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@33192
   426
(* string -> string *)
blanchet@34121
   427
fun short_name s =
blanchet@33192
   428
  case space_explode name_sep s of
blanchet@33192
   429
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   430
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   431
(* typ -> typ *)
blanchet@34121
   432
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   433
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   434
  | shorten_names_in_type T = T
blanchet@33192
   435
(* term -> term *)
blanchet@34121
   436
val shorten_names_in_term =
blanchet@34121
   437
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   438
  #> map_types shorten_names_in_type
blanchet@33192
   439
blanchet@33192
   440
(* theory -> typ * typ -> bool *)
blanchet@33192
   441
fun type_match thy (T1, T2) =
blanchet@33192
   442
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   443
  handle Type.TYPE_MATCH => false
blanchet@33192
   444
(* theory -> styp * styp -> bool *)
blanchet@33192
   445
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   446
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   447
(* theory -> term * term -> bool *)
blanchet@33192
   448
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   449
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   450
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   451
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   452
blanchet@33192
   453
(* typ -> bool *)
blanchet@33192
   454
fun is_TFree (TFree _) = true
blanchet@33192
   455
  | is_TFree _ = false
blanchet@33192
   456
fun is_higher_order_type (Type ("fun", _)) = true
blanchet@33192
   457
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   458
  | is_higher_order_type _ = false
blanchet@33192
   459
fun is_fun_type (Type ("fun", _)) = true
blanchet@33192
   460
  | is_fun_type _ = false
blanchet@33192
   461
fun is_set_type (Type ("fun", [_, @{typ bool}])) = true
blanchet@33192
   462
  | is_set_type _ = false
blanchet@33192
   463
fun is_pair_type (Type ("*", _)) = true
blanchet@33192
   464
  | is_pair_type _ = false
blanchet@33192
   465
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   466
  | is_lfp_iterator_type _ = false
blanchet@33192
   467
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   468
  | is_gfp_iterator_type _ = false
blanchet@33192
   469
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   470
fun is_iterator_type T =
blanchet@35280
   471
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   472
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   473
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   474
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   475
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   476
  | is_word_type _ = false
blanchet@35280
   477
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   478
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   479
(* theory -> typ -> bool *)
blanchet@33192
   480
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   481
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   482
  | is_frac_type _ _ = false
blanchet@35220
   483
fun is_number_type thy = is_integer_like_type orf is_frac_type thy
blanchet@33192
   484
blanchet@33192
   485
(* bool -> styp -> typ *)
blanchet@33192
   486
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   487
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   488
        binder_types T)
blanchet@33192
   489
(* typ -> styp *)
blanchet@33192
   490
fun const_for_iterator_type (Type (s, Ts)) = (after_name_sep s, Ts ---> bool_T)
blanchet@33192
   491
  | const_for_iterator_type T =
blanchet@33232
   492
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   493
blanchet@35070
   494
(* int -> typ -> typ list * typ *)
blanchet@33192
   495
fun strip_n_binders 0 T = ([], T)
blanchet@33192
   496
  | strip_n_binders n (Type ("fun", [T1, T2])) =
blanchet@33192
   497
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   498
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@33192
   499
    strip_n_binders n (Type ("fun", Ts))
blanchet@33232
   500
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   501
(* typ -> typ *)
blanchet@33192
   502
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   503
blanchet@33192
   504
(* typ -> int *)
blanchet@33192
   505
fun num_factors_in_type (Type ("*", [T1, T2])) =
blanchet@33192
   506
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   507
  | num_factors_in_type _ = 1
blanchet@33192
   508
fun num_binder_types (Type ("fun", [_, T2])) = 1 + num_binder_types T2
blanchet@33192
   509
  | num_binder_types _ = 0
blanchet@33192
   510
(* typ -> typ list *)
blanchet@33192
   511
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   512
fun maybe_curried_binder_types T =
blanchet@33192
   513
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   514
blanchet@33192
   515
(* typ -> term list -> term *)
blanchet@33192
   516
fun mk_flat_tuple _ [t] = t
blanchet@33192
   517
  | mk_flat_tuple (Type ("*", [T1, T2])) (t :: ts) =
blanchet@33192
   518
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   519
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   520
(* int -> term -> term list *)
blanchet@33192
   521
fun dest_n_tuple 1 t = [t]
blanchet@33192
   522
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   523
blanchet@33192
   524
(* int -> typ -> typ list *)
blanchet@33192
   525
fun dest_n_tuple_type 1 T = [T]
blanchet@33192
   526
  | dest_n_tuple_type n (Type (_, [T1, T2])) =
blanchet@33192
   527
    T1 :: dest_n_tuple_type (n - 1) T2
blanchet@33232
   528
  | dest_n_tuple_type _ T =
blanchet@33232
   529
    raise TYPE ("Nitpick_HOL.dest_n_tuple_type", [T], [])
blanchet@33192
   530
blanchet@35220
   531
type typedef_info =
blanchet@35220
   532
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   533
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   534
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   535
blanchet@35220
   536
(* theory -> string -> typedef_info *)
blanchet@35220
   537
fun typedef_info thy s =
blanchet@35220
   538
  if is_frac_type thy (Type (s, [])) then
blanchet@35220
   539
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@35220
   540
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@35220
   541
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@35220
   542
                          |> Logic.varify,
blanchet@35220
   543
          set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@35220
   544
  else case Typedef.get_info thy s of
blanchet@35220
   545
    SOME {abs_type, rep_type, Abs_name, Rep_name, set_def, Rep, Abs_inverse,
blanchet@35220
   546
          Rep_inverse, ...} =>
blanchet@35220
   547
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@35220
   548
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@35220
   549
          set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@35220
   550
          Rep_inverse = SOME Rep_inverse}
blanchet@35220
   551
  | NONE => NONE
blanchet@35220
   552
blanchet@35220
   553
(* theory -> string -> bool *)
blanchet@35220
   554
val is_typedef = is_some oo typedef_info
blanchet@35220
   555
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   556
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   557
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   558
blanchet@34121
   559
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   560
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   561
(* theory -> (typ option * bool) list -> string -> bool *)
blanchet@35220
   562
fun is_basic_datatype thy stds s =
blanchet@35220
   563
  member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@35220
   564
                 @{type_name int}, "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   565
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   566
blanchet@33192
   567
(* theory -> typ -> typ -> typ -> typ *)
blanchet@33192
   568
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   569
  Same.commit (Envir.subst_type_same
blanchet@35311
   570
                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
blanchet@33192
   571
  handle Type.TYPE_MATCH =>
blanchet@33232
   572
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@35311
   573
fun varify_and_instantiate_type thy T1 T1' T2 =
blanchet@35311
   574
  instantiate_type thy (Logic.varifyT T1) T1' (Logic.varifyT T2)
blanchet@33192
   575
blanchet@33192
   576
(* theory -> typ -> typ -> styp *)
blanchet@33192
   577
fun repair_constr_type thy body_T' T =
blanchet@35311
   578
  varify_and_instantiate_type thy (body_type T) body_T' T
blanchet@33192
   579
blanchet@33192
   580
(* string -> (string * string) list -> theory -> theory *)
blanchet@33192
   581
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   582
  let
blanchet@33583
   583
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   584
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   585
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   586
(* string -> theory -> theory *)
blanchet@33192
   587
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   588
blanchet@33192
   589
(* typ -> string -> styp list -> theory -> theory *)
blanchet@33192
   590
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   591
  let
blanchet@33583
   592
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   593
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   594
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   595
    val _ =
blanchet@34936
   596
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35220
   597
         co_s <> "fun" andalso
blanchet@35220
   598
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   599
        ()
blanchet@34121
   600
      else
blanchet@34121
   601
        raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   602
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   603
                                   codatatypes
blanchet@33583
   604
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   605
(* typ -> theory -> theory *)
blanchet@33192
   606
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   607
blanchet@33192
   608
(* theory -> typ -> bool *)
blanchet@35284
   609
fun is_quot_type thy (Type (s, _)) =
blanchet@35284
   610
    is_some (Quotient_Info.quotdata_lookup_raw thy s)
blanchet@34936
   611
  | is_quot_type _ _ = false
blanchet@35280
   612
fun is_codatatype thy (Type (s, _)) =
blanchet@33583
   613
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   614
               |> Option.map snd |> these))
blanchet@33192
   615
  | is_codatatype _ _ = false
blanchet@33192
   616
fun is_pure_typedef thy (T as Type (s, _)) =
blanchet@33192
   617
    is_typedef thy s andalso
blanchet@34936
   618
    not (is_real_datatype thy s orelse is_quot_type thy T orelse
blanchet@35220
   619
         is_codatatype thy T orelse is_record_type T orelse
blanchet@35220
   620
         is_integer_like_type T)
blanchet@33192
   621
  | is_pure_typedef _ _ = false
blanchet@33192
   622
fun is_univ_typedef thy (Type (s, _)) =
blanchet@33192
   623
    (case typedef_info thy s of
blanchet@33192
   624
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@35332
   625
       let
blanchet@35332
   626
         val t_opt =
blanchet@35332
   627
           case set_def of
blanchet@35332
   628
             SOME thm => try (snd o Logic.dest_equals o prop_of) thm
blanchet@35332
   629
           | NONE => try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop)
blanchet@35332
   630
                         prop_of_Rep
blanchet@35332
   631
       in
blanchet@35332
   632
         case t_opt of
blanchet@35332
   633
           SOME (Const (@{const_name top}, _)) => true
blanchet@35332
   634
         | SOME (Const (@{const_name Collect}, _)
blanchet@35332
   635
                 $ Abs (_, _, Const (@{const_name finite}, _) $ _)) => true
blanchet@35332
   636
         | _ => false
blanchet@35332
   637
       end
blanchet@33192
   638
     | NONE => false)
blanchet@33192
   639
  | is_univ_typedef _ _ = false
blanchet@35220
   640
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   641
fun is_datatype thy stds (T as Type (s, _)) =
blanchet@34936
   642
    (is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind} orelse
blanchet@35220
   643
     is_quot_type thy T) andalso not (is_basic_datatype thy stds s)
blanchet@35220
   644
  | is_datatype _ _ _ = false
blanchet@33192
   645
blanchet@33192
   646
(* theory -> typ -> (string * typ) list * (string * typ) *)
blanchet@33192
   647
fun all_record_fields thy T =
blanchet@33192
   648
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   649
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   650
  end
blanchet@33192
   651
  handle TYPE _ => []
blanchet@33192
   652
(* styp -> bool *)
blanchet@35280
   653
fun is_record_constr (s, T) =
blanchet@33192
   654
  String.isSuffix Record.extN s andalso
blanchet@33192
   655
  let val dataT = body_type T in
blanchet@33192
   656
    is_record_type dataT andalso
blanchet@33192
   657
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   658
  end
blanchet@33192
   659
(* theory -> typ -> int *)
blanchet@33192
   660
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   661
(* theory -> string -> typ -> int *)
blanchet@33192
   662
fun no_of_record_field thy s T1 =
blanchet@34121
   663
  find_index (curry (op =) s o fst)
blanchet@34121
   664
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@33192
   665
(* theory -> styp -> bool *)
blanchet@33192
   666
fun is_record_get thy (s, Type ("fun", [T1, _])) =
blanchet@34121
   667
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   668
  | is_record_get _ _ = false
blanchet@33192
   669
fun is_record_update thy (s, T) =
blanchet@33192
   670
  String.isSuffix Record.updateN s andalso
blanchet@34121
   671
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   672
         (all_record_fields thy (body_type T))
blanchet@33192
   673
  handle TYPE _ => false
blanchet@33192
   674
fun is_abs_fun thy (s, Type ("fun", [_, Type (s', _)])) =
blanchet@33192
   675
    (case typedef_info thy s' of
blanchet@33192
   676
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   677
     | NONE => false)
blanchet@33192
   678
  | is_abs_fun _ _ = false
blanchet@33192
   679
fun is_rep_fun thy (s, Type ("fun", [Type (s', _), _])) =
blanchet@33192
   680
    (case typedef_info thy s' of
blanchet@33192
   681
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   682
     | NONE => false)
blanchet@33192
   683
  | is_rep_fun _ _ = false
blanchet@34936
   684
(* Proof.context -> styp -> bool *)
blanchet@35284
   685
fun is_quot_abs_fun ctxt (x as (_, Type ("fun", [_, Type (s', _)]))) =
blanchet@35284
   686
    (try (Quotient_Term.absrep_const_chk Quotient_Term.AbsF ctxt) s'
blanchet@35284
   687
     = SOME (Const x))
blanchet@34936
   688
  | is_quot_abs_fun _ _ = false
blanchet@35284
   689
fun is_quot_rep_fun ctxt (x as (_, Type ("fun", [Type (s', _), _]))) =
blanchet@35284
   690
    (try (Quotient_Term.absrep_const_chk Quotient_Term.RepF ctxt) s'
blanchet@35284
   691
     = SOME (Const x))
blanchet@34936
   692
  | is_quot_rep_fun _ _ = false
blanchet@33192
   693
blanchet@33192
   694
(* theory -> styp -> styp *)
blanchet@33192
   695
fun mate_of_rep_fun thy (x as (_, Type ("fun", [T1 as Type (s', _), T2]))) =
blanchet@33192
   696
    (case typedef_info thy s' of
blanchet@33192
   697
       SOME {Abs_name, ...} => (Abs_name, Type ("fun", [T2, T1]))
blanchet@33232
   698
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   699
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@34936
   700
(* theory -> typ -> typ *)
blanchet@35284
   701
fun rep_type_for_quot_type thy (T as Type (s, _)) =
blanchet@35284
   702
  let val {qtyp, rtyp, ...} = Quotient_Info.quotdata_lookup thy s in
blanchet@35284
   703
    instantiate_type thy qtyp T rtyp
blanchet@35284
   704
  end
blanchet@34936
   705
(* theory -> typ -> term *)
blanchet@35284
   706
fun equiv_relation_for_quot_type thy (Type (s, Ts)) =
blanchet@35284
   707
    let
blanchet@35284
   708
      val {qtyp, equiv_rel, ...} = Quotient_Info.quotdata_lookup thy s
blanchet@35284
   709
      val Ts' = qtyp |> dest_Type |> snd
blanchet@35284
   710
    in subst_atomic_types (Ts' ~~ Ts) equiv_rel end
blanchet@34936
   711
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   712
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   713
blanchet@33192
   714
(* theory -> styp -> bool *)
blanchet@33192
   715
fun is_coconstr thy (s, T) =
blanchet@33192
   716
  let
blanchet@33583
   717
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   718
    val co_T = body_type T
blanchet@33192
   719
    val co_s = dest_Type co_T |> fst
blanchet@33192
   720
  in
blanchet@33192
   721
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   722
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   723
  end
blanchet@33192
   724
  handle TYPE ("dest_Type", _, _) => false
blanchet@33192
   725
fun is_constr_like thy (s, T) =
blanchet@34982
   726
  member (op =) [@{const_name FunBox}, @{const_name PairBox},
blanchet@34982
   727
                 @{const_name Quot}, @{const_name Zero_Rep},
blanchet@34982
   728
                 @{const_name Suc_Rep}] s orelse
blanchet@35280
   729
  let val (x as (_, T)) = (s, unarize_and_unbox_type T) in
blanchet@34936
   730
    Refute.is_IDT_constructor thy x orelse is_record_constr x orelse
blanchet@34936
   731
    (is_abs_fun thy x andalso is_pure_typedef thy (range_type T)) orelse
blanchet@34936
   732
    is_coconstr thy x
blanchet@33192
   733
  end
blanchet@33581
   734
fun is_stale_constr thy (x as (_, T)) =
blanchet@34936
   735
  is_codatatype thy (body_type T) andalso is_constr_like thy x andalso
blanchet@34936
   736
  not (is_coconstr thy x)
blanchet@35220
   737
(* theory -> (typ option * bool) list -> styp -> bool *)
blanchet@35220
   738
fun is_constr thy stds (x as (_, T)) =
blanchet@34936
   739
  is_constr_like thy x andalso
blanchet@35220
   740
  not (is_basic_datatype thy stds
blanchet@35220
   741
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@34936
   742
  not (is_stale_constr thy x)
blanchet@33192
   743
(* string -> bool *)
blanchet@33192
   744
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   745
val is_sel_like_and_no_discr =
blanchet@33192
   746
  String.isPrefix sel_prefix
blanchet@33192
   747
  orf (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   748
blanchet@33192
   749
(* boxability -> boxability *)
blanchet@33192
   750
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   751
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   752
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   753
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   754
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   755
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   756
blanchet@35070
   757
(* hol_context -> boxability -> typ -> bool *)
blanchet@35070
   758
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   759
  case T of
blanchet@33192
   760
    Type ("fun", _) =>
blanchet@34936
   761
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   762
    not (is_boolean_type (body_type T))
blanchet@33192
   763
  | Type ("*", Ts) =>
blanchet@34936
   764
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   765
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   766
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   767
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   768
  | _ => false
blanchet@35070
   769
(* hol_context -> boxability -> string * typ list -> string *)
blanchet@35280
   770
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   771
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   772
    SOME (SOME box_me) => box_me
blanchet@35070
   773
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   774
(* hol_context -> boxability -> typ -> typ *)
blanchet@35070
   775
and box_type hol_ctxt boxy T =
blanchet@33192
   776
  case T of
blanchet@33192
   777
    Type (z as ("fun", [T1, T2])) =>
blanchet@34936
   778
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   779
       should_box_type hol_ctxt boxy z then
blanchet@33192
   780
      Type (@{type_name fun_box},
blanchet@35070
   781
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   782
    else
blanchet@35070
   783
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   784
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@33192
   785
  | Type (z as ("*", Ts)) =>
blanchet@34982
   786
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   787
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   788
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   789
    else
blanchet@35070
   790
      Type ("*", map (box_type hol_ctxt
blanchet@34121
   791
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   792
                           else InPair)) Ts)
blanchet@33192
   793
  | _ => T
blanchet@33192
   794
blanchet@35190
   795
(* typ -> typ *)
blanchet@35190
   796
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   797
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   798
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   799
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   800
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   801
(* term -> term *)
blanchet@35190
   802
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   803
blanchet@33192
   804
(* styp -> styp *)
blanchet@33192
   805
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   806
blanchet@33192
   807
(* typ -> int *)
blanchet@33192
   808
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   809
(* string -> int -> string *)
blanchet@33192
   810
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   811
  if s = @{const_name Pair} then
blanchet@33192
   812
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   813
  else
blanchet@33192
   814
    sel_prefix_for n ^ s
blanchet@33192
   815
(* styp -> int -> styp *)
blanchet@33192
   816
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   817
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   818
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   819
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   820
(* hol_context -> bool -> styp -> int -> styp *)
blanchet@35190
   821
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   822
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   823
  oo nth_sel_for_constr
blanchet@33192
   824
blanchet@33192
   825
(* string -> int *)
blanchet@33192
   826
fun sel_no_from_name s =
blanchet@33192
   827
  if String.isPrefix discr_prefix s then
blanchet@33192
   828
    ~1
blanchet@33192
   829
  else if String.isPrefix sel_prefix s then
blanchet@33192
   830
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   831
  else if s = @{const_name snd} then
blanchet@33192
   832
    1
blanchet@33192
   833
  else
blanchet@33192
   834
    0
blanchet@33192
   835
blanchet@35078
   836
(* term -> term *)
blanchet@35078
   837
val close_form =
blanchet@35078
   838
  let
blanchet@35078
   839
    (* (indexname * typ) list -> (indexname * typ) list -> term -> term *)
blanchet@35078
   840
    fun close_up zs zs' =
blanchet@35078
   841
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   842
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   843
           (take (length zs' - length zs) zs')
blanchet@35078
   844
    (* (indexname * typ) list -> term -> term *)
blanchet@35078
   845
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   846
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   847
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   848
        end
blanchet@35078
   849
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   850
  in aux [] end
blanchet@35078
   851
blanchet@33192
   852
(* typ list -> term -> int -> term *)
blanchet@33192
   853
fun eta_expand _ t 0 = t
blanchet@33192
   854
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   855
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   856
  | eta_expand Ts t n =
blanchet@33192
   857
    fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
blanchet@33192
   858
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   859
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   860
blanchet@33192
   861
(* term -> term *)
blanchet@33192
   862
fun extensionalize t =
blanchet@33192
   863
  case t of
blanchet@33192
   864
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   865
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   866
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   867
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   868
    end
blanchet@33192
   869
  | _ => t
blanchet@33192
   870
blanchet@33192
   871
(* typ -> term list -> term *)
blanchet@33192
   872
fun distinctness_formula T =
blanchet@33192
   873
  all_distinct_unordered_pairs_of
blanchet@33192
   874
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   875
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   876
blanchet@33192
   877
(* typ -> term *)
blanchet@35220
   878
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   879
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   880
blanchet@35220
   881
(* hol_context -> typ -> styp list *)
blanchet@35220
   882
fun uncached_datatype_constrs ({thy, stds, ...} : hol_context)
blanchet@35220
   883
                              (T as Type (s, Ts)) =
blanchet@33583
   884
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@34982
   885
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   886
     | _ =>
blanchet@35220
   887
       if is_datatype thy stds T then
blanchet@33581
   888
         case Datatype.get_info thy s of
blanchet@33581
   889
           SOME {index, descr, ...} =>
blanchet@33581
   890
           let
blanchet@33581
   891
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   892
           in
blanchet@33581
   893
             map (fn (s', Us) =>
blanchet@33581
   894
                     (s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us
blanchet@33581
   895
                          ---> T)) constrs
blanchet@33581
   896
           end
blanchet@33581
   897
         | NONE =>
blanchet@33581
   898
           if is_record_type T then
blanchet@33581
   899
             let
blanchet@33581
   900
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   901
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   902
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   903
             in [(s', T')] end
blanchet@34936
   904
           else if is_quot_type thy T then
blanchet@34936
   905
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@33581
   906
           else case typedef_info thy s of
blanchet@33581
   907
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@35311
   908
             [(Abs_name,
blanchet@35311
   909
               varify_and_instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   910
           | NONE =>
blanchet@33581
   911
             if T = @{typ ind} then
blanchet@33581
   912
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   913
             else
blanchet@33581
   914
               []
blanchet@33581
   915
       else
blanchet@33581
   916
         [])
blanchet@33580
   917
  | uncached_datatype_constrs _ _ = []
blanchet@35070
   918
(* hol_context -> typ -> styp list *)
blanchet@35220
   919
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   920
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   921
    SOME xs => xs
blanchet@33580
   922
  | NONE =>
blanchet@35220
   923
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   924
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   925
    end
blanchet@35190
   926
(* hol_context -> bool -> typ -> styp list *)
blanchet@35190
   927
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   928
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   929
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@35070
   930
(* hol_context -> typ -> int *)
blanchet@33192
   931
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   932
blanchet@33192
   933
(* string -> string *)
blanchet@33192
   934
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   935
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   936
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   937
(* hol_context -> bool -> styp -> styp *)
blanchet@35190
   938
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   939
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   940
    AList.lookup (op =)
blanchet@35190
   941
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   942
        s
blanchet@33192
   943
    |> the |> pair s
blanchet@33192
   944
  end
blanchet@34982
   945
blanchet@35070
   946
(* hol_context -> styp -> term *)
blanchet@35070
   947
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   948
  let val dataT = body_type T in
blanchet@33192
   949
    if s = @{const_name Suc} then
blanchet@33192
   950
      Abs (Name.uu, dataT,
blanchet@33192
   951
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
   952
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
   953
      Const (discr_for_constr x)
blanchet@33192
   954
    else
blanchet@33192
   955
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   956
  end
blanchet@35070
   957
(* hol_context -> styp -> term -> term *)
blanchet@35280
   958
fun discriminate_value (hol_ctxt as {thy, ...}) x t =
blanchet@35280
   959
  case head_of t of
blanchet@35280
   960
    Const x' =>
blanchet@33192
   961
    if x = x' then @{const True}
blanchet@33192
   962
    else if is_constr_like thy x' then @{const False}
blanchet@35070
   963
    else betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@35070
   964
  | _ => betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
   965
blanchet@35220
   966
(* theory -> (typ option * bool) list -> styp -> term -> term *)
blanchet@35220
   967
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
   968
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
   969
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
   970
      @{term "%n::nat. n - 1"}
blanchet@33192
   971
    else if is_pair_type dataT then
blanchet@33192
   972
      Const (nth_sel_for_constr x n)
blanchet@33192
   973
    else
blanchet@33192
   974
      let
blanchet@33192
   975
        (* int -> typ -> int * term *)
blanchet@33192
   976
        fun aux m (Type ("*", [T1, T2])) =
blanchet@33192
   977
            let
blanchet@33192
   978
              val (m, t1) = aux m T1
blanchet@33192
   979
              val (m, t2) = aux m T2
blanchet@33192
   980
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   981
          | aux m T =
blanchet@33192
   982
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
   983
                    $ Bound 0)
blanchet@33192
   984
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
   985
                     (List.take (arg_Ts, n)) 0
blanchet@33192
   986
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
   987
  end
blanchet@35220
   988
(* theory -> (typ option * bool) list -> styp -> term -> int -> typ -> term *)
blanchet@35220
   989
fun select_nth_constr_arg thy stds x t n res_T =
blanchet@35220
   990
  (case strip_comb t of
blanchet@35220
   991
     (Const x', args) =>
blanchet@35220
   992
     if x = x' then nth args n
blanchet@35220
   993
     else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
blanchet@35220
   994
     else raise SAME ()
blanchet@35220
   995
   | _ => raise SAME())
blanchet@35220
   996
  handle SAME () => betapply (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@33192
   997
blanchet@35220
   998
(* theory -> (typ option * bool) list -> styp -> term list -> term *)
blanchet@35220
   999
fun construct_value _ _ x [] = Const x
blanchet@35220
  1000
  | construct_value thy stds (x as (s, _)) args =
blanchet@33192
  1001
    let val args = map Envir.eta_contract args in
blanchet@33192
  1002
      case hd args of
blanchet@35280
  1003
        Const (s', _) $ t =>
blanchet@34936
  1004
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
  1005
           constr_name_for_sel_like s' = s andalso
blanchet@35220
  1006
           forall (fn (n, t') =>
blanchet@35220
  1007
                      select_nth_constr_arg thy stds x t n dummyT = t')
blanchet@34936
  1008
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  1009
          t
blanchet@33192
  1010
        else
blanchet@33192
  1011
          list_comb (Const x, args)
blanchet@33192
  1012
      | _ => list_comb (Const x, args)
blanchet@33192
  1013
    end
blanchet@33192
  1014
blanchet@33192
  1015
(* (typ * int) list -> typ -> int *)
blanchet@34123
  1016
fun card_of_type assigns (Type ("fun", [T1, T2])) =
blanchet@34123
  1017
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@34123
  1018
  | card_of_type assigns (Type ("*", [T1, T2])) =
blanchet@34123
  1019
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1020
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1021
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1022
  | card_of_type _ @{typ bool} = 2
blanchet@33192
  1023
  | card_of_type _ @{typ unit} = 1
blanchet@34123
  1024
  | card_of_type assigns T =
blanchet@34123
  1025
    case AList.lookup (op =) assigns T of
blanchet@33192
  1026
      SOME k => k
blanchet@33192
  1027
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1028
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@33192
  1029
(* int -> (typ * int) list -> typ -> int *)
blanchet@34123
  1030
fun bounded_card_of_type max default_card assigns (Type ("fun", [T1, T2])) =
blanchet@33192
  1031
    let
blanchet@34123
  1032
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1033
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1034
    in
blanchet@33192
  1035
      if k1 = max orelse k2 = max then max
blanchet@33192
  1036
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1037
    end
blanchet@34123
  1038
  | bounded_card_of_type max default_card assigns (Type ("*", [T1, T2])) =
blanchet@33192
  1039
    let
blanchet@34123
  1040
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1041
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1042
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1043
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1044
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1045
                    card_of_type assigns T
blanchet@33192
  1046
                  else
blanchet@34123
  1047
                    card_of_type assigns T
blanchet@33232
  1048
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1049
                           default_card)
blanchet@35070
  1050
(* hol_context -> int -> (typ * int) list -> typ -> int *)
blanchet@35070
  1051
fun bounded_exact_card_of_type hol_ctxt max default_card assigns T =
blanchet@33192
  1052
  let
blanchet@33192
  1053
    (* typ list -> typ -> int *)
blanchet@33192
  1054
    fun aux avoid T =
blanchet@34121
  1055
      (if member (op =) avoid T then
blanchet@33192
  1056
         0
blanchet@33192
  1057
       else case T of
blanchet@33192
  1058
         Type ("fun", [T1, T2]) =>
blanchet@33192
  1059
         let
blanchet@33192
  1060
           val k1 = aux avoid T1
blanchet@33192
  1061
           val k2 = aux avoid T2
blanchet@33192
  1062
         in
blanchet@33192
  1063
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1064
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1065
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1066
         end
blanchet@33192
  1067
       | Type ("*", [T1, T2]) =>
blanchet@33192
  1068
         let
blanchet@33192
  1069
           val k1 = aux avoid T1
blanchet@33192
  1070
           val k2 = aux avoid T2
blanchet@33192
  1071
         in
blanchet@33192
  1072
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1073
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1074
           else Int.min (max, k1 * k2)
blanchet@33192
  1075
         end
blanchet@33192
  1076
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1077
       | @{typ prop} => 2
blanchet@33192
  1078
       | @{typ bool} => 2
blanchet@33192
  1079
       | @{typ unit} => 1
blanchet@33192
  1080
       | Type _ =>
blanchet@35070
  1081
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1082
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1083
                  else raise SAME ()
blanchet@33192
  1084
          | constrs =>
blanchet@33192
  1085
            let
blanchet@33192
  1086
              val constr_cards =
blanchet@35280
  1087
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1088
                    constrs
blanchet@33192
  1089
            in
blanchet@34121
  1090
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1091
              else Integer.sum constr_cards
blanchet@33192
  1092
            end)
blanchet@33192
  1093
       | _ => raise SAME ())
blanchet@34123
  1094
      handle SAME () =>
blanchet@34123
  1095
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1096
  in Int.min (max, aux [] T) end
blanchet@33192
  1097
blanchet@35070
  1098
(* hol_context -> typ -> bool *)
blanchet@35070
  1099
fun is_finite_type hol_ctxt =
blanchet@35070
  1100
  not_equal 0 o bounded_exact_card_of_type hol_ctxt 1 2 []
blanchet@33192
  1101
blanchet@33192
  1102
(* term -> bool *)
blanchet@33192
  1103
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1104
  | is_ground_term (Const _) = true
blanchet@33192
  1105
  | is_ground_term _ = false
blanchet@33192
  1106
blanchet@33192
  1107
(* term -> word -> word *)
blanchet@33192
  1108
fun hashw_term (t1 $ t2) = Polyhash.hashw (hashw_term t1, hashw_term t2)
blanchet@33192
  1109
  | hashw_term (Const (s, _)) = Polyhash.hashw_string (s, 0w0)
blanchet@33192
  1110
  | hashw_term _ = 0w0
blanchet@33192
  1111
(* term -> int *)
blanchet@33192
  1112
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1113
blanchet@33192
  1114
(* term list -> (indexname * typ) list *)
blanchet@33192
  1115
fun special_bounds ts =
blanchet@33192
  1116
  fold Term.add_vars ts [] |> sort (TermOrd.fast_indexname_ord o pairself fst)
blanchet@33192
  1117
blanchet@33192
  1118
(* indexname * typ -> term -> term *)
blanchet@33192
  1119
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
  1120
blanchet@33571
  1121
(* theory -> string -> bool *)
blanchet@33571
  1122
fun is_funky_typedef_name thy s =
blanchet@34121
  1123
  member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@34936
  1124
                 @{type_name int}] s orelse
blanchet@34936
  1125
  is_frac_type thy (Type (s, []))
blanchet@35070
  1126
(* theory -> typ -> bool *)
blanchet@33571
  1127
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
  1128
  | is_funky_typedef _ _ = false
blanchet@33192
  1129
(* term -> bool *)
blanchet@33192
  1130
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1131
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1132
  | is_arity_type_axiom _ = false
blanchet@33192
  1133
(* theory -> bool -> term -> bool *)
blanchet@33197
  1134
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
blanchet@33197
  1135
    is_typedef_axiom thy boring t2
blanchet@33197
  1136
  | is_typedef_axiom thy boring
blanchet@33192
  1137
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@33197
  1138
         $ Const (_, Type ("fun", [Type (s, _), _])) $ Const _ $ _)) =
blanchet@33571
  1139
    boring <> is_funky_typedef_name thy s andalso is_typedef thy s
blanchet@33192
  1140
  | is_typedef_axiom _ _ _ = false
blanchet@33192
  1141
blanchet@33192
  1142
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1143
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1144
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1145
   using "typedef_info". *)
blanchet@33192
  1146
(* theory -> (string * term) list -> string list -> term list * term list *)
blanchet@33192
  1147
fun partition_axioms_by_definitionality thy axioms def_names =
blanchet@33192
  1148
  let
blanchet@33192
  1149
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1150
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1151
    val nondefs =
blanchet@33192
  1152
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1153
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
blanchet@33192
  1154
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1155
blanchet@33197
  1156
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1157
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1158
   commands. *)
blanchet@33192
  1159
(* theory -> bool *)
blanchet@33192
  1160
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1161
blanchet@33192
  1162
(* term -> bool *)
blanchet@35283
  1163
val is_trivial_definition =
blanchet@35283
  1164
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1165
val is_plain_definition =
blanchet@33192
  1166
  let
blanchet@33192
  1167
    (* term -> bool *)
blanchet@33192
  1168
    fun do_lhs t1 =
blanchet@33192
  1169
      case strip_comb t1 of
blanchet@34936
  1170
        (Const _, args) =>
blanchet@34936
  1171
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1172
      | _ => false
blanchet@33192
  1173
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1174
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1175
        do_lhs t1
blanchet@33192
  1176
      | do_eq _ = false
blanchet@33192
  1177
  in do_eq end
blanchet@33192
  1178
blanchet@35335
  1179
(* theory -> (term * term) list -> term list * term list * term list *)
blanchet@35335
  1180
fun all_axioms_of thy subst =
blanchet@33192
  1181
  let
blanchet@33192
  1182
    (* theory list -> term list *)
blanchet@35335
  1183
    val axioms_of_thys =
blanchet@35335
  1184
      maps Thm.axioms_of #> map (apsnd (subst_atomic subst o prop_of))
blanchet@33192
  1185
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1186
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1187
                    |> OrdList.make fast_string_ord
blanchet@33192
  1188
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1189
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1190
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1191
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1192
    val (built_in_defs, built_in_nondefs) =
blanchet@33192
  1193
      partition_axioms_by_definitionality thy built_in_axioms def_names
blanchet@33197
  1194
      ||> filter (is_typedef_axiom thy false)
blanchet@33192
  1195
    val (user_defs, user_nondefs) =
blanchet@33192
  1196
      partition_axioms_by_definitionality thy user_axioms def_names
blanchet@33197
  1197
    val (built_in_nondefs, user_nondefs) =
blanchet@33197
  1198
      List.partition (is_typedef_axiom thy false) user_nondefs
blanchet@33197
  1199
      |>> append built_in_nondefs
blanchet@34121
  1200
    val defs =
blanchet@34121
  1201
      (thy |> PureThy.all_thms_of
blanchet@34121
  1202
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1203
           |> map (prop_of o snd)
blanchet@35283
  1204
           |> filter_out is_trivial_definition
blanchet@35283
  1205
           |> filter is_plain_definition) @
blanchet@34121
  1206
      user_defs @ built_in_defs
blanchet@33192
  1207
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1208
blanchet@35220
  1209
(* theory -> (typ option * bool) list -> bool -> styp -> int option *)
blanchet@35220
  1210
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1211
  if s = @{const_name If} then
blanchet@33192
  1212
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1213
  else
blanchet@35220
  1214
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1215
      case AList.lookup (op =)
blanchet@35220
  1216
                    (built_in_consts
blanchet@35220
  1217
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1218
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1219
        SOME n => SOME n
blanchet@35220
  1220
      | NONE =>
blanchet@35220
  1221
        case AList.lookup (op =)
blanchet@35220
  1222
                 (built_in_typed_consts
blanchet@35220
  1223
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1224
                 (s, unarize_type T) of
blanchet@35220
  1225
          SOME n => SOME n
blanchet@35220
  1226
        | NONE =>
blanchet@35280
  1227
          case s of
blanchet@35280
  1228
            @{const_name zero_class.zero} =>
blanchet@35280
  1229
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1230
          | @{const_name Suc} =>
blanchet@35280
  1231
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1232
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1233
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1234
                 else
blanchet@35280
  1235
                   NONE
blanchet@35220
  1236
    end
blanchet@35220
  1237
(* theory -> (typ option * bool) list -> bool -> styp -> bool *)
blanchet@35220
  1238
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1239
blanchet@33192
  1240
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1241
   simplification rules (equational specifications). *)
blanchet@33192
  1242
(* term -> term *)
blanchet@33192
  1243
fun term_under_def t =
blanchet@33192
  1244
  case t of
blanchet@33192
  1245
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1246
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1247
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1248
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1249
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1250
  | t1 $ _ => term_under_def t1
blanchet@33192
  1251
  | _ => t
blanchet@33192
  1252
blanchet@33192
  1253
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
blanchet@33192
  1254
   traversal of the term, without which the wrong occurrence of a constant could
blanchet@33192
  1255
   be matched in the face of overloading. *)
blanchet@35220
  1256
(* theory -> (typ option * bool) list -> bool -> const_table -> styp
blanchet@35220
  1257
   -> term list *)
blanchet@35220
  1258
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1259
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1260
    []
blanchet@33192
  1261
  else
blanchet@33192
  1262
    these (Symtab.lookup table s)
blanchet@33192
  1263
    |> map_filter (try (Refute.specialize_type thy x))
blanchet@34121
  1264
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1265
blanchet@35280
  1266
(* term -> term option *)
blanchet@35280
  1267
fun normalized_rhs_of t =
blanchet@33192
  1268
  let
blanchet@33743
  1269
    (* term option -> term option *)
blanchet@33743
  1270
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1271
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1272
      | aux _ _ = NONE
blanchet@33192
  1273
    val (lhs, rhs) =
blanchet@33192
  1274
      case t of
blanchet@33192
  1275
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1276
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1277
        (t1, t2)
blanchet@33232
  1278
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1279
    val args = strip_comb lhs |> snd
blanchet@33743
  1280
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1281
blanchet@33192
  1282
(* theory -> const_table -> styp -> term option *)
blanchet@33192
  1283
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1284
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1285
     original_name s <> s then
blanchet@33192
  1286
    NONE
blanchet@33192
  1287
  else
blanchet@35220
  1288
    x |> def_props_for_const thy [(NONE, false)] false table |> List.last
blanchet@35280
  1289
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1290
    handle List.Empty => NONE
blanchet@33192
  1291
blanchet@33192
  1292
(* term -> fixpoint_kind *)
blanchet@33192
  1293
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1294
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1295
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1296
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1297
blanchet@33192
  1298
(* theory -> const_table -> term -> bool *)
blanchet@33192
  1299
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1300
  let
blanchet@33192
  1301
    (* term -> bool *)
blanchet@33192
  1302
    fun is_good_arg (Bound _) = true
blanchet@33192
  1303
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1304
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1305
        s = @{const_name undefined}
blanchet@33192
  1306
      | is_good_arg _ = false
blanchet@33192
  1307
  in
blanchet@33192
  1308
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1309
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1310
      (case def_of_const thy table x of
blanchet@33192
  1311
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1312
       | NONE => false)
blanchet@33192
  1313
    | _ => false
blanchet@33192
  1314
  end
blanchet@33192
  1315
(* theory -> const_table -> term -> term *)
blanchet@33192
  1316
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1317
  map_aterms (fn t as Const x =>
blanchet@33192
  1318
                 (case def_of_const thy table x of
blanchet@33192
  1319
                    SOME t' =>
blanchet@33192
  1320
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1321
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1322
                      else t
blanchet@33192
  1323
                    end
blanchet@33192
  1324
                 | NONE => t)
blanchet@33192
  1325
               | t => t)
blanchet@33192
  1326
blanchet@33192
  1327
(* term -> string * term *)
blanchet@33192
  1328
fun pair_for_prop t =
blanchet@33192
  1329
  case term_under_def t of
blanchet@33192
  1330
    Const (s, _) => (s, t)
blanchet@33232
  1331
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@33192
  1332
blanchet@35335
  1333
(* (Proof.context -> term list) -> Proof.context -> (term * term) list
blanchet@35335
  1334
   -> const_table *)
blanchet@35335
  1335
fun table_for get ctxt subst =
blanchet@35335
  1336
  ctxt |> get |> map (pair_for_prop o subst_atomic subst)
blanchet@35335
  1337
       |> AList.group (op =) |> Symtab.make
blanchet@33192
  1338
blanchet@35220
  1339
(* theory -> (typ option * bool) list -> (string * int) list *)
blanchet@35220
  1340
fun case_const_names thy stds =
blanchet@33192
  1341
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@35220
  1342
                  if is_basic_datatype thy stds dtype_s then
blanchet@33192
  1343
                    I
blanchet@33192
  1344
                  else
blanchet@33192
  1345
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1346
                                     |> the |> #3 |> length))
blanchet@33192
  1347
              (Datatype.get_all thy) [] @
blanchet@33583
  1348
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1349
blanchet@35335
  1350
(* Proof.context -> (term * term) list -> term list -> const_table *)
blanchet@35335
  1351
fun const_def_table ctxt subst ts =
blanchet@35335
  1352
  table_for (map prop_of o Nitpick_Defs.get) ctxt subst
blanchet@33192
  1353
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@33192
  1354
          (map pair_for_prop ts)
blanchet@33192
  1355
(* term list -> const_table *)
blanchet@33192
  1356
fun const_nondef_table ts =
blanchet@33192
  1357
  fold (fn t => append (map (fn s => (s, t)) (Term.add_const_names t []))) ts []
blanchet@33192
  1358
  |> AList.group (op =) |> Symtab.make
blanchet@35335
  1359
(* Proof.context -> (term * term) list -> const_table *)
blanchet@33192
  1360
val const_simp_table = table_for (map prop_of o Nitpick_Simps.get)
blanchet@33192
  1361
val const_psimp_table = table_for (map prop_of o Nitpick_Psimps.get)
blanchet@35335
  1362
(* Proof.context -> (term * term) list -> const_table -> const_table *)
blanchet@35335
  1363
fun inductive_intro_table ctxt subst def_table =
blanchet@33192
  1364
  table_for (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
blanchet@33192
  1365
                                                  def_table o prop_of)
blanchet@35335
  1366
             o Nitpick_Intros.get) ctxt subst
blanchet@33192
  1367
(* theory -> term list Inttab.table *)
blanchet@33192
  1368
fun ground_theorem_table thy =
blanchet@33192
  1369
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@33192
  1370
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@33192
  1371
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@33192
  1372
blanchet@33192
  1373
val basic_ersatz_table =
blanchet@33192
  1374
  [(@{const_name prod_case}, @{const_name split}),
blanchet@33192
  1375
   (@{const_name card}, @{const_name card'}),
blanchet@33192
  1376
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@33192
  1377
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@33192
  1378
   (@{const_name wf}, @{const_name wf'}),
blanchet@33192
  1379
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@33192
  1380
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@33192
  1381
blanchet@33192
  1382
(* theory -> (string * string) list *)
blanchet@33192
  1383
fun ersatz_table thy =
blanchet@33583
  1384
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@33192
  1385
blanchet@33192
  1386
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
blanchet@33192
  1387
fun add_simps simp_table s eqs =
blanchet@33192
  1388
  Unsynchronized.change simp_table
blanchet@33192
  1389
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@33192
  1390
blanchet@34936
  1391
(* theory -> styp -> term list *)
blanchet@34936
  1392
fun inverse_axioms_for_rep_fun thy (x as (_, T)) =
blanchet@34936
  1393
  let val abs_T = domain_type T in
blanchet@34936
  1394
    typedef_info thy (fst (dest_Type abs_T)) |> the
blanchet@34936
  1395
    |> pairf #Abs_inverse #Rep_inverse
blanchet@34936
  1396
    |> pairself (Refute.specialize_type thy x o prop_of o the)
blanchet@34936
  1397
    ||> single |> op ::
blanchet@34936
  1398
  end
blanchet@35070
  1399
(* theory -> string * typ list -> term list *)
blanchet@35280
  1400
fun optimized_typedef_axioms thy (abs_z as (abs_s, _)) =
blanchet@34936
  1401
  let val abs_T = Type abs_z in
blanchet@33192
  1402
    if is_univ_typedef thy abs_T then
blanchet@33192
  1403
      []
blanchet@33192
  1404
    else case typedef_info thy abs_s of
blanchet@35280
  1405
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@33192
  1406
      let
blanchet@35311
  1407
        val rep_T = varify_and_instantiate_type thy abs_type abs_T rep_type
blanchet@33192
  1408
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@33192
  1409
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@33192
  1410
        val set_t' =
blanchet@33192
  1411
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@33192
  1412
                      |> Refute.specialize_type thy (dest_Const rep_t)
blanchet@33192
  1413
                      |> HOLogic.dest_mem |> snd
blanchet@33192
  1414
      in
blanchet@33192
  1415
        [HOLogic.all_const abs_T
blanchet@33192
  1416
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@33192
  1417
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@33192
  1418
        |> map HOLogic.mk_Trueprop
blanchet@33192
  1419
      end
blanchet@33192
  1420
    | NONE => []
blanchet@33192
  1421
  end
blanchet@35311
  1422
(* Proof.context -> string * typ list -> term list *)
blanchet@35311
  1423
fun optimized_quot_type_axioms ctxt stds abs_z =
blanchet@34936
  1424
  let
blanchet@35311
  1425
    val thy = ProofContext.theory_of ctxt
blanchet@34936
  1426
    val abs_T = Type abs_z
blanchet@34936
  1427
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@34936
  1428
    val equiv_rel = equiv_relation_for_quot_type thy abs_T
blanchet@34936
  1429
    val a_var = Var (("a", 0), abs_T)
blanchet@34936
  1430
    val x_var = Var (("x", 0), rep_T)
blanchet@34936
  1431
    val y_var = Var (("y", 0), rep_T)
blanchet@34936
  1432
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@35220
  1433
    val sel_a_t = select_nth_constr_arg thy stds x a_var 0 rep_T
blanchet@35311
  1434
    val normal_t = Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T)
blanchet@34936
  1435
    val normal_x = normal_t $ x_var
blanchet@34936
  1436
    val normal_y = normal_t $ y_var
blanchet@34936
  1437
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@34936
  1438
  in
blanchet@34982
  1439
    [Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
blanchet@34936
  1440
     Logic.list_implies
blanchet@34982
  1441
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@34936
  1442
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@34936
  1443
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@34936
  1444
           Logic.mk_equals (normal_x, normal_y)),
blanchet@34936
  1445
     @{const "==>"}
blanchet@34936
  1446
         $ (HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)))
blanchet@34936
  1447
         $ (HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@33864
  1448
  end
blanchet@33192
  1449
blanchet@35220
  1450
(* theory -> (typ option * bool) list -> int * styp -> term *)
blanchet@35220
  1451
fun constr_case_body thy stds (j, (x as (_, T))) =
blanchet@33192
  1452
  let val arg_Ts = binder_types T in
blanchet@35220
  1453
    list_comb (Bound j, map2 (select_nth_constr_arg thy stds x (Bound 0))
blanchet@33192
  1454
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1455
  end
blanchet@35070
  1456
(* hol_context -> typ -> int * styp -> term -> term *)
blanchet@35220
  1457
fun add_constr_case (hol_ctxt as {thy, stds, ...}) res_T (j, x) res_t =
blanchet@34124
  1458
  Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@35220
  1459
  $ discriminate_value hol_ctxt x (Bound 0) $ constr_case_body thy stds (j, x)
blanchet@33580
  1460
  $ res_t
blanchet@35070
  1461
(* hol_context -> typ -> typ -> term *)
blanchet@35220
  1462
fun optimized_case_def (hol_ctxt as {thy, stds, ...}) dataT res_T =
blanchet@33192
  1463
  let
blanchet@35070
  1464
    val xs = datatype_constrs hol_ctxt dataT
blanchet@35179
  1465
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs
blanchet@35179
  1466
    val (xs', x) = split_last xs
blanchet@33192
  1467
  in
blanchet@35220
  1468
    constr_case_body thy stds (1, x)
blanchet@35179
  1469
    |> fold_rev (add_constr_case hol_ctxt res_T) (length xs downto 2 ~~ xs')
blanchet@33192
  1470
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1471
  end
blanchet@33192
  1472
blanchet@35070
  1473
(* hol_context -> string -> typ -> typ -> term -> term *)
blanchet@35220
  1474
fun optimized_record_get (hol_ctxt as {thy, stds, ...}) s rec_T res_T t =
blanchet@35070
  1475
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1476
    case no_of_record_field thy s rec_T of
blanchet@33192
  1477
      ~1 => (case rec_T of
blanchet@33192
  1478
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1479
               let
blanchet@33192
  1480
                 val rec_T' = List.last Ts
blanchet@33192
  1481
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1482
               in
blanchet@35220
  1483
                 select_nth_constr_arg thy stds constr_x t j res_T
blanchet@35070
  1484
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1485
               end
blanchet@33232
  1486
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1487
                                []))
blanchet@35220
  1488
    | j => select_nth_constr_arg thy stds constr_x t j res_T
blanchet@33192
  1489
  end
blanchet@35070
  1490
(* hol_context -> string -> typ -> term -> term -> term *)
blanchet@35220
  1491
fun optimized_record_update (hol_ctxt as {thy, stds, ...}) s rec_T fun_t rec_t =
blanchet@33192
  1492
  let
blanchet@35070
  1493
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1494
    val Ts = binder_types constr_T
blanchet@33192
  1495
    val n = length Ts
blanchet@33192
  1496
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1497
    val ts =
blanchet@35220
  1498
      map2 (fn j => fn T =>
blanchet@35220
  1499
               let val t = select_nth_constr_arg thy stds constr_x rec_t j T in
blanchet@35220
  1500
                 if j = special_j then
blanchet@35220
  1501
                   betapply (fun_t, t)
blanchet@35220
  1502
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1503
                   optimized_record_update hol_ctxt s
blanchet@35220
  1504
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1505
                 else
blanchet@35220
  1506
                   t
blanchet@35220
  1507
               end) (index_seq 0 n) Ts
blanchet@33192
  1508
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1509
blanchet@33192
  1510
(* theory -> const_table -> string * typ -> fixpoint_kind *)
blanchet@33192
  1511
fun fixpoint_kind_of_const thy table x =
blanchet@35220
  1512
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@33192
  1513
    NoFp
blanchet@33192
  1514
  else
blanchet@33192
  1515
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@33192
  1516
    handle Option.Option => NoFp
blanchet@33192
  1517
blanchet@35070
  1518
(* hol_context -> styp -> bool *)
blanchet@35220
  1519
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35220
  1520
                             ...} : hol_context) x =
blanchet@35220
  1521
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35220
  1522
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@35220
  1523
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@35220
  1524
                             ...} : hol_context) x =
blanchet@35220
  1525
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@35220
  1526
                                                     x)))
blanchet@33192
  1527
         [!simp_table, psimp_table]
blanchet@35070
  1528
fun is_inductive_pred hol_ctxt =
blanchet@35070
  1529
  is_real_inductive_pred hol_ctxt andf (not o is_real_equational_fun hol_ctxt)
blanchet@35280
  1530
fun is_equational_fun hol_ctxt =
blanchet@35070
  1531
  (is_real_equational_fun hol_ctxt orf is_real_inductive_pred hol_ctxt
blanchet@33192
  1532
   orf (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1533
blanchet@33192
  1534
(* term * term -> term *)
blanchet@33192
  1535
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
blanchet@33192
  1536
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
blanchet@33192
  1537
  | s_betapply p = betapply p
blanchet@33192
  1538
(* term * term list -> term *)
blanchet@33192
  1539
val s_betapplys = Library.foldl s_betapply
blanchet@33192
  1540
blanchet@33192
  1541
(* term -> term *)
blanchet@33192
  1542
fun lhs_of_equation t =
blanchet@33192
  1543
  case t of
blanchet@33192
  1544
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1545
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1546
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1547
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@33192
  1548
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1549
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1550
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1551
  | _ => NONE
blanchet@33192
  1552
(* theory -> term -> bool *)
blanchet@33192
  1553
fun is_constr_pattern _ (Bound _) = true
blanchet@33864
  1554
  | is_constr_pattern _ (Var _) = true
blanchet@33192
  1555
  | is_constr_pattern thy t =
blanchet@33192
  1556
    case strip_comb t of
blanchet@35280
  1557
      (Const x, args) =>
blanchet@33192
  1558
      is_constr_like thy x andalso forall (is_constr_pattern thy) args
blanchet@33192
  1559
    | _ => false
blanchet@33192
  1560
fun is_constr_pattern_lhs thy t =
blanchet@33192
  1561
  forall (is_constr_pattern thy) (snd (strip_comb t))
blanchet@33192
  1562
fun is_constr_pattern_formula thy t =
blanchet@33192
  1563
  case lhs_of_equation t of
blanchet@33192
  1564
    SOME t' => is_constr_pattern_lhs thy t'
blanchet@33192
  1565
  | NONE => false
blanchet@33192
  1566
blanchet@35070
  1567
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1568
val unfold_max_depth = 255
blanchet@33192
  1569
blanchet@35070
  1570
(* hol_context -> term -> term *)
blanchet@35284
  1571
fun unfold_defs_in_term (hol_ctxt as {thy, ctxt, stds, fast_descrs, case_names,
blanchet@35280
  1572
                                      def_table, ground_thm_table, ersatz_table,
blanchet@35280
  1573
                                      ...}) =
blanchet@33192
  1574
  let
blanchet@33192
  1575
    (* int -> typ list -> term -> term *)
blanchet@33192
  1576
    fun do_term depth Ts t =
blanchet@33192
  1577
      case t of
blanchet@33192
  1578
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@33192
  1579
                      Type ("fun", [_, ran_T]))) $ t1 =>
blanchet@33192
  1580
        ((if is_number_type thy ran_T then
blanchet@33192
  1581
            let
blanchet@33192
  1582
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1583
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1584
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1585
            in
blanchet@35220
  1586
              if is_integer_like_type ran_T then
blanchet@35220
  1587
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1588
                  Const (s, ran_T)
blanchet@35220
  1589
                else
blanchet@35220
  1590
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1591
              else
blanchet@33192
  1592
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1593
                                  $ Const (s, int_T))
blanchet@33192
  1594
            end
blanchet@33192
  1595
            handle TERM _ => raise SAME ()
blanchet@33192
  1596
          else
blanchet@33192
  1597
            raise SAME ())
blanchet@33192
  1598
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1599
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1600
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1601
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1602
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1603
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1604
      | Const (x as (@{const_name distinct},
blanchet@33192
  1605
               Type ("fun", [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1606
        $ (t1 as _ $ _) =>
blanchet@33192
  1607
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1608
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1609
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1610
        if is_ground_term t1 andalso
blanchet@34936
  1611
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1612
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1613
          do_term depth Ts t2
blanchet@33192
  1614
        else
blanchet@33192
  1615
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1616
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1617
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1618
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1619
      | Const x => do_const depth Ts t x []
blanchet@33192
  1620
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1621
      | Free _ => t
blanchet@33192
  1622
      | Var _ => t
blanchet@33192
  1623
      | Bound _ => t
blanchet@33192
  1624
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1625
    (* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
blanchet@33192
  1626
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1627
        (Abs (Name.uu, body_type T,
blanchet@35220
  1628
              select_nth_constr_arg thy stds x (Bound 0) n res_T), [])
blanchet@33192
  1629
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@35220
  1630
        (select_nth_constr_arg thy stds x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1631
    (* int -> typ list -> term -> styp -> term list -> term *)
blanchet@33192
  1632
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1633
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1634
        SOME s' =>
blanchet@33192
  1635
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1636
      | NONE =>
blanchet@33192
  1637
        let
blanchet@33192
  1638
          val (const, ts) =
blanchet@35220
  1639
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1640
              (Const x, ts)
blanchet@33192
  1641
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1642
              SOME n =>
blanchet@33192
  1643
              let
blanchet@33192
  1644
                val (dataT, res_T) = nth_range_type n T
blanchet@33705
  1645
                                     |> pairf domain_type range_type
blanchet@33192
  1646
              in
blanchet@35070
  1647
                (optimized_case_def hol_ctxt dataT res_T
blanchet@33192
  1648
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1649
              end
blanchet@33192
  1650
            | _ =>
blanchet@35220
  1651
              if is_constr thy stds x then
blanchet@33192
  1652
                (Const x, ts)
blanchet@33581
  1653
              else if is_stale_constr thy x then
blanchet@34936
  1654
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1655
                                     \(\"" ^ s ^ "\")")
blanchet@35284
  1656
              else if is_quot_abs_fun ctxt x then
blanchet@34936
  1657
                let
blanchet@34936
  1658
                  val rep_T = domain_type T
blanchet@34936
  1659
                  val abs_T = range_type T
blanchet@34936
  1660
                in
blanchet@34936
  1661
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1662
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@35311
  1663
                               $ (Const (quot_normal_name_for_type ctxt abs_T,
blanchet@34936
  1664
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1665
                end
blanchet@35284
  1666
              else if is_quot_rep_fun ctxt x then
blanchet@34936
  1667
                let
blanchet@34936
  1668
                  val abs_T = domain_type T
blanchet@34936
  1669
                  val rep_T = range_type T
blanchet@34936
  1670
                  val x' = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1671
                in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
blanchet@33192
  1672
              else if is_record_get thy x then
blanchet@33192
  1673
                case length ts of
blanchet@33192
  1674
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1675
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1676
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1677
              else if is_record_update thy x then
blanchet@33192
  1678
                case length ts of
blanchet@35070
  1679
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1680
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1681
                            (do_term depth Ts (hd ts))
blanchet@33580
  1682
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1683
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@33192
  1684
              else if is_rep_fun thy x then
blanchet@33192
  1685
                let val x' = mate_of_rep_fun thy x in
blanchet@35220
  1686
                  if is_constr thy stds x' then
blanchet@33192
  1687
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1688
                                                    (range_type T)
blanchet@33192
  1689
                  else
blanchet@33192
  1690
                    (Const x, ts)
blanchet@33192
  1691
                end
blanchet@35070
  1692
              else if is_equational_fun hol_ctxt x then
blanchet@33192
  1693
                (Const x, ts)
blanchet@33192
  1694
              else case def_of_const thy def_table x of
blanchet@33192
  1695
                SOME def =>
blanchet@33192
  1696
                if depth > unfold_max_depth then
blanchet@34124
  1697
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1698
                                   "too many nested definitions (" ^
blanchet@34124
  1699
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1700
                                   quote s)
blanchet@33192
  1701
                else if s = @{const_name wfrec'} then
blanchet@33192
  1702
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1703
                else
blanchet@33192
  1704
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1705
              | NONE => (Const x, ts)
blanchet@33192
  1706
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1707
  in do_term 0 [] end
blanchet@33192
  1708
blanchet@35070
  1709
(* hol_context -> typ -> term list *)
blanchet@35220
  1710
fun codatatype_bisim_axioms (hol_ctxt as {thy, stds, ...}) T =
blanchet@33192
  1711
  let
blanchet@35070
  1712
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1713
    val set_T = T --> bool_T
blanchet@33192
  1714
    val iter_T = @{typ bisim_iterator}
blanchet@34124
  1715
    val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1716
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1717
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1718
    val n_var_minus_1 =
blanchet@33192
  1719
      Const (@{const_name Tha}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1720
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1721
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1722
    val x_var = Var (("x", 0), T)
blanchet@33192
  1723
    val y_var = Var (("y", 0), T)
blanchet@33192
  1724
    (* styp -> int -> typ -> term *)
blanchet@33192
  1725
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1726
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1727
       else HOLogic.eq_const nth_T)
blanchet@35220
  1728
      $ select_nth_constr_arg thy stds x x_var n nth_T
blanchet@35220
  1729
      $ select_nth_constr_arg thy stds x y_var n nth_T
blanchet@33192
  1730
    (* styp -> term *)
blanchet@33192
  1731
    fun case_func (x as (_, T)) =
blanchet@33192
  1732
      let
blanchet@33192
  1733
        val arg_Ts = binder_types T
blanchet@33192
  1734
        val core_t =
blanchet@35070
  1735
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1736
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1737
          |> foldr1 s_conj
blanchet@33192
  1738
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1739
  in
blanchet@33192
  1740
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1741
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@35070
  1742
        $ (betapplys (optimized_case_def hol_ctxt T bool_T,
blanchet@33192
  1743
                      map case_func xs @ [x_var]))),
blanchet@33192
  1744
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@34124
  1745
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  1746
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  1747
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1748
  end
blanchet@33192
  1749
blanchet@33192
  1750
exception NO_TRIPLE of unit
blanchet@33192
  1751
blanchet@33192
  1752
(* theory -> styp -> term -> term list * term list * term *)
blanchet@33192
  1753
fun triple_for_intro_rule thy x t =
blanchet@33192
  1754
  let
blanchet@33192
  1755
    val prems = Logic.strip_imp_prems t |> map (ObjectLogic.atomize_term thy)
blanchet@33192
  1756
    val concl = Logic.strip_imp_concl t |> ObjectLogic.atomize_term thy
blanchet@34121
  1757
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@33192
  1758
    (* term -> bool *)
blanchet@34121
  1759
     val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  1760
  in
blanchet@33192
  1761
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1762
  end
blanchet@33192
  1763
blanchet@33192
  1764
(* term -> term *)
blanchet@33192
  1765
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1766
blanchet@33192
  1767
(* indexname * typ -> term list -> term -> term -> term *)
blanchet@33192
  1768
fun wf_constraint_for rel side concl main =
blanchet@33192
  1769
  let
blanchet@33192
  1770
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1771
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1772
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1773
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1774
  in
blanchet@33192
  1775
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1776
                      HOLogic.all_const T
blanchet@33192
  1777
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1778
                  (t, vars)
blanchet@33192
  1779
  end
blanchet@33192
  1780
blanchet@33192
  1781
(* indexname * typ -> term list * term list * term -> term *)
blanchet@33192
  1782
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1783
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1784
blanchet@33192
  1785
(* Proof.context -> Time.time option -> thm
blanchet@33192
  1786
   -> (Proof.context -> tactic -> tactic) -> bool *)
blanchet@33192
  1787
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1788
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1789
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1790
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1791
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1792
blanchet@35181
  1793
val max_cached_wfs = 50
blanchet@35181
  1794
val cached_timeout =
blanchet@35181
  1795
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  1796
val cached_wf_props =
blanchet@35181
  1797
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  1798
krauss@33351
  1799
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1800
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1801
blanchet@35070
  1802
(* hol_context -> const_table -> styp -> bool *)
blanchet@33580
  1803
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  1804
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  1805
         : hol_context) (x as (_, T)) =
blanchet@35220
  1806
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  1807
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  1808
                      [Const x])
blanchet@33192
  1809
  | intro_ts =>
blanchet@33192
  1810
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1811
          |> filter_out (null o #2) of
blanchet@33192
  1812
       [] => true
blanchet@33192
  1813
     | triples =>
blanchet@33192
  1814
       let
blanchet@33192
  1815
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1816
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  1817
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  1818
         val rel = (("R", j), rel_T)
blanchet@33192
  1819
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1820
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1821
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1822
         val _ = if debug then
blanchet@33192
  1823
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1824
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1825
                 else
blanchet@33192
  1826
                   ()
blanchet@33192
  1827
       in
blanchet@35181
  1828
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  1829
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  1830
           ()
blanchet@33557
  1831
         else
blanchet@35181
  1832
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  1833
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  1834
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  1835
           SOME wf => wf
blanchet@33192
  1836
         | NONE =>
blanchet@33192
  1837
           let
blanchet@33192
  1838
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  1839
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  1840
                             termination_tacs
blanchet@35181
  1841
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1842
       end)
blanchet@35309
  1843
    handle List.Empty => false | NO_TRIPLE () => false
blanchet@33192
  1844
blanchet@35070
  1845
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  1846
blanchet@35070
  1847
(* hol_context -> styp -> bool *)
blanchet@33192
  1848
fun is_well_founded_inductive_pred
blanchet@35070
  1849
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  1850
        (x as (s, _)) =
blanchet@33192
  1851
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1852
    SOME (SOME b) => b
blanchet@34936
  1853
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  1854
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  1855
           SOME (_, wf) => wf
blanchet@35181
  1856
         | NONE =>
blanchet@35181
  1857
           let
blanchet@35181
  1858
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  1859
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  1860
           in
blanchet@35181
  1861
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  1862
           end
blanchet@33192
  1863
blanchet@35280
  1864
(* typ list -> typ -> term -> term *)
blanchet@35280
  1865
fun ap_curry [_] _ t = t
blanchet@35280
  1866
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  1867
    let val n = length arg_Ts in
blanchet@33192
  1868
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1869
                incr_boundvars n t
blanchet@33192
  1870
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1871
    end
blanchet@33192
  1872
blanchet@33192
  1873
(* int -> term -> int *)
blanchet@33192
  1874
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1875
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  1876
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  1877
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1878
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1879
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1880
blanchet@33192
  1881
(* term -> bool *)
blanchet@33192
  1882
val is_linear_inductive_pred_def =
blanchet@33192
  1883
  let
blanchet@33192
  1884
    (* int -> term -> bool *)
blanchet@33192
  1885
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  1886
        do_disjunct (j + 1) t2
blanchet@33192
  1887
      | do_disjunct j t =
blanchet@33192
  1888
        case num_occs_of_bound_in_term j t of
blanchet@33192
  1889
          0 => true
blanchet@35070
  1890
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  1891
        | _ => false
blanchet@33192
  1892
    (* term -> bool *)
blanchet@33192
  1893
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1894
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  1895
          case length xs of
blanchet@33192
  1896
            1 => false
blanchet@35070
  1897
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  1898
        end
blanchet@33192
  1899
      | do_lfp_def _ = false
blanchet@33192
  1900
  in do_lfp_def o strip_abs_body end
blanchet@33192
  1901
blanchet@33851
  1902
(* int -> int list list *)
blanchet@33851
  1903
fun n_ptuple_paths 0 = []
blanchet@33851
  1904
  | n_ptuple_paths 1 = []
blanchet@33851
  1905
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  1906
(* int -> typ -> typ -> term -> term *)
blanchet@33851
  1907
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  1908
blanchet@33192
  1909
(* term -> term * term *)
blanchet@33192
  1910
val linear_pred_base_and_step_rhss =
blanchet@33192
  1911
  let
blanchet@33192
  1912
    (* term -> term *)
blanchet@33192
  1913
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1914
        let
blanchet@33192
  1915
          val (xs, body) = strip_abs t2
blanchet@33192
  1916
          val arg_Ts = map snd (tl xs)
blanchet@33192
  1917
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  1918
          val j = length arg_Ts
blanchet@33192
  1919
          (* int -> term -> term *)
blanchet@33192
  1920
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  1921
              Const (@{const_name Ex}, T1)
blanchet@33192
  1922
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  1923
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  1924
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  1925
            | repair_rec j t =
blanchet@33192
  1926
              let val (head, args) = strip_comb t in
blanchet@33192
  1927
                if head = Bound j then
blanchet@33192
  1928
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  1929
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  1930
                else
blanchet@33192
  1931
                  t
blanchet@33192
  1932
              end
blanchet@33192
  1933
          val (nonrecs, recs) =
blanchet@34121
  1934
            List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
blanchet@35070
  1935
                           (disjuncts_of body)
blanchet@33192
  1936
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  1937
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  1938
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  1939
        in
blanchet@33192
  1940
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  1941
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  1942
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  1943
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  1944
        end
blanchet@33192
  1945
      | aux t =
blanchet@33232
  1946
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  1947
  in aux end
blanchet@33192
  1948
blanchet@35070
  1949
(* hol_context -> styp -> term -> term *)
blanchet@35280
  1950
fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (s, T) def =
blanchet@33192
  1951
  let
blanchet@33192
  1952
    val j = maxidx_of_term def + 1
blanchet@33192
  1953
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1954
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1955
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  1956
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  1957
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  1958
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  1959
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  1960
    val set_T = tuple_T --> bool_T
blanchet@33192
  1961
    val curried_T = tuple_T --> set_T
blanchet@33192
  1962
    val uncurried_T = Type ("*", [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  1963
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  1964
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  1965
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  1966
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1967
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  1968
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  1969
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  1970
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1971
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  1972
  in
blanchet@33192
  1973
    list_abs (outer,
blanchet@33192
  1974
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  1975
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  1976
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  1977
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  1978
              $ list_comb (Const base_x, outer_bounds)
blanchet@35280
  1979
              |> ap_curry tuple_arg_Ts tuple_T)
blanchet@35070
  1980
    |> unfold_defs_in_term hol_ctxt
blanchet@33192
  1981
  end
blanchet@33192
  1982
blanchet@35070
  1983
(* hol_context -> bool -> styp -> term *)
blanchet@35070
  1984
fun unrolled_inductive_pred_const (hol_ctxt as {thy, star_linear_preds,
blanchet@33192
  1985
                                                def_table, simp_table, ...})
blanchet@33192
  1986
                                  gfp (x as (s, T)) =
blanchet@33192
  1987
  let
blanchet@33192
  1988
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  1989
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  1990
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  1991
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1992
  in
blanchet@35070
  1993
    if is_equational_fun hol_ctxt x' then
blanchet@33192
  1994
      unrolled_const (* already done *)
blanchet@34936
  1995
    else if not gfp andalso is_linear_inductive_pred_def def andalso
blanchet@34936
  1996
         star_linear_preds then
blanchet@35070
  1997
      starred_linear_pred_const hol_ctxt x def
blanchet@33192
  1998
    else
blanchet@33192
  1999
      let
blanchet@33192
  2000
        val j = maxidx_of_term def + 1
blanchet@33192
  2001
        val (outer, fp_app) = strip_abs def
blanchet@33192
  2002
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2003
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  2004
        val next = suc_const iter_T $ cur
blanchet@33192
  2005
        val rhs = case fp_app of
blanchet@33192
  2006
                    Const _ $ t =>
blanchet@33192
  2007
                    betapply (t, list_comb (Const x', next :: outer_bounds))
blanchet@33232
  2008
                  | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_\
blanchet@33232
  2009
                                     \const", [fp_app])
blanchet@33192
  2010
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  2011
        val all = outer @ inner
blanchet@33192
  2012
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  2013
        val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  2014
        val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
blanchet@33192
  2015
                 |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  2016
        val _ = add_simps simp_table s' [eq]
blanchet@33192
  2017
      in unrolled_const end
blanchet@33192
  2018
  end
blanchet@33192
  2019
blanchet@35070
  2020
(* hol_context -> styp -> term *)
blanchet@35070
  2021
fun raw_inductive_pred_axiom ({thy, def_table, ...} : hol_context) x =
blanchet@33192
  2022
  let
blanchet@33192
  2023
    val def = the (def_of_const thy def_table x)
blanchet@33192
  2024
    val (outer, fp_app) = strip_abs def
blanchet@33192
  2025
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2026
    val rhs = case fp_app of
blanchet@33192
  2027
                Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
blanchet@33232
  2028
              | _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom",
blanchet@33192
  2029
                                 [fp_app])
blanchet@33192
  2030
    val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  2031
    val all = outer @ inner
blanchet@33192
  2032
    val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  2033
    val j = maxidx_of_term def + 1
blanchet@33192
  2034
    val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  2035
  in
blanchet@33192
  2036
    HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
blanchet@33192
  2037
    |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  2038
  end
blanchet@35070
  2039
fun inductive_pred_axiom hol_ctxt (x as (s, T)) =
blanchet@33192
  2040
  if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
blanchet@33192
  2041
    let val x' = (after_name_sep s, T) in
blanchet@35070
  2042
      raw_inductive_pred_axiom hol_ctxt x' |> subst_atomic [(Const x', Const x)]
blanchet@33192
  2043
    end
blanchet@33192
  2044
  else
blanchet@35070
  2045
    raw_inductive_pred_axiom hol_ctxt x
blanchet@33192
  2046
blanchet@35070
  2047
(* hol_context -> styp -> term list *)
blanchet@35220
  2048
fun raw_equational_fun_axioms (hol_ctxt as {thy, stds, fast_descrs, simp_table,
blanchet@35280
  2049
                                            psimp_table, ...}) x =
blanchet@35220
  2050
  case def_props_for_const thy stds fast_descrs (!simp_table) x of
blanchet@35220
  2051
    [] => (case def_props_for_const thy stds fast_descrs psimp_table x of
blanchet@35070
  2052
             [] => [inductive_pred_axiom hol_ctxt x]
blanchet@33192
  2053
           | psimps => psimps)
blanchet@33192
  2054
  | simps => simps
blanchet@33192
  2055
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
blanchet@35070
  2056
(* hol_context -> styp -> bool *)
blanchet@35070
  2057
fun is_equational_fun_surely_complete hol_ctxt x =
blanchet@35070
  2058
  case raw_equational_fun_axioms hol_ctxt x of
blanchet@35070
  2059
    [@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)] =>
blanchet@35070
  2060
    strip_comb t1 |> snd |> forall is_Var
blanchet@35070
  2061
  | _ => false
blanchet@33192
  2062
blanchet@33192
  2063
(* term list -> term list *)
blanchet@33556
  2064
fun merge_type_vars_in_terms ts =
blanchet@33192
  2065
  let
blanchet@33192
  2066
    (* typ -> (sort * string) list -> (sort * string) list *)
blanchet@33192
  2067
    fun add_type (TFree (s, S)) table =
blanchet@33192
  2068
        (case AList.lookup (op =) table S of
blanchet@33192
  2069
           SOME s' =>
blanchet@33192
  2070
           if string_ord (s', s) = LESS then AList.update (op =) (S, s') table
blanchet@33192
  2071
           else table
blanchet@33192
  2072
         | NONE => (S, s) :: table)
blanchet@33192
  2073
      | add_type _ table = table
blanchet@33192
  2074
    val table = fold (fold_types (fold_atyps add_type)) ts []
blanchet@33192
  2075
    (* typ -> typ *)
blanchet@35280
  2076
    fun coalesce (TFree (_, S)) = TFree (AList.lookup (op =) table S |> the, S)
blanchet@33192
  2077
      | coalesce T = T
blanchet@33192
  2078
  in map (map_types (map_atyps coalesce)) ts end
blanchet@33192
  2079
blanchet@35190
  2080
(* hol_context -> bool -> typ -> typ list -> typ list *)
blanchet@35190
  2081
fun add_ground_types hol_ctxt binarize =
blanchet@35190
  2082
  let
blanchet@35190
  2083
    fun aux T accum =
blanchet@35190
  2084
      case T of
blanchet@35190
  2085
        Type ("fun", Ts) => fold aux Ts accum
blanchet@35190
  2086
      | Type ("*", Ts) => fold aux Ts accum
blanchet@35190
  2087
      | Type (@{type_name itself}, [T1]) => aux T1 accum
blanchet@35190
  2088
      | Type (_, Ts) =>
blanchet@35190
  2089
        if member (op =) (@{typ prop} :: @{typ bool} :: @{typ unit} :: accum)
blanchet@35190
  2090
                  T then
blanchet@35190
  2091
          accum
blanchet@35190
  2092
        else
blanchet@35190
  2093
          T :: accum
blanchet@35190
  2094
          |> fold aux (case binarized_and_boxed_datatype_constrs hol_ctxt
blanchet@35190
  2095
                                                                 binarize T of
blanchet@35190
  2096
                         [] => Ts
blanchet@35190
  2097
                       | xs => map snd xs)
blanchet@35190
  2098
      | _ => insert (op =) T accum
blanchet@35190
  2099
  in aux end
blanchet@33192
  2100
blanchet@35190
  2101
(* hol_context -> bool -> typ -> typ list *)
blanchet@35190
  2102
fun ground_types_in_type hol_ctxt binarize T =
blanchet@35190
  2103
  add_ground_types hol_ctxt binarize T []
blanchet@35070
  2104
(* hol_context -> term list -> typ list *)
blanchet@35190
  2105
fun ground_types_in_terms hol_ctxt binarize ts =
blanchet@35190
  2106
  fold (fold_types (add_ground_types hol_ctxt binarize)) ts []
blanchet@33192
  2107
blanchet@33192
  2108
(* theory -> const_table -> styp -> int list *)
blanchet@33192
  2109
fun const_format thy def_table (x as (s, T)) =
blanchet@33192
  2110
  if String.isPrefix unrolled_prefix s then
blanchet@33192
  2111
    const_format thy def_table (original_name s, range_type T)
blanchet@33192
  2112
  else if String.isPrefix skolem_prefix s then
blanchet@33192
  2113
    let
blanchet@33192
  2114
      val k = unprefix skolem_prefix s
blanchet@33192
  2115
              |> strip_first_name_sep |> fst |> space_explode "@"
blanchet@33192
  2116
              |> hd |> Int.fromString |> the
blanchet@33192
  2117
    in [k, num_binder_types T - k] end
blanchet@33192
  2118
  else if original_name s <> s then
blanchet@33192
  2119
    [num_binder_types T]
blanchet@33192
  2120
  else case def_of_const thy def_table x of
blanchet@33192
  2121
    SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
blanchet@33192
  2122
                 let val k = length (strip_abs_vars t') in
blanchet@33192
  2123
                   [k, num_binder_types T - k]
blanchet@33192
  2124
                 end
blanchet@33192
  2125
               else
blanchet@33192
  2126
                 [num_binder_types T]
blanchet@33192
  2127
  | NONE => [num_binder_types T]
blanchet@33192
  2128
(* int list -> int list -> int list *)
blanchet@33192
  2129
fun intersect_formats _ [] = []
blanchet@33192
  2130
  | intersect_formats [] _ = []
blanchet@33192
  2131
  | intersect_formats ks1 ks2 =
blanchet@33192
  2132
    let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
blanchet@33192
  2133
      intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
blanchet@33192
  2134
                        (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
blanchet@33192
  2135
      [Int.min (k1, k2)]
blanchet@33192
  2136
    end
blanchet@33192
  2137
blanchet@33192
  2138
(* theory -> const_table -> (term option * int list) list -> term -> int list *)
blanchet@33192
  2139
fun lookup_format thy def_table formats t =
blanchet@33192
  2140
  case AList.lookup (fn (SOME x, SOME y) =>