src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Mon Feb 22 14:36:10 2010 +0100 (2010-02-22)
changeset 35283 7ae51d5ea05d
parent 35280 54ab4921f826
child 35284 9edc2bd6d2bd
permissions -rw-r--r--
filter out trivial definitions in Nitpick (e.g. "Topology.topo" from AFP)
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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 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 : theory -> 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 : Proof.context -> term list -> const_table
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  val const_nondef_table : term list -> const_table
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  val const_simp_table : Proof.context -> const_table
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  val const_psimp_table : Proof.context -> const_table
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  val inductive_intro_table : Proof.context -> const_table -> const_table
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  val ground_theorem_table : theory -> term list Inttab.table
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  val ersatz_table : theory -> (string * string) list
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  val 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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    theory -> (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 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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(* 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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(* term * term -> term *)
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fun s_conj (t1, @{const True}) = t1
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  | s_conj (@{const True}, t2) = t2
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  | s_conj (t1, t2) =
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    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
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    else HOLogic.mk_conj (t1, t2)
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fun s_disj (t1, @{const False}) = t1
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   300
  | s_disj (@{const False}, t2) = t2
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   301
  | s_disj (t1, t2) =
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   302
    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
blanchet@34998
   303
    else HOLogic.mk_disj (t1, t2)
blanchet@34998
   304
blanchet@34998
   305
(* term -> term -> term list *)
blanchet@34998
   306
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
blanchet@34998
   307
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
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   308
  | strip_connective _ t = [t]
blanchet@34998
   309
(* term -> term list * term *)
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   310
fun strip_any_connective (t as (t0 $ _ $ _)) =
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   311
    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
blanchet@34998
   312
      (strip_connective t0 t, t0)
blanchet@34998
   313
    else
blanchet@34998
   314
      ([t], @{const Not})
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   315
  | strip_any_connective t = ([t], @{const Not})
blanchet@34998
   316
(* term -> term list *)
blanchet@35070
   317
val conjuncts_of = strip_connective @{const "op &"}
blanchet@35070
   318
val disjuncts_of = strip_connective @{const "op |"}
blanchet@34998
   319
blanchet@33192
   320
(* When you add constants to these lists, make sure to handle them in
blanchet@33232
   321
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
blanchet@33192
   322
   well. *)
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   323
val built_in_consts =
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   324
  [(@{const_name all}, 1),
blanchet@33192
   325
   (@{const_name "=="}, 2),
blanchet@33192
   326
   (@{const_name "==>"}, 2),
blanchet@33192
   327
   (@{const_name Pure.conjunction}, 2),
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   328
   (@{const_name Trueprop}, 1),
blanchet@33192
   329
   (@{const_name Not}, 1),
blanchet@33192
   330
   (@{const_name False}, 0),
blanchet@33192
   331
   (@{const_name True}, 0),
blanchet@33192
   332
   (@{const_name All}, 1),
blanchet@33192
   333
   (@{const_name Ex}, 1),
blanchet@33192
   334
   (@{const_name "op ="}, 2),
blanchet@33192
   335
   (@{const_name "op &"}, 2),
blanchet@33192
   336
   (@{const_name "op |"}, 2),
blanchet@33192
   337
   (@{const_name "op -->"}, 2),
blanchet@33192
   338
   (@{const_name If}, 3),
blanchet@33192
   339
   (@{const_name Let}, 2),
blanchet@33192
   340
   (@{const_name Unity}, 0),
blanchet@33192
   341
   (@{const_name Pair}, 2),
blanchet@33192
   342
   (@{const_name fst}, 1),
blanchet@33192
   343
   (@{const_name snd}, 1),
blanchet@33192
   344
   (@{const_name Id}, 0),
blanchet@33192
   345
   (@{const_name insert}, 2),
blanchet@33192
   346
   (@{const_name converse}, 1),
blanchet@33192
   347
   (@{const_name trancl}, 1),
blanchet@33192
   348
   (@{const_name rel_comp}, 2),
blanchet@33192
   349
   (@{const_name image}, 2),
blanchet@33192
   350
   (@{const_name finite}, 1),
blanchet@34936
   351
   (@{const_name unknown}, 0),
blanchet@34936
   352
   (@{const_name is_unknown}, 1),
blanchet@33192
   353
   (@{const_name Tha}, 1),
blanchet@33192
   354
   (@{const_name Frac}, 0),
blanchet@33192
   355
   (@{const_name norm_frac}, 0)]
blanchet@35220
   356
val built_in_nat_consts =
blanchet@35220
   357
  [(@{const_name Suc}, 0),
blanchet@35220
   358
   (@{const_name nat}, 0),
blanchet@35220
   359
   (@{const_name nat_gcd}, 0),
blanchet@35220
   360
   (@{const_name nat_lcm}, 0)]
blanchet@33192
   361
val built_in_descr_consts =
blanchet@33192
   362
  [(@{const_name The}, 1),
blanchet@33192
   363
   (@{const_name Eps}, 1)]
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   364
val built_in_typed_consts =
blanchet@35220
   365
  [((@{const_name zero_class.zero}, int_T), 0),
blanchet@35220
   366
   ((@{const_name one_class.one}, int_T), 0),
blanchet@35220
   367
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   368
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   369
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
blanchet@35220
   370
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
blanchet@35220
   371
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
blanchet@35220
   372
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
blanchet@35220
   373
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
blanchet@35220
   374
val built_in_typed_nat_consts =
blanchet@35220
   375
  [((@{const_name zero_class.zero}, nat_T), 0),
blanchet@35220
   376
   ((@{const_name one_class.one}, nat_T), 0),
blanchet@35220
   377
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   378
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   379
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   380
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   381
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   382
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   383
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   384
val built_in_set_consts =
blanchet@35220
   385
  [(@{const_name semilattice_inf_class.inf}, 2),
blanchet@35220
   386
   (@{const_name semilattice_sup_class.sup}, 2),
blanchet@35220
   387
   (@{const_name minus_class.minus}, 2),
blanchet@35220
   388
   (@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   389
blanchet@33192
   390
(* typ -> typ *)
blanchet@35190
   391
fun unarize_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   392
  | unarize_type @{typ "signed_bit word"} = int_T
blanchet@35190
   393
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
blanchet@35190
   394
  | unarize_type T = T
blanchet@35190
   395
fun unarize_and_unbox_type (Type (@{type_name fun_box}, Ts)) =
blanchet@35190
   396
    unarize_and_unbox_type (Type ("fun", Ts))
blanchet@35190
   397
  | unarize_and_unbox_type (Type (@{type_name pair_box}, Ts)) =
blanchet@35190
   398
    Type ("*", map unarize_and_unbox_type Ts)
blanchet@35190
   399
  | unarize_and_unbox_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   400
  | unarize_and_unbox_type @{typ "signed_bit word"} = int_T
blanchet@35190
   401
  | unarize_and_unbox_type (Type (s, Ts as _ :: _)) =
blanchet@35190
   402
    Type (s, map unarize_and_unbox_type Ts)
blanchet@35190
   403
  | unarize_and_unbox_type T = T
blanchet@35280
   404
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   405
  | uniterize_type @{typ bisim_iterator} = nat_T
blanchet@35280
   406
  | uniterize_type T = T
blanchet@35280
   407
val unarize_unbox_and_uniterize_type = uniterize_type o unarize_and_unbox_type
blanchet@35280
   408
blanchet@33192
   409
(* Proof.context -> typ -> string *)
blanchet@35190
   410
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_and_unbox_type
blanchet@33192
   411
blanchet@33192
   412
(* string -> string -> string *)
blanchet@33192
   413
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@33192
   414
(* string -> string *)
blanchet@34121
   415
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   416
(* string -> term -> term *)
blanchet@33192
   417
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@33192
   418
(* string -> string *)
blanchet@34121
   419
fun short_name s =
blanchet@33192
   420
  case space_explode name_sep s of
blanchet@33192
   421
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   422
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   423
(* typ -> typ *)
blanchet@34121
   424
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   425
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   426
  | shorten_names_in_type T = T
blanchet@33192
   427
(* term -> term *)
blanchet@34121
   428
val shorten_names_in_term =
blanchet@34121
   429
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   430
  #> map_types shorten_names_in_type
blanchet@33192
   431
blanchet@33192
   432
(* theory -> typ * typ -> bool *)
blanchet@33192
   433
fun type_match thy (T1, T2) =
blanchet@33192
   434
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   435
  handle Type.TYPE_MATCH => false
blanchet@33192
   436
(* theory -> styp * styp -> bool *)
blanchet@33192
   437
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   438
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   439
(* theory -> term * term -> bool *)
blanchet@33192
   440
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   441
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   442
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   443
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   444
blanchet@33192
   445
(* typ -> bool *)
blanchet@33192
   446
fun is_TFree (TFree _) = true
blanchet@33192
   447
  | is_TFree _ = false
blanchet@33192
   448
fun is_higher_order_type (Type ("fun", _)) = true
blanchet@33192
   449
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   450
  | is_higher_order_type _ = false
blanchet@33192
   451
fun is_fun_type (Type ("fun", _)) = true
blanchet@33192
   452
  | is_fun_type _ = false
blanchet@33192
   453
fun is_set_type (Type ("fun", [_, @{typ bool}])) = true
blanchet@33192
   454
  | is_set_type _ = false
blanchet@33192
   455
fun is_pair_type (Type ("*", _)) = true
blanchet@33192
   456
  | is_pair_type _ = false
blanchet@33192
   457
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   458
  | is_lfp_iterator_type _ = false
blanchet@33192
   459
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   460
  | is_gfp_iterator_type _ = false
blanchet@33192
   461
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   462
fun is_iterator_type T =
blanchet@35280
   463
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   464
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   465
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   466
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   467
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   468
  | is_word_type _ = false
blanchet@35280
   469
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   470
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   471
(* theory -> typ -> bool *)
blanchet@33192
   472
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   473
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   474
  | is_frac_type _ _ = false
blanchet@35220
   475
fun is_number_type thy = is_integer_like_type orf is_frac_type thy
blanchet@33192
   476
blanchet@33192
   477
(* bool -> styp -> typ *)
blanchet@33192
   478
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   479
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   480
        binder_types T)
blanchet@33192
   481
(* typ -> styp *)
blanchet@33192
   482
fun const_for_iterator_type (Type (s, Ts)) = (after_name_sep s, Ts ---> bool_T)
blanchet@33192
   483
  | const_for_iterator_type T =
blanchet@33232
   484
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   485
blanchet@35070
   486
(* int -> typ -> typ list * typ *)
blanchet@33192
   487
fun strip_n_binders 0 T = ([], T)
blanchet@33192
   488
  | strip_n_binders n (Type ("fun", [T1, T2])) =
blanchet@33192
   489
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   490
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@33192
   491
    strip_n_binders n (Type ("fun", Ts))
blanchet@33232
   492
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   493
(* typ -> typ *)
blanchet@33192
   494
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   495
blanchet@33192
   496
(* typ -> int *)
blanchet@33192
   497
fun num_factors_in_type (Type ("*", [T1, T2])) =
blanchet@33192
   498
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   499
  | num_factors_in_type _ = 1
blanchet@33192
   500
fun num_binder_types (Type ("fun", [_, T2])) = 1 + num_binder_types T2
blanchet@33192
   501
  | num_binder_types _ = 0
blanchet@33192
   502
(* typ -> typ list *)
blanchet@33192
   503
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   504
fun maybe_curried_binder_types T =
blanchet@33192
   505
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   506
blanchet@33192
   507
(* typ -> term list -> term *)
blanchet@33192
   508
fun mk_flat_tuple _ [t] = t
blanchet@33192
   509
  | mk_flat_tuple (Type ("*", [T1, T2])) (t :: ts) =
blanchet@33192
   510
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   511
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   512
(* int -> term -> term list *)
blanchet@33192
   513
fun dest_n_tuple 1 t = [t]
blanchet@33192
   514
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   515
blanchet@33192
   516
(* int -> typ -> typ list *)
blanchet@33192
   517
fun dest_n_tuple_type 1 T = [T]
blanchet@33192
   518
  | dest_n_tuple_type n (Type (_, [T1, T2])) =
blanchet@33192
   519
    T1 :: dest_n_tuple_type (n - 1) T2
blanchet@33232
   520
  | dest_n_tuple_type _ T =
blanchet@33232
   521
    raise TYPE ("Nitpick_HOL.dest_n_tuple_type", [T], [])
blanchet@33192
   522
blanchet@35220
   523
type typedef_info =
blanchet@35220
   524
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   525
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   526
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   527
blanchet@35220
   528
(* theory -> string -> typedef_info *)
blanchet@35220
   529
fun typedef_info thy s =
blanchet@35220
   530
  if is_frac_type thy (Type (s, [])) then
blanchet@35220
   531
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@35220
   532
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@35220
   533
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@35220
   534
                          |> Logic.varify,
blanchet@35220
   535
          set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@35220
   536
  else case Typedef.get_info thy s of
blanchet@35220
   537
    SOME {abs_type, rep_type, Abs_name, Rep_name, set_def, Rep, Abs_inverse,
blanchet@35220
   538
          Rep_inverse, ...} =>
blanchet@35220
   539
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@35220
   540
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@35220
   541
          set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@35220
   542
          Rep_inverse = SOME Rep_inverse}
blanchet@35220
   543
  | NONE => NONE
blanchet@35220
   544
blanchet@35220
   545
(* theory -> string -> bool *)
blanchet@35220
   546
val is_typedef = is_some oo typedef_info
blanchet@35220
   547
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   548
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   549
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   550
blanchet@34121
   551
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   552
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   553
(* theory -> (typ option * bool) list -> string -> bool *)
blanchet@35220
   554
fun is_basic_datatype thy stds s =
blanchet@35220
   555
  member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@35220
   556
                 @{type_name int}, "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   557
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   558
blanchet@33192
   559
(* theory -> typ -> typ -> typ -> typ *)
blanchet@33192
   560
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   561
  Same.commit (Envir.subst_type_same
blanchet@33192
   562
                   (Sign.typ_match thy (Logic.varifyT T1, T1') Vartab.empty))
blanchet@33192
   563
              (Logic.varifyT T2)
blanchet@33192
   564
  handle Type.TYPE_MATCH =>
blanchet@33232
   565
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@33192
   566
blanchet@33192
   567
(* theory -> typ -> typ -> styp *)
blanchet@33192
   568
fun repair_constr_type thy body_T' T =
blanchet@33192
   569
  instantiate_type thy (body_type T) body_T' T
blanchet@33192
   570
blanchet@33192
   571
(* string -> (string * string) list -> theory -> theory *)
blanchet@33192
   572
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   573
  let
blanchet@33583
   574
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   575
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   576
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   577
(* string -> theory -> theory *)
blanchet@33192
   578
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   579
blanchet@33192
   580
(* typ -> string -> styp list -> theory -> theory *)
blanchet@33192
   581
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   582
  let
blanchet@33583
   583
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   584
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   585
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   586
    val _ =
blanchet@34936
   587
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35220
   588
         co_s <> "fun" andalso
blanchet@35220
   589
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   590
        ()
blanchet@34121
   591
      else
blanchet@34121
   592
        raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   593
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   594
                                   codatatypes
blanchet@33583
   595
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   596
(* typ -> theory -> theory *)
blanchet@33192
   597
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   598
blanchet@33192
   599
(* theory -> typ -> bool *)
blanchet@34982
   600
fun is_quot_type _ (Type ("IntEx.my_int", _)) = true (* FIXME *)
blanchet@35070
   601
  | is_quot_type _ (Type ("FSet.fset", _)) = true
blanchet@34936
   602
  | is_quot_type _ _ = false
blanchet@35280
   603
fun is_codatatype thy (Type (s, _)) =
blanchet@33583
   604
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   605
               |> Option.map snd |> these))
blanchet@33192
   606
  | is_codatatype _ _ = false
blanchet@33192
   607
fun is_pure_typedef thy (T as Type (s, _)) =
blanchet@33192
   608
    is_typedef thy s andalso
blanchet@34936
   609
    not (is_real_datatype thy s orelse is_quot_type thy T orelse
blanchet@35220
   610
         is_codatatype thy T orelse is_record_type T orelse
blanchet@35220
   611
         is_integer_like_type T)
blanchet@33192
   612
  | is_pure_typedef _ _ = false
blanchet@33192
   613
fun is_univ_typedef thy (Type (s, _)) =
blanchet@33192
   614
    (case typedef_info thy s of
blanchet@33192
   615
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@33192
   616
       (case set_def of
blanchet@33192
   617
          SOME thm =>
blanchet@33192
   618
          try (fst o dest_Const o snd o Logic.dest_equals o prop_of) thm
blanchet@33192
   619
        | NONE =>
blanchet@33192
   620
          try (fst o dest_Const o snd o HOLogic.dest_mem
blanchet@33864
   621
               o HOLogic.dest_Trueprop) prop_of_Rep) = SOME @{const_name top}
blanchet@33192
   622
     | NONE => false)
blanchet@33192
   623
  | is_univ_typedef _ _ = false
blanchet@35220
   624
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   625
fun is_datatype thy stds (T as Type (s, _)) =
blanchet@34936
   626
    (is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind} orelse
blanchet@35220
   627
     is_quot_type thy T) andalso not (is_basic_datatype thy stds s)
blanchet@35220
   628
  | is_datatype _ _ _ = false
blanchet@33192
   629
blanchet@33192
   630
(* theory -> typ -> (string * typ) list * (string * typ) *)
blanchet@33192
   631
fun all_record_fields thy T =
blanchet@33192
   632
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   633
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   634
  end
blanchet@33192
   635
  handle TYPE _ => []
blanchet@33192
   636
(* styp -> bool *)
blanchet@35280
   637
fun is_record_constr (s, T) =
blanchet@33192
   638
  String.isSuffix Record.extN s andalso
blanchet@33192
   639
  let val dataT = body_type T in
blanchet@33192
   640
    is_record_type dataT andalso
blanchet@33192
   641
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   642
  end
blanchet@33192
   643
(* theory -> typ -> int *)
blanchet@33192
   644
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   645
(* theory -> string -> typ -> int *)
blanchet@33192
   646
fun no_of_record_field thy s T1 =
blanchet@34121
   647
  find_index (curry (op =) s o fst)
blanchet@34121
   648
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@33192
   649
(* theory -> styp -> bool *)
blanchet@33192
   650
fun is_record_get thy (s, Type ("fun", [T1, _])) =
blanchet@34121
   651
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   652
  | is_record_get _ _ = false
blanchet@33192
   653
fun is_record_update thy (s, T) =
blanchet@33192
   654
  String.isSuffix Record.updateN s andalso
blanchet@34121
   655
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   656
         (all_record_fields thy (body_type T))
blanchet@33192
   657
  handle TYPE _ => false
blanchet@33192
   658
fun is_abs_fun thy (s, Type ("fun", [_, Type (s', _)])) =
blanchet@33192
   659
    (case typedef_info thy s' of
blanchet@33192
   660
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   661
     | NONE => false)
blanchet@33192
   662
  | is_abs_fun _ _ = false
blanchet@33192
   663
fun is_rep_fun thy (s, Type ("fun", [Type (s', _), _])) =
blanchet@33192
   664
    (case typedef_info thy s' of
blanchet@33192
   665
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   666
     | NONE => false)
blanchet@33192
   667
  | is_rep_fun _ _ = false
blanchet@34936
   668
(* Proof.context -> styp -> bool *)
blanchet@35070
   669
fun is_quot_abs_fun _ ("IntEx.abs_my_int", _) = true
blanchet@35070
   670
  | is_quot_abs_fun _ ("FSet.abs_fset", _) = true
blanchet@34936
   671
  | is_quot_abs_fun _ _ = false
blanchet@35070
   672
fun is_quot_rep_fun _ ("IntEx.rep_my_int", _) = true
blanchet@35070
   673
  | is_quot_rep_fun _ ("FSet.rep_fset", _) = true
blanchet@34936
   674
  | is_quot_rep_fun _ _ = false
blanchet@33192
   675
blanchet@33192
   676
(* theory -> styp -> styp *)
blanchet@33192
   677
fun mate_of_rep_fun thy (x as (_, Type ("fun", [T1 as Type (s', _), T2]))) =
blanchet@33192
   678
    (case typedef_info thy s' of
blanchet@33192
   679
       SOME {Abs_name, ...} => (Abs_name, Type ("fun", [T2, T1]))
blanchet@33232
   680
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   681
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@34936
   682
(* theory -> typ -> typ *)
blanchet@34936
   683
fun rep_type_for_quot_type _ (Type ("IntEx.my_int", [])) = @{typ "nat * nat"}
blanchet@34998
   684
  | rep_type_for_quot_type _ (Type ("FSet.fset", [T])) =
blanchet@34998
   685
    Type (@{type_name list}, [T])
blanchet@34936
   686
  | rep_type_for_quot_type _ T =
blanchet@34936
   687
    raise TYPE ("Nitpick_HOL.rep_type_for_quot_type", [T], [])
blanchet@34936
   688
(* theory -> typ -> term *)
blanchet@34936
   689
fun equiv_relation_for_quot_type _ (Type ("IntEx.my_int", [])) =
blanchet@34936
   690
    Const ("IntEx.intrel", @{typ "(nat * nat) => (nat * nat) => bool"})
blanchet@34998
   691
  | equiv_relation_for_quot_type _ (Type ("FSet.fset", [T])) =
blanchet@34998
   692
    Const ("FSet.list_eq",
blanchet@34998
   693
           Type (@{type_name list}, [T]) --> Type (@{type_name list}, [T])
blanchet@34998
   694
           --> bool_T)
blanchet@34936
   695
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   696
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   697
blanchet@33192
   698
(* theory -> styp -> bool *)
blanchet@33192
   699
fun is_coconstr thy (s, T) =
blanchet@33192
   700
  let
blanchet@33583
   701
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   702
    val co_T = body_type T
blanchet@33192
   703
    val co_s = dest_Type co_T |> fst
blanchet@33192
   704
  in
blanchet@33192
   705
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   706
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   707
  end
blanchet@33192
   708
  handle TYPE ("dest_Type", _, _) => false
blanchet@33192
   709
fun is_constr_like thy (s, T) =
blanchet@34982
   710
  member (op =) [@{const_name FunBox}, @{const_name PairBox},
blanchet@34982
   711
                 @{const_name Quot}, @{const_name Zero_Rep},
blanchet@34982
   712
                 @{const_name Suc_Rep}] s orelse
blanchet@35280
   713
  let val (x as (_, T)) = (s, unarize_and_unbox_type T) in
blanchet@34936
   714
    Refute.is_IDT_constructor thy x orelse is_record_constr x orelse
blanchet@34936
   715
    (is_abs_fun thy x andalso is_pure_typedef thy (range_type T)) orelse
blanchet@34936
   716
    is_coconstr thy x
blanchet@33192
   717
  end
blanchet@33581
   718
fun is_stale_constr thy (x as (_, T)) =
blanchet@34936
   719
  is_codatatype thy (body_type T) andalso is_constr_like thy x andalso
blanchet@34936
   720
  not (is_coconstr thy x)
blanchet@35220
   721
(* theory -> (typ option * bool) list -> styp -> bool *)
blanchet@35220
   722
fun is_constr thy stds (x as (_, T)) =
blanchet@34936
   723
  is_constr_like thy x andalso
blanchet@35220
   724
  not (is_basic_datatype thy stds
blanchet@35220
   725
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@34936
   726
  not (is_stale_constr thy x)
blanchet@33192
   727
(* string -> bool *)
blanchet@33192
   728
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   729
val is_sel_like_and_no_discr =
blanchet@33192
   730
  String.isPrefix sel_prefix
blanchet@33192
   731
  orf (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   732
blanchet@33192
   733
(* boxability -> boxability *)
blanchet@33192
   734
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   735
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   736
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   737
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   738
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   739
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   740
blanchet@35070
   741
(* hol_context -> boxability -> typ -> bool *)
blanchet@35070
   742
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   743
  case T of
blanchet@33192
   744
    Type ("fun", _) =>
blanchet@34936
   745
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   746
    not (is_boolean_type (body_type T))
blanchet@33192
   747
  | Type ("*", Ts) =>
blanchet@34936
   748
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   749
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   750
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   751
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   752
  | _ => false
blanchet@35070
   753
(* hol_context -> boxability -> string * typ list -> string *)
blanchet@35280
   754
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   755
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   756
    SOME (SOME box_me) => box_me
blanchet@35070
   757
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   758
(* hol_context -> boxability -> typ -> typ *)
blanchet@35070
   759
and box_type hol_ctxt boxy T =
blanchet@33192
   760
  case T of
blanchet@33192
   761
    Type (z as ("fun", [T1, T2])) =>
blanchet@34936
   762
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   763
       should_box_type hol_ctxt boxy z then
blanchet@33192
   764
      Type (@{type_name fun_box},
blanchet@35070
   765
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   766
    else
blanchet@35070
   767
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   768
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@33192
   769
  | Type (z as ("*", Ts)) =>
blanchet@34982
   770
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   771
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   772
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   773
    else
blanchet@35070
   774
      Type ("*", map (box_type hol_ctxt
blanchet@34121
   775
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   776
                           else InPair)) Ts)
blanchet@33192
   777
  | _ => T
blanchet@33192
   778
blanchet@35190
   779
(* typ -> typ *)
blanchet@35190
   780
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   781
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   782
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   783
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   784
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   785
(* term -> term *)
blanchet@35190
   786
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   787
blanchet@33192
   788
(* styp -> styp *)
blanchet@33192
   789
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   790
blanchet@33192
   791
(* typ -> int *)
blanchet@33192
   792
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   793
(* string -> int -> string *)
blanchet@33192
   794
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   795
  if s = @{const_name Pair} then
blanchet@33192
   796
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   797
  else
blanchet@33192
   798
    sel_prefix_for n ^ s
blanchet@33192
   799
(* styp -> int -> styp *)
blanchet@33192
   800
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   801
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   802
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   803
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   804
(* hol_context -> bool -> styp -> int -> styp *)
blanchet@35190
   805
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   806
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   807
  oo nth_sel_for_constr
blanchet@33192
   808
blanchet@33192
   809
(* string -> int *)
blanchet@33192
   810
fun sel_no_from_name s =
blanchet@33192
   811
  if String.isPrefix discr_prefix s then
blanchet@33192
   812
    ~1
blanchet@33192
   813
  else if String.isPrefix sel_prefix s then
blanchet@33192
   814
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   815
  else if s = @{const_name snd} then
blanchet@33192
   816
    1
blanchet@33192
   817
  else
blanchet@33192
   818
    0
blanchet@33192
   819
blanchet@35078
   820
(* term -> term *)
blanchet@35078
   821
val close_form =
blanchet@35078
   822
  let
blanchet@35078
   823
    (* (indexname * typ) list -> (indexname * typ) list -> term -> term *)
blanchet@35078
   824
    fun close_up zs zs' =
blanchet@35078
   825
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   826
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   827
           (take (length zs' - length zs) zs')
blanchet@35078
   828
    (* (indexname * typ) list -> term -> term *)
blanchet@35078
   829
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   830
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   831
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   832
        end
blanchet@35078
   833
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   834
  in aux [] end
blanchet@35078
   835
blanchet@33192
   836
(* typ list -> term -> int -> term *)
blanchet@33192
   837
fun eta_expand _ t 0 = t
blanchet@33192
   838
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   839
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   840
  | eta_expand Ts t n =
blanchet@33192
   841
    fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
blanchet@33192
   842
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   843
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   844
blanchet@33192
   845
(* term -> term *)
blanchet@33192
   846
fun extensionalize t =
blanchet@33192
   847
  case t of
blanchet@33192
   848
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   849
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   850
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   851
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   852
    end
blanchet@33192
   853
  | _ => t
blanchet@33192
   854
blanchet@33192
   855
(* typ -> term list -> term *)
blanchet@33192
   856
fun distinctness_formula T =
blanchet@33192
   857
  all_distinct_unordered_pairs_of
blanchet@33192
   858
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   859
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   860
blanchet@33192
   861
(* typ -> term *)
blanchet@35220
   862
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   863
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   864
blanchet@35220
   865
(* hol_context -> typ -> styp list *)
blanchet@35220
   866
fun uncached_datatype_constrs ({thy, stds, ...} : hol_context)
blanchet@35220
   867
                              (T as Type (s, Ts)) =
blanchet@33583
   868
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@34982
   869
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   870
     | _ =>
blanchet@35220
   871
       if is_datatype thy stds T then
blanchet@33581
   872
         case Datatype.get_info thy s of
blanchet@33581
   873
           SOME {index, descr, ...} =>
blanchet@33581
   874
           let
blanchet@33581
   875
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   876
           in
blanchet@33581
   877
             map (fn (s', Us) =>
blanchet@33581
   878
                     (s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us
blanchet@33581
   879
                          ---> T)) constrs
blanchet@33581
   880
           end
blanchet@33581
   881
         | NONE =>
blanchet@33581
   882
           if is_record_type T then
blanchet@33581
   883
             let
blanchet@33581
   884
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   885
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   886
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   887
             in [(s', T')] end
blanchet@34936
   888
           else if is_quot_type thy T then
blanchet@34936
   889
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@33581
   890
           else case typedef_info thy s of
blanchet@33581
   891
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@33581
   892
             [(Abs_name, instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   893
           | NONE =>
blanchet@33581
   894
             if T = @{typ ind} then
blanchet@33581
   895
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   896
             else
blanchet@33581
   897
               []
blanchet@33581
   898
       else
blanchet@33581
   899
         [])
blanchet@33580
   900
  | uncached_datatype_constrs _ _ = []
blanchet@35070
   901
(* hol_context -> typ -> styp list *)
blanchet@35220
   902
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   903
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   904
    SOME xs => xs
blanchet@33580
   905
  | NONE =>
blanchet@35220
   906
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   907
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   908
    end
blanchet@35190
   909
(* hol_context -> bool -> typ -> styp list *)
blanchet@35190
   910
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   911
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   912
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@35070
   913
(* hol_context -> typ -> int *)
blanchet@33192
   914
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   915
blanchet@33192
   916
(* string -> string *)
blanchet@33192
   917
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   918
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   919
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   920
(* hol_context -> bool -> styp -> styp *)
blanchet@35190
   921
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   922
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   923
    AList.lookup (op =)
blanchet@35190
   924
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   925
        s
blanchet@33192
   926
    |> the |> pair s
blanchet@33192
   927
  end
blanchet@34982
   928
blanchet@35070
   929
(* hol_context -> styp -> term *)
blanchet@35070
   930
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   931
  let val dataT = body_type T in
blanchet@33192
   932
    if s = @{const_name Suc} then
blanchet@33192
   933
      Abs (Name.uu, dataT,
blanchet@33192
   934
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
   935
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
   936
      Const (discr_for_constr x)
blanchet@33192
   937
    else
blanchet@33192
   938
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   939
  end
blanchet@35070
   940
(* hol_context -> styp -> term -> term *)
blanchet@35280
   941
fun discriminate_value (hol_ctxt as {thy, ...}) x t =
blanchet@35280
   942
  case head_of t of
blanchet@35280
   943
    Const x' =>
blanchet@33192
   944
    if x = x' then @{const True}
blanchet@33192
   945
    else if is_constr_like thy x' then @{const False}
blanchet@35070
   946
    else betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@35070
   947
  | _ => betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
   948
blanchet@35220
   949
(* theory -> (typ option * bool) list -> styp -> term -> term *)
blanchet@35220
   950
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
   951
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
   952
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
   953
      @{term "%n::nat. n - 1"}
blanchet@33192
   954
    else if is_pair_type dataT then
blanchet@33192
   955
      Const (nth_sel_for_constr x n)
blanchet@33192
   956
    else
blanchet@33192
   957
      let
blanchet@33192
   958
        (* int -> typ -> int * term *)
blanchet@33192
   959
        fun aux m (Type ("*", [T1, T2])) =
blanchet@33192
   960
            let
blanchet@33192
   961
              val (m, t1) = aux m T1
blanchet@33192
   962
              val (m, t2) = aux m T2
blanchet@33192
   963
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   964
          | aux m T =
blanchet@33192
   965
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
   966
                    $ Bound 0)
blanchet@33192
   967
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
   968
                     (List.take (arg_Ts, n)) 0
blanchet@33192
   969
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
   970
  end
blanchet@35220
   971
(* theory -> (typ option * bool) list -> styp -> term -> int -> typ -> term *)
blanchet@35220
   972
fun select_nth_constr_arg thy stds x t n res_T =
blanchet@35220
   973
  (case strip_comb t of
blanchet@35220
   974
     (Const x', args) =>
blanchet@35220
   975
     if x = x' then nth args n
blanchet@35220
   976
     else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
blanchet@35220
   977
     else raise SAME ()
blanchet@35220
   978
   | _ => raise SAME())
blanchet@35220
   979
  handle SAME () => betapply (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@33192
   980
blanchet@35220
   981
(* theory -> (typ option * bool) list -> styp -> term list -> term *)
blanchet@35220
   982
fun construct_value _ _ x [] = Const x
blanchet@35220
   983
  | construct_value thy stds (x as (s, _)) args =
blanchet@33192
   984
    let val args = map Envir.eta_contract args in
blanchet@33192
   985
      case hd args of
blanchet@35280
   986
        Const (s', _) $ t =>
blanchet@34936
   987
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
   988
           constr_name_for_sel_like s' = s andalso
blanchet@35220
   989
           forall (fn (n, t') =>
blanchet@35220
   990
                      select_nth_constr_arg thy stds x t n dummyT = t')
blanchet@34936
   991
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
   992
          t
blanchet@33192
   993
        else
blanchet@33192
   994
          list_comb (Const x, args)
blanchet@33192
   995
      | _ => list_comb (Const x, args)
blanchet@33192
   996
    end
blanchet@33192
   997
blanchet@33192
   998
(* (typ * int) list -> typ -> int *)
blanchet@34123
   999
fun card_of_type assigns (Type ("fun", [T1, T2])) =
blanchet@34123
  1000
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@34123
  1001
  | card_of_type assigns (Type ("*", [T1, T2])) =
blanchet@34123
  1002
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1003
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1004
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1005
  | card_of_type _ @{typ bool} = 2
blanchet@33192
  1006
  | card_of_type _ @{typ unit} = 1
blanchet@34123
  1007
  | card_of_type assigns T =
blanchet@34123
  1008
    case AList.lookup (op =) assigns T of
blanchet@33192
  1009
      SOME k => k
blanchet@33192
  1010
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1011
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@33192
  1012
(* int -> (typ * int) list -> typ -> int *)
blanchet@34123
  1013
fun bounded_card_of_type max default_card assigns (Type ("fun", [T1, T2])) =
blanchet@33192
  1014
    let
blanchet@34123
  1015
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1016
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1017
    in
blanchet@33192
  1018
      if k1 = max orelse k2 = max then max
blanchet@33192
  1019
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1020
    end
blanchet@34123
  1021
  | bounded_card_of_type max default_card assigns (Type ("*", [T1, T2])) =
blanchet@33192
  1022
    let
blanchet@34123
  1023
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1024
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1025
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1026
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1027
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1028
                    card_of_type assigns T
blanchet@33192
  1029
                  else
blanchet@34123
  1030
                    card_of_type assigns T
blanchet@33232
  1031
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1032
                           default_card)
blanchet@35070
  1033
(* hol_context -> int -> (typ * int) list -> typ -> int *)
blanchet@35070
  1034
fun bounded_exact_card_of_type hol_ctxt max default_card assigns T =
blanchet@33192
  1035
  let
blanchet@33192
  1036
    (* typ list -> typ -> int *)
blanchet@33192
  1037
    fun aux avoid T =
blanchet@34121
  1038
      (if member (op =) avoid T then
blanchet@33192
  1039
         0
blanchet@33192
  1040
       else case T of
blanchet@33192
  1041
         Type ("fun", [T1, T2]) =>
blanchet@33192
  1042
         let
blanchet@33192
  1043
           val k1 = aux avoid T1
blanchet@33192
  1044
           val k2 = aux avoid T2
blanchet@33192
  1045
         in
blanchet@33192
  1046
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1047
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1048
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1049
         end
blanchet@33192
  1050
       | Type ("*", [T1, T2]) =>
blanchet@33192
  1051
         let
blanchet@33192
  1052
           val k1 = aux avoid T1
blanchet@33192
  1053
           val k2 = aux avoid T2
blanchet@33192
  1054
         in
blanchet@33192
  1055
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1056
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1057
           else Int.min (max, k1 * k2)
blanchet@33192
  1058
         end
blanchet@33192
  1059
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1060
       | @{typ prop} => 2
blanchet@33192
  1061
       | @{typ bool} => 2
blanchet@33192
  1062
       | @{typ unit} => 1
blanchet@33192
  1063
       | Type _ =>
blanchet@35070
  1064
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1065
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1066
                  else raise SAME ()
blanchet@33192
  1067
          | constrs =>
blanchet@33192
  1068
            let
blanchet@33192
  1069
              val constr_cards =
blanchet@35280
  1070
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1071
                    constrs
blanchet@33192
  1072
            in
blanchet@34121
  1073
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1074
              else Integer.sum constr_cards
blanchet@33192
  1075
            end)
blanchet@33192
  1076
       | _ => raise SAME ())
blanchet@34123
  1077
      handle SAME () =>
blanchet@34123
  1078
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1079
  in Int.min (max, aux [] T) end
blanchet@33192
  1080
blanchet@35070
  1081
(* hol_context -> typ -> bool *)
blanchet@35070
  1082
fun is_finite_type hol_ctxt =
blanchet@35070
  1083
  not_equal 0 o bounded_exact_card_of_type hol_ctxt 1 2 []
blanchet@33192
  1084
blanchet@33192
  1085
(* term -> bool *)
blanchet@33192
  1086
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1087
  | is_ground_term (Const _) = true
blanchet@33192
  1088
  | is_ground_term _ = false
blanchet@33192
  1089
blanchet@33192
  1090
(* term -> word -> word *)
blanchet@33192
  1091
fun hashw_term (t1 $ t2) = Polyhash.hashw (hashw_term t1, hashw_term t2)
blanchet@33192
  1092
  | hashw_term (Const (s, _)) = Polyhash.hashw_string (s, 0w0)
blanchet@33192
  1093
  | hashw_term _ = 0w0
blanchet@33192
  1094
(* term -> int *)
blanchet@33192
  1095
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1096
blanchet@33192
  1097
(* term list -> (indexname * typ) list *)
blanchet@33192
  1098
fun special_bounds ts =
blanchet@33192
  1099
  fold Term.add_vars ts [] |> sort (TermOrd.fast_indexname_ord o pairself fst)
blanchet@33192
  1100
blanchet@33192
  1101
(* indexname * typ -> term -> term *)
blanchet@33192
  1102
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
  1103
blanchet@33571
  1104
(* theory -> string -> bool *)
blanchet@33571
  1105
fun is_funky_typedef_name thy s =
blanchet@34121
  1106
  member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@34936
  1107
                 @{type_name int}] s orelse
blanchet@34936
  1108
  is_frac_type thy (Type (s, []))
blanchet@35070
  1109
(* theory -> typ -> bool *)
blanchet@33571
  1110
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
  1111
  | is_funky_typedef _ _ = false
blanchet@33192
  1112
(* term -> bool *)
blanchet@33192
  1113
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1114
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1115
  | is_arity_type_axiom _ = false
blanchet@33192
  1116
(* theory -> bool -> term -> bool *)
blanchet@33197
  1117
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
blanchet@33197
  1118
    is_typedef_axiom thy boring t2
blanchet@33197
  1119
  | is_typedef_axiom thy boring
blanchet@33192
  1120
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@33197
  1121
         $ Const (_, Type ("fun", [Type (s, _), _])) $ Const _ $ _)) =
blanchet@33571
  1122
    boring <> is_funky_typedef_name thy s andalso is_typedef thy s
blanchet@33192
  1123
  | is_typedef_axiom _ _ _ = false
blanchet@33192
  1124
blanchet@33192
  1125
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1126
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1127
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1128
   using "typedef_info". *)
blanchet@33192
  1129
(* theory -> (string * term) list -> string list -> term list * term list *)
blanchet@33192
  1130
fun partition_axioms_by_definitionality thy axioms def_names =
blanchet@33192
  1131
  let
blanchet@33192
  1132
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1133
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1134
    val nondefs =
blanchet@33192
  1135
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1136
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
blanchet@33192
  1137
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1138
blanchet@33197
  1139
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1140
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1141
   commands. *)
blanchet@33192
  1142
(* theory -> bool *)
blanchet@33192
  1143
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1144
blanchet@33192
  1145
(* term -> bool *)
blanchet@35283
  1146
val is_trivial_definition =
blanchet@35283
  1147
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1148
val is_plain_definition =
blanchet@33192
  1149
  let
blanchet@33192
  1150
    (* term -> bool *)
blanchet@33192
  1151
    fun do_lhs t1 =
blanchet@33192
  1152
      case strip_comb t1 of
blanchet@34936
  1153
        (Const _, args) =>
blanchet@34936
  1154
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1155
      | _ => false
blanchet@33192
  1156
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1157
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1158
        do_lhs t1
blanchet@33192
  1159
      | do_eq _ = false
blanchet@33192
  1160
  in do_eq end
blanchet@33192
  1161
blanchet@33192
  1162
(* theory -> term list * term list * term list *)
blanchet@33192
  1163
fun all_axioms_of thy =
blanchet@33192
  1164
  let
blanchet@33192
  1165
    (* theory list -> term list *)
blanchet@33192
  1166
    val axioms_of_thys = maps Thm.axioms_of #> map (apsnd prop_of)
blanchet@33192
  1167
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1168
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1169
                    |> OrdList.make fast_string_ord
blanchet@33192
  1170
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1171
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1172
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1173
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1174
    val (built_in_defs, built_in_nondefs) =
blanchet@33192
  1175
      partition_axioms_by_definitionality thy built_in_axioms def_names
blanchet@33197
  1176
      ||> filter (is_typedef_axiom thy false)
blanchet@33192
  1177
    val (user_defs, user_nondefs) =
blanchet@33192
  1178
      partition_axioms_by_definitionality thy user_axioms def_names
blanchet@33197
  1179
    val (built_in_nondefs, user_nondefs) =
blanchet@33197
  1180
      List.partition (is_typedef_axiom thy false) user_nondefs
blanchet@33197
  1181
      |>> append built_in_nondefs
blanchet@34121
  1182
    val defs =
blanchet@34121
  1183
      (thy |> PureThy.all_thms_of
blanchet@34121
  1184
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1185
           |> map (prop_of o snd)
blanchet@35283
  1186
           |> filter_out is_trivial_definition
blanchet@35283
  1187
           |> filter is_plain_definition) @
blanchet@34121
  1188
      user_defs @ built_in_defs
blanchet@33192
  1189
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1190
blanchet@35220
  1191
(* theory -> (typ option * bool) list -> bool -> styp -> int option *)
blanchet@35220
  1192
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1193
  if s = @{const_name If} then
blanchet@33192
  1194
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1195
  else
blanchet@35220
  1196
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1197
      case AList.lookup (op =)
blanchet@35220
  1198
                    (built_in_consts
blanchet@35220
  1199
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1200
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1201
        SOME n => SOME n
blanchet@35220
  1202
      | NONE =>
blanchet@35220
  1203
        case AList.lookup (op =)
blanchet@35220
  1204
                 (built_in_typed_consts
blanchet@35220
  1205
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1206
                 (s, unarize_type T) of
blanchet@35220
  1207
          SOME n => SOME n
blanchet@35220
  1208
        | NONE =>
blanchet@35280
  1209
          case s of
blanchet@35280
  1210
            @{const_name zero_class.zero} =>
blanchet@35280
  1211
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1212
          | @{const_name Suc} =>
blanchet@35280
  1213
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1214
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1215
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1216
                 else
blanchet@35280
  1217
                   NONE
blanchet@35220
  1218
    end
blanchet@35220
  1219
(* theory -> (typ option * bool) list -> bool -> styp -> bool *)
blanchet@35220
  1220
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1221
blanchet@33192
  1222
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1223
   simplification rules (equational specifications). *)
blanchet@33192
  1224
(* term -> term *)
blanchet@33192
  1225
fun term_under_def t =
blanchet@33192
  1226
  case t of
blanchet@33192
  1227
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1228
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1229
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1230
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1231
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1232
  | t1 $ _ => term_under_def t1
blanchet@33192
  1233
  | _ => t
blanchet@33192
  1234
blanchet@33192
  1235
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
blanchet@33192
  1236
   traversal of the term, without which the wrong occurrence of a constant could
blanchet@33192
  1237
   be matched in the face of overloading. *)
blanchet@35220
  1238
(* theory -> (typ option * bool) list -> bool -> const_table -> styp
blanchet@35220
  1239
   -> term list *)
blanchet@35220
  1240
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1241
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1242
    []
blanchet@33192
  1243
  else
blanchet@33192
  1244
    these (Symtab.lookup table s)
blanchet@33192
  1245
    |> map_filter (try (Refute.specialize_type thy x))
blanchet@34121
  1246
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1247
blanchet@35280
  1248
(* term -> term option *)
blanchet@35280
  1249
fun normalized_rhs_of t =
blanchet@33192
  1250
  let
blanchet@33743
  1251
    (* term option -> term option *)
blanchet@33743
  1252
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1253
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1254
      | aux _ _ = NONE
blanchet@33192
  1255
    val (lhs, rhs) =
blanchet@33192
  1256
      case t of
blanchet@33192
  1257
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1258
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1259
        (t1, t2)
blanchet@33232
  1260
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1261
    val args = strip_comb lhs |> snd
blanchet@33743
  1262
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1263
blanchet@33192
  1264
(* theory -> const_table -> styp -> term option *)
blanchet@33192
  1265
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1266
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1267
     original_name s <> s then
blanchet@33192
  1268
    NONE
blanchet@33192
  1269
  else
blanchet@35220
  1270
    x |> def_props_for_const thy [(NONE, false)] false table |> List.last
blanchet@35280
  1271
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1272
    handle List.Empty => NONE
blanchet@33192
  1273
blanchet@33192
  1274
(* term -> fixpoint_kind *)
blanchet@33192
  1275
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1276
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1277
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1278
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1279
blanchet@33192
  1280
(* theory -> const_table -> term -> bool *)
blanchet@33192
  1281
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1282
  let
blanchet@33192
  1283
    (* term -> bool *)
blanchet@33192
  1284
    fun is_good_arg (Bound _) = true
blanchet@33192
  1285
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1286
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1287
        s = @{const_name undefined}
blanchet@33192
  1288
      | is_good_arg _ = false
blanchet@33192
  1289
  in
blanchet@33192
  1290
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1291
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1292
      (case def_of_const thy table x of
blanchet@33192
  1293
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1294
       | NONE => false)
blanchet@33192
  1295
    | _ => false
blanchet@33192
  1296
  end
blanchet@33192
  1297
(* theory -> const_table -> term -> term *)
blanchet@33192
  1298
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1299
  map_aterms (fn t as Const x =>
blanchet@33192
  1300
                 (case def_of_const thy table x of
blanchet@33192
  1301
                    SOME t' =>
blanchet@33192
  1302
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1303
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1304
                      else t
blanchet@33192
  1305
                    end
blanchet@33192
  1306
                 | NONE => t)
blanchet@33192
  1307
               | t => t)
blanchet@33192
  1308
blanchet@33192
  1309
(* term -> string * term *)
blanchet@33192
  1310
fun pair_for_prop t =
blanchet@33192
  1311
  case term_under_def t of
blanchet@33192
  1312
    Const (s, _) => (s, t)
blanchet@33192
  1313
  | Free _ => raise NOT_SUPPORTED "local definitions"
blanchet@33232
  1314
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@33192
  1315
blanchet@33192
  1316
(* (Proof.context -> term list) -> Proof.context -> const_table *)
blanchet@33192
  1317
fun table_for get ctxt =
blanchet@33192
  1318
  get ctxt |> map pair_for_prop |> AList.group (op =) |> Symtab.make
blanchet@33192
  1319
blanchet@35220
  1320
(* theory -> (typ option * bool) list -> (string * int) list *)
blanchet@35220
  1321
fun case_const_names thy stds =
blanchet@33192
  1322
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@35220
  1323
                  if is_basic_datatype thy stds dtype_s then
blanchet@33192
  1324
                    I
blanchet@33192
  1325
                  else
blanchet@33192
  1326
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1327
                                     |> the |> #3 |> length))
blanchet@33192
  1328
              (Datatype.get_all thy) [] @
blanchet@33583
  1329
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1330
blanchet@33192
  1331
(* Proof.context -> term list -> const_table *)
blanchet@33192
  1332
fun const_def_table ctxt ts =
blanchet@34126
  1333
  table_for (map prop_of o Nitpick_Defs.get) ctxt
blanchet@33192
  1334
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@33192
  1335
          (map pair_for_prop ts)
blanchet@33192
  1336
(* term list -> const_table *)
blanchet@33192
  1337
fun const_nondef_table ts =
blanchet@33192
  1338
  fold (fn t => append (map (fn s => (s, t)) (Term.add_const_names t []))) ts []
blanchet@33192
  1339
  |> AList.group (op =) |> Symtab.make
blanchet@33192
  1340
(* Proof.context -> const_table *)
blanchet@33192
  1341
val const_simp_table = table_for (map prop_of o Nitpick_Simps.get)
blanchet@33192
  1342
val const_psimp_table = table_for (map prop_of o Nitpick_Psimps.get)
blanchet@33192
  1343
(* Proof.context -> const_table -> const_table *)
blanchet@33192
  1344
fun inductive_intro_table ctxt def_table =
blanchet@33192
  1345
  table_for (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
blanchet@33192
  1346
                                                  def_table o prop_of)
blanchet@33192
  1347
             o Nitpick_Intros.get) ctxt
blanchet@33192
  1348
(* theory -> term list Inttab.table *)
blanchet@33192
  1349
fun ground_theorem_table thy =
blanchet@33192
  1350
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@33192
  1351
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@33192
  1352
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@33192
  1353
blanchet@33192
  1354
val basic_ersatz_table =
blanchet@33192
  1355
  [(@{const_name prod_case}, @{const_name split}),
blanchet@33192
  1356
   (@{const_name card}, @{const_name card'}),
blanchet@33192
  1357
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@33192
  1358
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@33192
  1359
   (@{const_name wf}, @{const_name wf'}),
blanchet@33192
  1360
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@33192
  1361
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@33192
  1362
blanchet@33192
  1363
(* theory -> (string * string) list *)
blanchet@33192
  1364
fun ersatz_table thy =
blanchet@33583
  1365
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@33192
  1366
blanchet@33192
  1367
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
blanchet@33192
  1368
fun add_simps simp_table s eqs =
blanchet@33192
  1369
  Unsynchronized.change simp_table
blanchet@33192
  1370
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@33192
  1371
blanchet@34936
  1372
(* theory -> styp -> term list *)
blanchet@34936
  1373
fun inverse_axioms_for_rep_fun thy (x as (_, T)) =
blanchet@34936
  1374
  let val abs_T = domain_type T in
blanchet@34936
  1375
    typedef_info thy (fst (dest_Type abs_T)) |> the
blanchet@34936
  1376
    |> pairf #Abs_inverse #Rep_inverse
blanchet@34936
  1377
    |> pairself (Refute.specialize_type thy x o prop_of o the)
blanchet@34936
  1378
    ||> single |> op ::
blanchet@34936
  1379
  end
blanchet@35070
  1380
(* theory -> string * typ list -> term list *)
blanchet@35280
  1381
fun optimized_typedef_axioms thy (abs_z as (abs_s, _)) =
blanchet@34936
  1382
  let val abs_T = Type abs_z in
blanchet@33192
  1383
    if is_univ_typedef thy abs_T then
blanchet@33192
  1384
      []
blanchet@33192
  1385
    else case typedef_info thy abs_s of
blanchet@35280
  1386
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@33192
  1387
      let
blanchet@33192
  1388
        val rep_T = instantiate_type thy abs_type abs_T rep_type
blanchet@33192
  1389
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@33192
  1390
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@33192
  1391
        val set_t' =
blanchet@33192
  1392
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@33192
  1393
                      |> Refute.specialize_type thy (dest_Const rep_t)
blanchet@33192
  1394
                      |> HOLogic.dest_mem |> snd
blanchet@33192
  1395
      in
blanchet@33192
  1396
        [HOLogic.all_const abs_T
blanchet@33192
  1397
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@33192
  1398
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@33192
  1399
        |> map HOLogic.mk_Trueprop
blanchet@33192
  1400
      end
blanchet@33192
  1401
    | NONE => []
blanchet@33192
  1402
  end
blanchet@35220
  1403
fun optimized_quot_type_axioms thy stds abs_z =
blanchet@34936
  1404
  let
blanchet@34936
  1405
    val abs_T = Type abs_z
blanchet@34936
  1406
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@34936
  1407
    val equiv_rel = equiv_relation_for_quot_type thy abs_T
blanchet@34936
  1408
    val a_var = Var (("a", 0), abs_T)
blanchet@34936
  1409
    val x_var = Var (("x", 0), rep_T)
blanchet@34936
  1410
    val y_var = Var (("y", 0), rep_T)
blanchet@34936
  1411
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@35220
  1412
    val sel_a_t = select_nth_constr_arg thy stds x a_var 0 rep_T
blanchet@34936
  1413
    val normal_t = Const (@{const_name quot_normal}, rep_T --> rep_T)
blanchet@34936
  1414
    val normal_x = normal_t $ x_var
blanchet@34936
  1415
    val normal_y = normal_t $ y_var
blanchet@34936
  1416
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@34936
  1417
  in
blanchet@34982
  1418
    [Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
blanchet@34936
  1419
     Logic.list_implies
blanchet@34982
  1420
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@34936
  1421
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@34936
  1422
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@34936
  1423
           Logic.mk_equals (normal_x, normal_y)),
blanchet@34936
  1424
     @{const "==>"}
blanchet@34936
  1425
         $ (HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)))
blanchet@34936
  1426
         $ (HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@33864
  1427
  end
blanchet@33192
  1428
blanchet@35220
  1429
(* theory -> (typ option * bool) list -> int * styp -> term *)
blanchet@35220
  1430
fun constr_case_body thy stds (j, (x as (_, T))) =
blanchet@33192
  1431
  let val arg_Ts = binder_types T in
blanchet@35220
  1432
    list_comb (Bound j, map2 (select_nth_constr_arg thy stds x (Bound 0))
blanchet@33192
  1433
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1434
  end
blanchet@35070
  1435
(* hol_context -> typ -> int * styp -> term -> term *)
blanchet@35220
  1436
fun add_constr_case (hol_ctxt as {thy, stds, ...}) res_T (j, x) res_t =
blanchet@34124
  1437
  Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@35220
  1438
  $ discriminate_value hol_ctxt x (Bound 0) $ constr_case_body thy stds (j, x)
blanchet@33580
  1439
  $ res_t
blanchet@35070
  1440
(* hol_context -> typ -> typ -> term *)
blanchet@35220
  1441
fun optimized_case_def (hol_ctxt as {thy, stds, ...}) dataT res_T =
blanchet@33192
  1442
  let
blanchet@35070
  1443
    val xs = datatype_constrs hol_ctxt dataT
blanchet@35179
  1444
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs
blanchet@35179
  1445
    val (xs', x) = split_last xs
blanchet@33192
  1446
  in
blanchet@35220
  1447
    constr_case_body thy stds (1, x)
blanchet@35179
  1448
    |> fold_rev (add_constr_case hol_ctxt res_T) (length xs downto 2 ~~ xs')
blanchet@33192
  1449
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1450
  end
blanchet@33192
  1451
blanchet@35070
  1452
(* hol_context -> string -> typ -> typ -> term -> term *)
blanchet@35220
  1453
fun optimized_record_get (hol_ctxt as {thy, stds, ...}) s rec_T res_T t =
blanchet@35070
  1454
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1455
    case no_of_record_field thy s rec_T of
blanchet@33192
  1456
      ~1 => (case rec_T of
blanchet@33192
  1457
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1458
               let
blanchet@33192
  1459
                 val rec_T' = List.last Ts
blanchet@33192
  1460
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1461
               in
blanchet@35220
  1462
                 select_nth_constr_arg thy stds constr_x t j res_T
blanchet@35070
  1463
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1464
               end
blanchet@33232
  1465
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1466
                                []))
blanchet@35220
  1467
    | j => select_nth_constr_arg thy stds constr_x t j res_T
blanchet@33192
  1468
  end
blanchet@35070
  1469
(* hol_context -> string -> typ -> term -> term -> term *)
blanchet@35220
  1470
fun optimized_record_update (hol_ctxt as {thy, stds, ...}) s rec_T fun_t rec_t =
blanchet@33192
  1471
  let
blanchet@35070
  1472
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1473
    val Ts = binder_types constr_T
blanchet@33192
  1474
    val n = length Ts
blanchet@33192
  1475
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1476
    val ts =
blanchet@35220
  1477
      map2 (fn j => fn T =>
blanchet@35220
  1478
               let val t = select_nth_constr_arg thy stds constr_x rec_t j T in
blanchet@35220
  1479
                 if j = special_j then
blanchet@35220
  1480
                   betapply (fun_t, t)
blanchet@35220
  1481
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1482
                   optimized_record_update hol_ctxt s
blanchet@35220
  1483
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1484
                 else
blanchet@35220
  1485
                   t
blanchet@35220
  1486
               end) (index_seq 0 n) Ts
blanchet@33192
  1487
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1488
blanchet@33192
  1489
(* theory -> const_table -> string * typ -> fixpoint_kind *)
blanchet@33192
  1490
fun fixpoint_kind_of_const thy table x =
blanchet@35220
  1491
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@33192
  1492
    NoFp
blanchet@33192
  1493
  else
blanchet@33192
  1494
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@33192
  1495
    handle Option.Option => NoFp
blanchet@33192
  1496
blanchet@35070
  1497
(* hol_context -> styp -> bool *)
blanchet@35220
  1498
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35220
  1499
                             ...} : hol_context) x =
blanchet@35220
  1500
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35220
  1501
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@35220
  1502
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@35220
  1503
                             ...} : hol_context) x =
blanchet@35220
  1504
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@35220
  1505
                                                     x)))
blanchet@33192
  1506
         [!simp_table, psimp_table]
blanchet@35070
  1507
fun is_inductive_pred hol_ctxt =
blanchet@35070
  1508
  is_real_inductive_pred hol_ctxt andf (not o is_real_equational_fun hol_ctxt)
blanchet@35280
  1509
fun is_equational_fun hol_ctxt =
blanchet@35070
  1510
  (is_real_equational_fun hol_ctxt orf is_real_inductive_pred hol_ctxt
blanchet@33192
  1511
   orf (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1512
blanchet@33192
  1513
(* term * term -> term *)
blanchet@33192
  1514
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
blanchet@33192
  1515
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
blanchet@33192
  1516
  | s_betapply p = betapply p
blanchet@33192
  1517
(* term * term list -> term *)
blanchet@33192
  1518
val s_betapplys = Library.foldl s_betapply
blanchet@33192
  1519
blanchet@33192
  1520
(* term -> term *)
blanchet@33192
  1521
fun lhs_of_equation t =
blanchet@33192
  1522
  case t of
blanchet@33192
  1523
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1524
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1525
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1526
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@33192
  1527
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1528
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1529
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1530
  | _ => NONE
blanchet@33192
  1531
(* theory -> term -> bool *)
blanchet@33192
  1532
fun is_constr_pattern _ (Bound _) = true
blanchet@33864
  1533
  | is_constr_pattern _ (Var _) = true
blanchet@33192
  1534
  | is_constr_pattern thy t =
blanchet@33192
  1535
    case strip_comb t of
blanchet@35280
  1536
      (Const x, args) =>
blanchet@33192
  1537
      is_constr_like thy x andalso forall (is_constr_pattern thy) args
blanchet@33192
  1538
    | _ => false
blanchet@33192
  1539
fun is_constr_pattern_lhs thy t =
blanchet@33192
  1540
  forall (is_constr_pattern thy) (snd (strip_comb t))
blanchet@33192
  1541
fun is_constr_pattern_formula thy t =
blanchet@33192
  1542
  case lhs_of_equation t of
blanchet@33192
  1543
    SOME t' => is_constr_pattern_lhs thy t'
blanchet@33192
  1544
  | NONE => false
blanchet@33192
  1545
blanchet@35070
  1546
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1547
val unfold_max_depth = 255
blanchet@33192
  1548
blanchet@35070
  1549
(* hol_context -> term -> term *)
blanchet@35280
  1550
fun unfold_defs_in_term (hol_ctxt as {thy, stds, fast_descrs, case_names,
blanchet@35280
  1551
                                      def_table, ground_thm_table, ersatz_table,
blanchet@35280
  1552
                                      ...}) =
blanchet@33192
  1553
  let
blanchet@33192
  1554
    (* int -> typ list -> term -> term *)
blanchet@33192
  1555
    fun do_term depth Ts t =
blanchet@33192
  1556
      case t of
blanchet@33192
  1557
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@33192
  1558
                      Type ("fun", [_, ran_T]))) $ t1 =>
blanchet@33192
  1559
        ((if is_number_type thy ran_T then
blanchet@33192
  1560
            let
blanchet@33192
  1561
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1562
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1563
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1564
            in
blanchet@35220
  1565
              if is_integer_like_type ran_T then
blanchet@35220
  1566
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1567
                  Const (s, ran_T)
blanchet@35220
  1568
                else
blanchet@35220
  1569
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1570
              else
blanchet@33192
  1571
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1572
                                  $ Const (s, int_T))
blanchet@33192
  1573
            end
blanchet@33192
  1574
            handle TERM _ => raise SAME ()
blanchet@33192
  1575
          else
blanchet@33192
  1576
            raise SAME ())
blanchet@33192
  1577
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1578
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1579
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1580
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1581
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1582
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1583
      | Const (x as (@{const_name distinct},
blanchet@33192
  1584
               Type ("fun", [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1585
        $ (t1 as _ $ _) =>
blanchet@33192
  1586
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1587
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1588
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1589
        if is_ground_term t1 andalso
blanchet@34936
  1590
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1591
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1592
          do_term depth Ts t2
blanchet@33192
  1593
        else
blanchet@33192
  1594
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1595
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1596
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1597
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1598
      | Const x => do_const depth Ts t x []
blanchet@33192
  1599
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1600
      | Free _ => t
blanchet@33192
  1601
      | Var _ => t
blanchet@33192
  1602
      | Bound _ => t
blanchet@33192
  1603
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1604
    (* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
blanchet@33192
  1605
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1606
        (Abs (Name.uu, body_type T,
blanchet@35220
  1607
              select_nth_constr_arg thy stds x (Bound 0) n res_T), [])
blanchet@33192
  1608
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@35220
  1609
        (select_nth_constr_arg thy stds x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1610
    (* int -> typ list -> term -> styp -> term list -> term *)
blanchet@33192
  1611
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1612
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1613
        SOME s' =>
blanchet@33192
  1614
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1615
      | NONE =>
blanchet@33192
  1616
        let
blanchet@33192
  1617
          val (const, ts) =
blanchet@35220
  1618
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1619
              (Const x, ts)
blanchet@33192
  1620
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1621
              SOME n =>
blanchet@33192
  1622
              let
blanchet@33192
  1623
                val (dataT, res_T) = nth_range_type n T
blanchet@33705
  1624
                                     |> pairf domain_type range_type
blanchet@33192
  1625
              in
blanchet@35070
  1626
                (optimized_case_def hol_ctxt dataT res_T
blanchet@33192
  1627
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1628
              end
blanchet@33192
  1629
            | _ =>
blanchet@35220
  1630
              if is_constr thy stds x then
blanchet@33192
  1631
                (Const x, ts)
blanchet@33581
  1632
              else if is_stale_constr thy x then
blanchet@34936
  1633
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1634
                                     \(\"" ^ s ^ "\")")
blanchet@34936
  1635
              else if is_quot_abs_fun thy x then
blanchet@34936
  1636
                let
blanchet@34936
  1637
                  val rep_T = domain_type T
blanchet@34936
  1638
                  val abs_T = range_type T
blanchet@34936
  1639
                in
blanchet@34936
  1640
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1641
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1642
                               $ (Const (@{const_name quot_normal},
blanchet@34936
  1643
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1644
                end
blanchet@34936
  1645
              else if is_quot_rep_fun thy x then
blanchet@34936
  1646
                let
blanchet@34936
  1647
                  val abs_T = domain_type T
blanchet@34936
  1648
                  val rep_T = range_type T
blanchet@34936
  1649
                  val x' = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1650
                in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
blanchet@33192
  1651
              else if is_record_get thy x then
blanchet@33192
  1652
                case length ts of
blanchet@33192
  1653
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1654
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1655
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1656
              else if is_record_update thy x then
blanchet@33192
  1657
                case length ts of
blanchet@35070
  1658
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1659
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1660
                            (do_term depth Ts (hd ts))
blanchet@33580
  1661
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1662
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@33192
  1663
              else if is_rep_fun thy x then
blanchet@33192
  1664
                let val x' = mate_of_rep_fun thy x in
blanchet@35220
  1665
                  if is_constr thy stds x' then
blanchet@33192
  1666
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1667
                                                    (range_type T)
blanchet@33192
  1668
                  else
blanchet@33192
  1669
                    (Const x, ts)
blanchet@33192
  1670
                end
blanchet@35070
  1671
              else if is_equational_fun hol_ctxt x then
blanchet@33192
  1672
                (Const x, ts)
blanchet@33192
  1673
              else case def_of_const thy def_table x of
blanchet@33192
  1674
                SOME def =>
blanchet@33192
  1675
                if depth > unfold_max_depth then
blanchet@34124
  1676
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1677
                                   "too many nested definitions (" ^
blanchet@34124
  1678
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1679
                                   quote s)
blanchet@33192
  1680
                else if s = @{const_name wfrec'} then
blanchet@33192
  1681
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1682
                else
blanchet@33192
  1683
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1684
              | NONE => (Const x, ts)
blanchet@33192
  1685
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1686
  in do_term 0 [] end
blanchet@33192
  1687
blanchet@35070
  1688
(* hol_context -> typ -> term list *)
blanchet@35220
  1689
fun codatatype_bisim_axioms (hol_ctxt as {thy, stds, ...}) T =
blanchet@33192
  1690
  let
blanchet@35070
  1691
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1692
    val set_T = T --> bool_T
blanchet@33192
  1693
    val iter_T = @{typ bisim_iterator}
blanchet@34124
  1694
    val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1695
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1696
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1697
    val n_var_minus_1 =
blanchet@33192
  1698
      Const (@{const_name Tha}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1699
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1700
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1701
    val x_var = Var (("x", 0), T)
blanchet@33192
  1702
    val y_var = Var (("y", 0), T)
blanchet@33192
  1703
    (* styp -> int -> typ -> term *)
blanchet@33192
  1704
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1705
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1706
       else HOLogic.eq_const nth_T)
blanchet@35220
  1707
      $ select_nth_constr_arg thy stds x x_var n nth_T
blanchet@35220
  1708
      $ select_nth_constr_arg thy stds x y_var n nth_T
blanchet@33192
  1709
    (* styp -> term *)
blanchet@33192
  1710
    fun case_func (x as (_, T)) =
blanchet@33192
  1711
      let
blanchet@33192
  1712
        val arg_Ts = binder_types T
blanchet@33192
  1713
        val core_t =
blanchet@35070
  1714
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1715
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1716
          |> foldr1 s_conj
blanchet@33192
  1717
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1718
  in
blanchet@33192
  1719
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1720
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@35070
  1721
        $ (betapplys (optimized_case_def hol_ctxt T bool_T,
blanchet@33192
  1722
                      map case_func xs @ [x_var]))),
blanchet@33192
  1723
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@34124
  1724
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  1725
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  1726
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1727
  end
blanchet@33192
  1728
blanchet@33192
  1729
exception NO_TRIPLE of unit
blanchet@33192
  1730
blanchet@33192
  1731
(* theory -> styp -> term -> term list * term list * term *)
blanchet@33192
  1732
fun triple_for_intro_rule thy x t =
blanchet@33192
  1733
  let
blanchet@33192
  1734
    val prems = Logic.strip_imp_prems t |> map (ObjectLogic.atomize_term thy)
blanchet@33192
  1735
    val concl = Logic.strip_imp_concl t |> ObjectLogic.atomize_term thy
blanchet@34121
  1736
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@33192
  1737
    (* term -> bool *)
blanchet@34121
  1738
     val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  1739
  in
blanchet@33192
  1740
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1741
  end
blanchet@33192
  1742
blanchet@33192
  1743
(* term -> term *)
blanchet@33192
  1744
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1745
blanchet@33192
  1746
(* indexname * typ -> term list -> term -> term -> term *)
blanchet@33192
  1747
fun wf_constraint_for rel side concl main =
blanchet@33192
  1748
  let
blanchet@33192
  1749
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1750
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1751
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1752
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1753
  in
blanchet@33192
  1754
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1755
                      HOLogic.all_const T
blanchet@33192
  1756
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1757
                  (t, vars)
blanchet@33192
  1758
  end
blanchet@33192
  1759
blanchet@33192
  1760
(* indexname * typ -> term list * term list * term -> term *)
blanchet@33192
  1761
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1762
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1763
blanchet@33192
  1764
(* Proof.context -> Time.time option -> thm
blanchet@33192
  1765
   -> (Proof.context -> tactic -> tactic) -> bool *)
blanchet@33192
  1766
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1767
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1768
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1769
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1770
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1771
blanchet@35181
  1772
val max_cached_wfs = 50
blanchet@35181
  1773
val cached_timeout =
blanchet@35181
  1774
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  1775
val cached_wf_props =
blanchet@35181
  1776
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  1777
krauss@33351
  1778
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1779
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1780
blanchet@35070
  1781
(* hol_context -> const_table -> styp -> bool *)
blanchet@33580
  1782
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  1783
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  1784
         : hol_context) (x as (_, T)) =
blanchet@35220
  1785
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  1786
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  1787
                      [Const x])
blanchet@33192
  1788
  | intro_ts =>
blanchet@33192
  1789
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1790
          |> filter_out (null o #2) of
blanchet@33192
  1791
       [] => true
blanchet@33192
  1792
     | triples =>
blanchet@33192
  1793
       let
blanchet@33192
  1794
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1795
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  1796
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  1797
         val rel = (("R", j), rel_T)
blanchet@33192
  1798
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1799
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1800
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1801
         val _ = if debug then
blanchet@33192
  1802
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1803
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1804
                 else
blanchet@33192
  1805
                   ()
blanchet@33192
  1806
       in
blanchet@35181
  1807
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  1808
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  1809
           ()
blanchet@33557
  1810
         else
blanchet@35181
  1811
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  1812
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  1813
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  1814
           SOME wf => wf
blanchet@33192
  1815
         | NONE =>
blanchet@33192
  1816
           let
blanchet@33192
  1817
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  1818
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  1819
                             termination_tacs
blanchet@35181
  1820
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1821
       end)
blanchet@33192
  1822
    handle List.Empty => false
blanchet@33192
  1823
         | NO_TRIPLE () => false
blanchet@33192
  1824
blanchet@35070
  1825
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  1826
blanchet@35070
  1827
(* hol_context -> styp -> bool *)
blanchet@33192
  1828
fun is_well_founded_inductive_pred
blanchet@35070
  1829
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  1830
        (x as (s, _)) =
blanchet@33192
  1831
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1832
    SOME (SOME b) => b
blanchet@34936
  1833
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  1834
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  1835
           SOME (_, wf) => wf
blanchet@35181
  1836
         | NONE =>
blanchet@35181
  1837
           let
blanchet@35181
  1838
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  1839
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  1840
           in
blanchet@35181
  1841
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  1842
           end
blanchet@33192
  1843
blanchet@35280
  1844
(* typ list -> typ -> term -> term *)
blanchet@35280
  1845
fun ap_curry [_] _ t = t
blanchet@35280
  1846
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  1847
    let val n = length arg_Ts in
blanchet@33192
  1848
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1849
                incr_boundvars n t
blanchet@33192
  1850
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1851
    end
blanchet@33192
  1852
blanchet@33192
  1853
(* int -> term -> int *)
blanchet@33192
  1854
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1855
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  1856
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  1857
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1858
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1859
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1860
blanchet@33192
  1861
(* term -> bool *)
blanchet@33192
  1862
val is_linear_inductive_pred_def =
blanchet@33192
  1863
  let
blanchet@33192
  1864
    (* int -> term -> bool *)
blanchet@33192
  1865
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  1866
        do_disjunct (j + 1) t2
blanchet@33192
  1867
      | do_disjunct j t =
blanchet@33192
  1868
        case num_occs_of_bound_in_term j t of
blanchet@33192
  1869
          0 => true
blanchet@35070
  1870
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  1871
        | _ => false
blanchet@33192
  1872
    (* term -> bool *)
blanchet@33192
  1873
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1874
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  1875
          case length xs of
blanchet@33192
  1876
            1 => false
blanchet@35070
  1877
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  1878
        end
blanchet@33192
  1879
      | do_lfp_def _ = false
blanchet@33192
  1880
  in do_lfp_def o strip_abs_body end
blanchet@33192
  1881
blanchet@33851
  1882
(* int -> int list list *)
blanchet@33851
  1883
fun n_ptuple_paths 0 = []
blanchet@33851
  1884
  | n_ptuple_paths 1 = []
blanchet@33851
  1885
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  1886
(* int -> typ -> typ -> term -> term *)
blanchet@33851
  1887
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  1888
blanchet@33192
  1889
(* term -> term * term *)
blanchet@33192
  1890
val linear_pred_base_and_step_rhss =
blanchet@33192
  1891
  let
blanchet@33192
  1892
    (* term -> term *)
blanchet@33192
  1893
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  1894
        let
blanchet@33192
  1895
          val (xs, body) = strip_abs t2
blanchet@33192
  1896
          val arg_Ts = map snd (tl xs)
blanchet@33192
  1897
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  1898
          val j = length arg_Ts
blanchet@33192
  1899
          (* int -> term -> term *)
blanchet@33192
  1900
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  1901
              Const (@{const_name Ex}, T1)
blanchet@33192
  1902
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  1903
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  1904
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  1905
            | repair_rec j t =
blanchet@33192
  1906
              let val (head, args) = strip_comb t in
blanchet@33192
  1907
                if head = Bound j then
blanchet@33192
  1908
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  1909
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  1910
                else
blanchet@33192
  1911
                  t
blanchet@33192
  1912
              end
blanchet@33192
  1913
          val (nonrecs, recs) =
blanchet@34121
  1914
            List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
blanchet@35070
  1915
                           (disjuncts_of body)
blanchet@33192
  1916
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  1917
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  1918
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  1919
        in
blanchet@33192
  1920
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  1921
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  1922
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  1923
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  1924
        end
blanchet@33192
  1925
      | aux t =
blanchet@33232
  1926
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  1927
  in aux end
blanchet@33192
  1928
blanchet@35070
  1929
(* hol_context -> styp -> term -> term *)
blanchet@35280
  1930
fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (s, T) def =
blanchet@33192
  1931
  let
blanchet@33192
  1932
    val j = maxidx_of_term def + 1
blanchet@33192
  1933
    val (outer, fp_app) = strip_abs def
blanchet@33192
  1934
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1935
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  1936
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  1937
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  1938
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  1939
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  1940
    val set_T = tuple_T --> bool_T
blanchet@33192
  1941
    val curried_T = tuple_T --> set_T
blanchet@33192
  1942
    val uncurried_T = Type ("*", [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  1943
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  1944
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  1945
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  1946
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1947
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  1948
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  1949
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  1950
                  |> HOLogic.mk_Trueprop
blanchet@33192
  1951
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  1952
  in
blanchet@33192
  1953
    list_abs (outer,
blanchet@33192
  1954
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  1955
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  1956
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  1957
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  1958
              $ list_comb (Const base_x, outer_bounds)
blanchet@35280
  1959
              |> ap_curry tuple_arg_Ts tuple_T)
blanchet@35070
  1960
    |> unfold_defs_in_term hol_ctxt
blanchet@33192
  1961
  end
blanchet@33192
  1962
blanchet@35070
  1963
(* hol_context -> bool -> styp -> term *)
blanchet@35070
  1964
fun unrolled_inductive_pred_const (hol_ctxt as {thy, star_linear_preds,
blanchet@33192
  1965
                                                def_table, simp_table, ...})
blanchet@33192
  1966
                                  gfp (x as (s, T)) =
blanchet@33192
  1967
  let
blanchet@33192
  1968
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  1969
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  1970
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  1971
    val def = the (def_of_const thy def_table x)
blanchet@33192
  1972
  in
blanchet@35070
  1973
    if is_equational_fun hol_ctxt x' then
blanchet@33192
  1974
      unrolled_const (* already done *)
blanchet@34936
  1975
    else if not gfp andalso is_linear_inductive_pred_def def andalso
blanchet@34936
  1976
         star_linear_preds then
blanchet@35070
  1977
      starred_linear_pred_const hol_ctxt x def
blanchet@33192
  1978
    else
blanchet@33192
  1979
      let
blanchet@33192
  1980
        val j = maxidx_of_term def + 1
blanchet@33192
  1981
        val (outer, fp_app) = strip_abs def
blanchet@33192
  1982
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  1983
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  1984
        val next = suc_const iter_T $ cur
blanchet@33192
  1985
        val rhs = case fp_app of
blanchet@33192
  1986
                    Const _ $ t =>
blanchet@33192
  1987
                    betapply (t, list_comb (Const x', next :: outer_bounds))
blanchet@33232
  1988
                  | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_\
blanchet@33232
  1989
                                     \const", [fp_app])
blanchet@33192
  1990
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  1991
        val all = outer @ inner
blanchet@33192
  1992
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  1993
        val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  1994
        val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
blanchet@33192
  1995
                 |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  1996
        val _ = add_simps simp_table s' [eq]
blanchet@33192
  1997
      in unrolled_const end
blanchet@33192
  1998
  end
blanchet@33192
  1999
blanchet@35070
  2000
(* hol_context -> styp -> term *)
blanchet@35070
  2001
fun raw_inductive_pred_axiom ({thy, def_table, ...} : hol_context) x =
blanchet@33192
  2002
  let
blanchet@33192
  2003
    val def = the (def_of_const thy def_table x)
blanchet@33192
  2004
    val (outer, fp_app) = strip_abs def
blanchet@33192
  2005
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2006
    val rhs = case fp_app of
blanchet@33192
  2007
                Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
blanchet@33232
  2008
              | _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom",
blanchet@33192
  2009
                                 [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 j = maxidx_of_term def + 1
blanchet@33192
  2014
    val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  2015
  in
blanchet@33192
  2016
    HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
blanchet@33192
  2017
    |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  2018
  end
blanchet@35070
  2019
fun inductive_pred_axiom hol_ctxt (x as (s, T)) =
blanchet@33192
  2020
  if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
blanchet@33192
  2021
    let val x' = (after_name_sep s, T) in
blanchet@35070
  2022
      raw_inductive_pred_axiom hol_ctxt x' |> subst_atomic [(Const x', Const x)]
blanchet@33192
  2023
    end
blanchet@33192
  2024
  else
blanchet@35070
  2025
    raw_inductive_pred_axiom hol_ctxt x
blanchet@33192
  2026
blanchet@35070
  2027
(* hol_context -> styp -> term list *)
blanchet@35220
  2028
fun raw_equational_fun_axioms (hol_ctxt as {thy, stds, fast_descrs, simp_table,
blanchet@35280
  2029
                                            psimp_table, ...}) x =
blanchet@35220
  2030
  case def_props_for_const thy stds fast_descrs (!simp_table) x of
blanchet@35220
  2031
    [] => (case def_props_for_const thy stds fast_descrs psimp_table x of
blanchet@35070
  2032
             [] => [inductive_pred_axiom hol_ctxt x]
blanchet@33192
  2033
           | psimps => psimps)
blanchet@33192
  2034
  | simps => simps
blanchet@33192
  2035
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
blanchet@35070
  2036
(* hol_context -> styp -> bool *)
blanchet@35070
  2037
fun is_equational_fun_surely_complete hol_ctxt x =
blanchet@35070
  2038
  case raw_equational_fun_axioms hol_ctxt x of
blanchet@35070
  2039
    [@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)] =>
blanchet@35070
  2040
    strip_comb t1 |> snd |> forall is_Var
blanchet@35070
  2041
  | _ => false
blanchet@33192
  2042
blanchet@33192
  2043
(* term list -> term list *)
blanchet@33556
  2044
fun merge_type_vars_in_terms ts =
blanchet@33192
  2045
  let
blanchet@33192
  2046
    (* typ -> (sort * string) list -> (sort * string) list *)
blanchet@33192
  2047
    fun add_type (TFree (s, S)) table =
blanchet@33192
  2048
        (case AList.lookup (op =) table S of
blanchet@33192
  2049
           SOME s' =>
blanchet@33192
  2050
           if string_ord (s', s) = LESS then AList.update (op =) (S, s') table
blanchet@33192
  2051
           else table
blanchet@33192
  2052
         | NONE => (S, s) :: table)
blanchet@33192
  2053
      | add_type _ table = table
blanchet@33192
  2054
    val table = fold (fold_types (fold_atyps add_type)) ts []
blanchet@33192
  2055
    (* typ -> typ *)
blanchet@35280
  2056
    fun coalesce (TFree (_, S)) = TFree (AList.lookup (op =) table S |> the, S)
blanchet@33192
  2057
      | coalesce T = T
blanchet@33192
  2058
  in map (map_types (map_atyps coalesce)) ts end
blanchet@33192
  2059
blanchet@35190
  2060
(* hol_context -> bool -> typ -> typ list -> typ list *)
blanchet@35190
  2061
fun add_ground_types hol_ctxt binarize =
blanchet@35190
  2062
  let
blanchet@35190
  2063
    fun aux T accum =
blanchet@35190
  2064
      case T of
blanchet@35190
  2065
        Type ("fun", Ts) => fold aux Ts accum
blanchet@35190
  2066
      | Type ("*", Ts) => fold aux Ts accum
blanchet@35190
  2067
      | Type (@{type_name itself}, [T1]) => aux T1 accum
blanchet@35190
  2068
      | Type (_, Ts) =>
blanchet@35190
  2069
        if member (op =) (@{typ prop} :: @{typ bool} :: @{typ unit} :: accum)
blanchet@35190
  2070
                  T then
blanchet@35190
  2071
          accum
blanchet@35190
  2072
        else
blanchet@35190
  2073
          T :: accum
blanchet@35190
  2074
          |> fold aux (case binarized_and_boxed_datatype_constrs hol_ctxt
blanchet@35190
  2075
                                                                 binarize T of
blanchet@35190
  2076
                         [] => Ts
blanchet@35190
  2077
                       | xs => map snd xs)
blanchet@35190
  2078
      | _ => insert (op =) T accum
blanchet@35190
  2079
  in aux end
blanchet@33192
  2080
blanchet@35190
  2081
(* hol_context -> bool -> typ -> typ list *)
blanchet@35190
  2082
fun ground_types_in_type hol_ctxt binarize T =
blanchet@35190
  2083
  add_ground_types hol_ctxt binarize T []
blanchet@35070
  2084
(* hol_context -> term list -> typ list *)
blanchet@35190
  2085
fun ground_types_in_terms hol_ctxt binarize ts =
blanchet@35190
  2086
  fold (fold_types (add_ground_types hol_ctxt binarize)) ts []
blanchet@33192
  2087
blanchet@33192
  2088
(* theory -> const_table -> styp -> int list *)
blanchet@33192
  2089
fun const_format thy def_table (x as (s, T)) =
blanchet@33192
  2090
  if String.isPrefix unrolled_prefix s then
blanchet@33192
  2091
    const_format thy def_table (original_name s, range_type T)
blanchet@33192
  2092
  else if String.isPrefix skolem_prefix s then
blanchet@33192
  2093
    let
blanchet@33192
  2094
      val k = unprefix skolem_prefix s
blanchet@33192
  2095
              |> strip_first_name_sep |> fst |> space_explode "@"
blanchet@33192
  2096
              |> hd |> Int.fromString |> the
blanchet@33192
  2097
    in [k, num_binder_types T - k] end
blanchet@33192
  2098
  else if original_name s <> s then
blanchet@33192
  2099
    [num_binder_types T]
blanchet@33192
  2100
  else case def_of_const thy def_table x of
blanchet@33192
  2101
    SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
blanchet@33192
  2102
                 let val k = length (strip_abs_vars t') in
blanchet@33192
  2103
                   [k, num_binder_types T - k]
blanchet@33192
  2104
                 end
blanchet@33192
  2105
               else
blanchet@33192
  2106
                 [num_binder_types T]
blanchet@33192
  2107
  | NONE => [num_binder_types T]
blanchet@33192
  2108
(* int list -> int list -> int list *)
blanchet@33192
  2109
fun intersect_formats _ [] = []
blanchet@33192
  2110
  | intersect_formats [] _ = []
blanchet@33192
  2111
  | intersect_formats ks1 ks2 =
blanchet@33192
  2112
    let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
blanchet@33192
  2113
      intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
blanchet@33192
  2114
                        (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
blanchet@33192
  2115
      [Int.min (k1, k2)]
blanchet@33192
  2116
    end
blanchet@33192
  2117
blanchet@33192
  2118
(* theory -> const_table -> (term option * int list) list -> term -> int list *)
blanchet@33192
  2119
fun lookup_format thy def_table formats t =
blanchet@33192
  2120
  case AList.lookup (fn (SOME x, SOME y) =>
blanchet@33192
  2121
                        (term_match thy) (x, y) | _ => false)
blanchet@33192
  2122
                    formats (SOME t) of
blanchet@33192
  2123
    SOME format => format
blanchet@33192
  2124
  | NONE => let val format = the (AList.lookup (op =) formats NONE) in
blanchet@33192
  2125
              case t of
blanchet@33192
  2126
                Const x => intersect_formats format
blanchet@33192
  2127
                                             (const_format thy def_table x)
blanchet@33192
  2128
              | _ => format