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(* Title: HOL/Tools/Nitpick/nitpick_hol.ML
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Author: Jasmin Blanchette, TU Muenchen
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Copyright 2008, 2009, 2010
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Auxiliary HOL-related functions used by Nitpick.
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*)
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signature NITPICK_HOL =
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sig
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type styp = Nitpick_Util.styp
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type const_table = term list Symtab.table
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type special_fun = (styp * int list * term list) * styp
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type unrolled = styp * styp
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type wf_cache = (styp * (bool * bool)) list
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type extended_context = {
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thy: theory,
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ctxt: Proof.context,
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max_bisim_depth: int,
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boxes: (typ option * bool option) list,
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stds: (typ option * bool) list,
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wfs: (styp option * bool option) list,
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user_axioms: bool option,
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debug: bool,
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binary_ints: bool option,
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destroy_constrs: bool,
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specialize: bool,
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skolemize: bool,
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star_linear_preds: bool,
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uncurry: bool,
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fast_descrs: bool,
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tac_timeout: Time.time option,
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evals: term list,
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case_names: (string * int) list,
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def_table: const_table,
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nondef_table: const_table,
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user_nondefs: term list,
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simp_table: const_table Unsynchronized.ref,
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psimp_table: const_table,
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intro_table: const_table,
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ground_thm_table: term list Inttab.table,
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ersatz_table: (string * string) list,
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skolems: (string * string list) list Unsynchronized.ref,
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special_funs: special_fun list Unsynchronized.ref,
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unrolled_preds: unrolled list Unsynchronized.ref,
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wf_cache: wf_cache Unsynchronized.ref,
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constr_cache: (typ * styp list) list Unsynchronized.ref}
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val name_sep : string
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val numeral_prefix : string
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val skolem_prefix : string
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val eval_prefix : string
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val original_name : string -> string
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val s_conj : term * term -> term
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val unbit_and_unbox_type : typ -> typ
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val string_for_type : Proof.context -> typ -> string
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val prefix_name : string -> string -> string
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val shortest_name : string -> string
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val short_name : string -> string
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val shorten_names_in_term : term -> term
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val type_match : theory -> typ * typ -> bool
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val const_match : theory -> styp * styp -> bool
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val term_match : theory -> term * term -> bool
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val is_TFree : typ -> bool
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val is_higher_order_type : typ -> bool
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val is_fun_type : typ -> bool
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val is_set_type : typ -> bool
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val is_pair_type : typ -> bool
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val is_lfp_iterator_type : typ -> bool
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val is_gfp_iterator_type : typ -> bool
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val is_fp_iterator_type : typ -> bool
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val is_boolean_type : typ -> bool
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val is_integer_type : typ -> bool
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val is_bit_type : typ -> bool
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val is_word_type : typ -> bool
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val is_record_type : typ -> bool
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val is_number_type : theory -> typ -> bool
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val const_for_iterator_type : typ -> styp
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val nth_range_type : int -> typ -> typ
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val num_factors_in_type : typ -> int
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val num_binder_types : typ -> int
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val curried_binder_types : typ -> typ list
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val mk_flat_tuple : typ -> term list -> term
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val dest_n_tuple : int -> term -> term list
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val instantiate_type : theory -> typ -> typ -> typ -> typ
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val is_real_datatype : theory -> string -> bool
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val is_quot_type : theory -> typ -> bool
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val is_codatatype : theory -> typ -> bool
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val is_pure_typedef : theory -> typ -> bool
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val is_univ_typedef : theory -> typ -> bool
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val is_datatype : theory -> typ -> bool
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val is_record_constr : styp -> bool
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val is_record_get : theory -> styp -> bool
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val is_record_update : theory -> styp -> bool
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val is_abs_fun : theory -> styp -> bool
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val is_rep_fun : theory -> styp -> bool
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val is_quot_abs_fun : Proof.context -> styp -> bool
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val is_quot_rep_fun : Proof.context -> styp -> bool
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val is_constr : theory -> styp -> bool
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val is_stale_constr : theory -> styp -> bool
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val is_sel : string -> bool
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val is_sel_like_and_no_discr : string -> bool
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val discr_for_constr : styp -> styp
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val num_sels_for_constr_type : typ -> int
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val nth_sel_name_for_constr_name : string -> int -> string
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val nth_sel_for_constr : styp -> int -> styp
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val boxed_nth_sel_for_constr : extended_context -> styp -> int -> styp
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val sel_no_from_name : string -> int
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val eta_expand : typ list -> term -> int -> term
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val extensionalize : term -> term
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val distinctness_formula : typ -> term list -> term
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val register_frac_type : string -> (string * string) list -> theory -> theory
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val unregister_frac_type : string -> theory -> theory
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val register_codatatype : typ -> string -> styp list -> theory -> theory
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val unregister_codatatype : typ -> theory -> theory
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val datatype_constrs : extended_context -> typ -> styp list
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val boxed_datatype_constrs : extended_context -> typ -> styp list
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val num_datatype_constrs : extended_context -> typ -> int
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val constr_name_for_sel_like : string -> string
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val boxed_constr_for_sel : extended_context -> styp -> styp
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val card_of_type : (typ * int) list -> typ -> int
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val bounded_card_of_type : int -> int -> (typ * int) list -> typ -> int
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val bounded_exact_card_of_type :
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extended_context -> int -> int -> (typ * int) list -> typ -> int
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val is_finite_type : extended_context -> typ -> bool
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val all_axioms_of : theory -> term list * term list * term list
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val arity_of_built_in_const : bool -> styp -> int option
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val is_built_in_const : bool -> styp -> bool
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val case_const_names : theory -> (string * int) list
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val const_def_table : Proof.context -> term list -> const_table
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val const_nondef_table : term list -> const_table
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val const_simp_table : Proof.context -> const_table
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val const_psimp_table : Proof.context -> const_table
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val inductive_intro_table : Proof.context -> const_table -> const_table
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val ground_theorem_table : theory -> term list Inttab.table
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val ersatz_table : theory -> (string * string) list
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val def_of_const : theory -> const_table -> styp -> term option
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val is_inductive_pred : extended_context -> styp -> bool
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val is_constr_pattern_lhs : theory -> term -> bool
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val is_constr_pattern_formula : theory -> term -> bool
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val merge_type_vars_in_terms : term list -> term list
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val ground_types_in_type : extended_context -> typ -> typ list
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val ground_types_in_terms : extended_context -> term list -> typ list
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val format_type : int list -> int list -> typ -> typ
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val format_term_type :
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theory -> const_table -> (term option * int list) list -> term -> typ
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val user_friendly_const :
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extended_context -> string * string -> (term option * int list) list
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-> styp -> term * typ
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val assign_operator_for_const : styp -> string
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val preprocess_term :
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extended_context -> term -> ((term list * term list) * (bool * bool)) * term
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end;
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structure Nitpick_HOL : NITPICK_HOL =
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struct
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open Nitpick_Util
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type const_table = term list Symtab.table
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type special_fun = (styp * int list * term list) * styp
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type unrolled = styp * styp
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type wf_cache = (styp * (bool * bool)) list
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type extended_context = {
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thy: theory,
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ctxt: Proof.context,
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max_bisim_depth: int,
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boxes: (typ option * bool option) list,
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stds: (typ option * bool) list,
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wfs: (styp option * bool option) list,
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user_axioms: bool option,
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debug: bool,
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binary_ints: bool option,
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destroy_constrs: bool,
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specialize: bool,
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skolemize: bool,
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star_linear_preds: bool,
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uncurry: bool,
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fast_descrs: bool,
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tac_timeout: Time.time option,
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evals: term list,
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case_names: (string * int) list,
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def_table: const_table,
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nondef_table: const_table,
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user_nondefs: term list,
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simp_table: const_table Unsynchronized.ref,
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psimp_table: const_table,
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intro_table: const_table,
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ground_thm_table: term list Inttab.table,
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ersatz_table: (string * string) list,
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skolems: (string * string list) list Unsynchronized.ref,
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special_funs: special_fun list Unsynchronized.ref,
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unrolled_preds: unrolled list Unsynchronized.ref,
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wf_cache: wf_cache Unsynchronized.ref,
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constr_cache: (typ * styp list) list Unsynchronized.ref}
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structure Data = Theory_Data(
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type T = {frac_types: (string * (string * string) list) list,
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codatatypes: (string * (string * styp list)) list}
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val empty = {frac_types = [], codatatypes = []}
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val extend = I
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fun merge ({frac_types = fs1, codatatypes = cs1},
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{frac_types = fs2, codatatypes = cs2}) : T =
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{frac_types = AList.merge (op =) (K true) (fs1, fs2),
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codatatypes = AList.merge (op =) (K true) (cs1, cs2)})
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val name_sep = "$"
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val numeral_prefix = nitpick_prefix ^ "num" ^ name_sep
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val sel_prefix = nitpick_prefix ^ "sel"
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val discr_prefix = nitpick_prefix ^ "is" ^ name_sep
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val set_prefix = nitpick_prefix ^ "set" ^ name_sep
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val lfp_iterator_prefix = nitpick_prefix ^ "lfpit" ^ name_sep
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val gfp_iterator_prefix = nitpick_prefix ^ "gfpit" ^ name_sep
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val nwf_prefix = nitpick_prefix ^ "nwf" ^ name_sep
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val unrolled_prefix = nitpick_prefix ^ "unroll" ^ name_sep
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val base_prefix = nitpick_prefix ^ "base" ^ name_sep
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val step_prefix = nitpick_prefix ^ "step" ^ name_sep
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val ubfp_prefix = nitpick_prefix ^ "ubfp" ^ name_sep
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val lbfp_prefix = nitpick_prefix ^ "lbfp" ^ name_sep
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val skolem_prefix = nitpick_prefix ^ "sk"
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val special_prefix = nitpick_prefix ^ "sp"
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val uncurry_prefix = nitpick_prefix ^ "unc"
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val eval_prefix = nitpick_prefix ^ "eval"
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val bound_var_prefix = "b"
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val cong_var_prefix = "c"
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val iter_var_prefix = "i"
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val val_var_prefix = nitpick_prefix ^ "v"
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val arg_var_prefix = "x"
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(* int -> string *)
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fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
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fun special_prefix_for j = special_prefix ^ string_of_int j ^ name_sep
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(* int -> int -> string *)
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fun skolem_prefix_for k j =
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skolem_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
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fun uncurry_prefix_for k j =
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uncurry_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
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(* string -> string * string *)
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val strip_first_name_sep =
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Substring.full #> Substring.position name_sep ##> Substring.triml 1
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#> pairself Substring.string
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(* string -> string *)
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fun original_name s =
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if String.isPrefix nitpick_prefix s then
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case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
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else
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s
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val after_name_sep = snd o strip_first_name_sep
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(* 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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257 |
else HOLogic.mk_conj (t1, t2)
|
blanchet@34985
|
258 |
fun s_disj (t1, @{const False}) = t1
|
blanchet@34985
|
259 |
| s_disj (@{const False}, t2) = t2
|
blanchet@34985
|
260 |
| s_disj (t1, t2) =
|
blanchet@34985
|
261 |
if t1 = @{const True} orelse t2 = @{const True} then @{const True}
|
blanchet@34985
|
262 |
else HOLogic.mk_disj (t1, t2)
|
blanchet@34985
|
263 |
(* term -> term -> term *)
|
blanchet@34985
|
264 |
fun mk_exists v t =
|
blanchet@34985
|
265 |
HOLogic.exists_const (fastype_of v) $ lambda v (incr_boundvars 1 t)
|
blanchet@34985
|
266 |
|
blanchet@34985
|
267 |
(* term -> term -> term list *)
|
blanchet@34985
|
268 |
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
|
blanchet@34985
|
269 |
if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
|
blanchet@34985
|
270 |
| strip_connective _ t = [t]
|
blanchet@34985
|
271 |
(* term -> term list * term *)
|
blanchet@34985
|
272 |
fun strip_any_connective (t as (t0 $ t1 $ t2)) =
|
blanchet@34985
|
273 |
if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
|
blanchet@34985
|
274 |
(strip_connective t0 t, t0)
|
blanchet@34985
|
275 |
else
|
blanchet@34985
|
276 |
([t], @{const Not})
|
blanchet@34985
|
277 |
| strip_any_connective t = ([t], @{const Not})
|
blanchet@34985
|
278 |
(* term -> term list *)
|
blanchet@34985
|
279 |
val conjuncts = strip_connective @{const "op &"}
|
blanchet@34985
|
280 |
val disjuncts = strip_connective @{const "op |"}
|
blanchet@34985
|
281 |
|
blanchet@33192
|
282 |
(* When you add constants to these lists, make sure to handle them in
|
blanchet@33224
|
283 |
"Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
|
blanchet@33192
|
284 |
well. *)
|
blanchet@33192
|
285 |
val built_in_consts =
|
blanchet@33192
|
286 |
[(@{const_name all}, 1),
|
blanchet@33192
|
287 |
(@{const_name "=="}, 2),
|
blanchet@33192
|
288 |
(@{const_name "==>"}, 2),
|
blanchet@33192
|
289 |
(@{const_name Pure.conjunction}, 2),
|
blanchet@33192
|
290 |
(@{const_name Trueprop}, 1),
|
blanchet@33192
|
291 |
(@{const_name Not}, 1),
|
blanchet@33192
|
292 |
(@{const_name False}, 0),
|
blanchet@33192
|
293 |
(@{const_name True}, 0),
|
blanchet@33192
|
294 |
(@{const_name All}, 1),
|
blanchet@33192
|
295 |
(@{const_name Ex}, 1),
|
blanchet@33192
|
296 |
(@{const_name "op ="}, 2),
|
blanchet@33192
|
297 |
(@{const_name "op &"}, 2),
|
blanchet@33192
|
298 |
(@{const_name "op |"}, 2),
|
blanchet@33192
|
299 |
(@{const_name "op -->"}, 2),
|
blanchet@33192
|
300 |
(@{const_name If}, 3),
|
blanchet@33192
|
301 |
(@{const_name Let}, 2),
|
blanchet@33192
|
302 |
(@{const_name Unity}, 0),
|
blanchet@33192
|
303 |
(@{const_name Pair}, 2),
|
blanchet@33192
|
304 |
(@{const_name fst}, 1),
|
blanchet@33192
|
305 |
(@{const_name snd}, 1),
|
blanchet@33192
|
306 |
(@{const_name Id}, 0),
|
blanchet@33192
|
307 |
(@{const_name insert}, 2),
|
blanchet@33192
|
308 |
(@{const_name converse}, 1),
|
blanchet@33192
|
309 |
(@{const_name trancl}, 1),
|
blanchet@33192
|
310 |
(@{const_name rel_comp}, 2),
|
blanchet@33192
|
311 |
(@{const_name image}, 2),
|
blanchet@33192
|
312 |
(@{const_name Suc}, 0),
|
blanchet@33192
|
313 |
(@{const_name finite}, 1),
|
blanchet@33192
|
314 |
(@{const_name nat}, 0),
|
blanchet@33192
|
315 |
(@{const_name zero_nat_inst.zero_nat}, 0),
|
blanchet@33192
|
316 |
(@{const_name one_nat_inst.one_nat}, 0),
|
blanchet@33192
|
317 |
(@{const_name plus_nat_inst.plus_nat}, 0),
|
blanchet@33192
|
318 |
(@{const_name minus_nat_inst.minus_nat}, 0),
|
blanchet@33192
|
319 |
(@{const_name times_nat_inst.times_nat}, 0),
|
blanchet@33192
|
320 |
(@{const_name div_nat_inst.div_nat}, 0),
|
blanchet@33192
|
321 |
(@{const_name ord_nat_inst.less_nat}, 2),
|
blanchet@33192
|
322 |
(@{const_name ord_nat_inst.less_eq_nat}, 2),
|
blanchet@33192
|
323 |
(@{const_name nat_gcd}, 0),
|
blanchet@33192
|
324 |
(@{const_name nat_lcm}, 0),
|
blanchet@33192
|
325 |
(@{const_name zero_int_inst.zero_int}, 0),
|
blanchet@33192
|
326 |
(@{const_name one_int_inst.one_int}, 0),
|
blanchet@33192
|
327 |
(@{const_name plus_int_inst.plus_int}, 0),
|
blanchet@33192
|
328 |
(@{const_name minus_int_inst.minus_int}, 0),
|
blanchet@33192
|
329 |
(@{const_name times_int_inst.times_int}, 0),
|
blanchet@33192
|
330 |
(@{const_name div_int_inst.div_int}, 0),
|
blanchet@33562
|
331 |
(@{const_name uminus_int_inst.uminus_int}, 0),
|
blanchet@33192
|
332 |
(@{const_name ord_int_inst.less_int}, 2),
|
blanchet@33192
|
333 |
(@{const_name ord_int_inst.less_eq_int}, 2),
|
blanchet@34923
|
334 |
(@{const_name unknown}, 0),
|
blanchet@34923
|
335 |
(@{const_name is_unknown}, 1),
|
blanchet@33192
|
336 |
(@{const_name Tha}, 1),
|
blanchet@33192
|
337 |
(@{const_name Frac}, 0),
|
blanchet@33192
|
338 |
(@{const_name norm_frac}, 0)]
|
blanchet@33192
|
339 |
val built_in_descr_consts =
|
blanchet@33192
|
340 |
[(@{const_name The}, 1),
|
blanchet@33192
|
341 |
(@{const_name Eps}, 1)]
|
blanchet@33192
|
342 |
val built_in_typed_consts =
|
blanchet@34121
|
343 |
[((@{const_name of_nat}, nat_T --> int_T), 0),
|
blanchet@34121
|
344 |
((@{const_name of_nat}, @{typ "unsigned_bit word => signed_bit word"}), 0)]
|
blanchet@33192
|
345 |
val built_in_set_consts =
|
haftmann@35028
|
346 |
[(@{const_name semilattice_inf_fun_inst.inf_fun}, 2),
|
haftmann@35028
|
347 |
(@{const_name semilattice_sup_fun_inst.sup_fun}, 2),
|
blanchet@33192
|
348 |
(@{const_name minus_fun_inst.minus_fun}, 2),
|
blanchet@33192
|
349 |
(@{const_name ord_fun_inst.less_eq_fun}, 2)]
|
blanchet@33192
|
350 |
|
blanchet@33192
|
351 |
(* typ -> typ *)
|
blanchet@34121
|
352 |
fun unbit_type @{typ "unsigned_bit word"} = nat_T
|
blanchet@34121
|
353 |
| unbit_type @{typ "signed_bit word"} = int_T
|
blanchet@34121
|
354 |
| unbit_type @{typ bisim_iterator} = nat_T
|
blanchet@34121
|
355 |
| unbit_type (Type (s, Ts as _ :: _)) = Type (s, map unbit_type Ts)
|
blanchet@34121
|
356 |
| unbit_type T = T
|
blanchet@34121
|
357 |
fun unbit_and_unbox_type (Type (@{type_name fun_box}, Ts)) =
|
blanchet@34121
|
358 |
unbit_and_unbox_type (Type ("fun", Ts))
|
blanchet@34121
|
359 |
| unbit_and_unbox_type (Type (@{type_name pair_box}, Ts)) =
|
blanchet@34121
|
360 |
Type ("*", map unbit_and_unbox_type Ts)
|
blanchet@34121
|
361 |
| unbit_and_unbox_type @{typ "unsigned_bit word"} = nat_T
|
blanchet@34121
|
362 |
| unbit_and_unbox_type @{typ "signed_bit word"} = int_T
|
blanchet@34121
|
363 |
| unbit_and_unbox_type @{typ bisim_iterator} = nat_T
|
blanchet@34121
|
364 |
| unbit_and_unbox_type (Type (s, Ts as _ :: _)) =
|
blanchet@34121
|
365 |
Type (s, map unbit_and_unbox_type Ts)
|
blanchet@34121
|
366 |
| unbit_and_unbox_type T = T
|
blanchet@33192
|
367 |
(* Proof.context -> typ -> string *)
|
blanchet@34121
|
368 |
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unbit_and_unbox_type
|
blanchet@33192
|
369 |
|
blanchet@33192
|
370 |
(* string -> string -> string *)
|
blanchet@33192
|
371 |
val prefix_name = Long_Name.qualify o Long_Name.base_name
|
blanchet@33192
|
372 |
(* string -> string *)
|
blanchet@34118
|
373 |
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
|
blanchet@33192
|
374 |
(* string -> term -> term *)
|
blanchet@33192
|
375 |
val prefix_abs_vars = Term.map_abs_vars o prefix_name
|
blanchet@33192
|
376 |
(* term -> term *)
|
blanchet@34118
|
377 |
val shorten_abs_vars = Term.map_abs_vars shortest_name
|
blanchet@33192
|
378 |
(* string -> string *)
|
blanchet@34118
|
379 |
fun short_name s =
|
blanchet@33192
|
380 |
case space_explode name_sep s of
|
blanchet@33192
|
381 |
[_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
|
blanchet@34118
|
382 |
| ss => map shortest_name ss |> space_implode "_"
|
blanchet@34118
|
383 |
(* typ -> typ *)
|
blanchet@34118
|
384 |
fun shorten_names_in_type (Type (s, Ts)) =
|
blanchet@34118
|
385 |
Type (short_name s, map shorten_names_in_type Ts)
|
blanchet@34118
|
386 |
| shorten_names_in_type T = T
|
blanchet@33192
|
387 |
(* term -> term *)
|
blanchet@34118
|
388 |
val shorten_names_in_term =
|
blanchet@34118
|
389 |
map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
|
blanchet@34118
|
390 |
#> map_types shorten_names_in_type
|
blanchet@33192
|
391 |
|
blanchet@33192
|
392 |
(* theory -> typ * typ -> bool *)
|
blanchet@33192
|
393 |
fun type_match thy (T1, T2) =
|
blanchet@33192
|
394 |
(Sign.typ_match thy (T2, T1) Vartab.empty; true)
|
blanchet@33192
|
395 |
handle Type.TYPE_MATCH => false
|
blanchet@33192
|
396 |
(* theory -> styp * styp -> bool *)
|
blanchet@33192
|
397 |
fun const_match thy ((s1, T1), (s2, T2)) =
|
blanchet@33192
|
398 |
s1 = s2 andalso type_match thy (T1, T2)
|
blanchet@33192
|
399 |
(* theory -> term * term -> bool *)
|
blanchet@33192
|
400 |
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
|
blanchet@33192
|
401 |
| term_match thy (Free (s1, T1), Free (s2, T2)) =
|
blanchet@34118
|
402 |
const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
|
blanchet@33192
|
403 |
| term_match thy (t1, t2) = t1 aconv t2
|
blanchet@33192
|
404 |
|
blanchet@33192
|
405 |
(* typ -> bool *)
|
blanchet@33192
|
406 |
fun is_TFree (TFree _) = true
|
blanchet@33192
|
407 |
| is_TFree _ = false
|
blanchet@33192
|
408 |
fun is_higher_order_type (Type ("fun", _)) = true
|
blanchet@33192
|
409 |
| is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
|
blanchet@33192
|
410 |
| is_higher_order_type _ = false
|
blanchet@33192
|
411 |
fun is_fun_type (Type ("fun", _)) = true
|
blanchet@33192
|
412 |
| is_fun_type _ = false
|
blanchet@33192
|
413 |
fun is_set_type (Type ("fun", [_, @{typ bool}])) = true
|
blanchet@33192
|
414 |
| is_set_type _ = false
|
blanchet@33192
|
415 |
fun is_pair_type (Type ("*", _)) = true
|
blanchet@33192
|
416 |
| is_pair_type _ = false
|
blanchet@33192
|
417 |
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
|
blanchet@33192
|
418 |
| is_lfp_iterator_type _ = false
|
blanchet@33192
|
419 |
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
|
blanchet@33192
|
420 |
| is_gfp_iterator_type _ = false
|
blanchet@33192
|
421 |
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
|
blanchet@34118
|
422 |
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
|
blanchet@33192
|
423 |
val is_integer_type =
|
blanchet@33192
|
424 |
member (op =) [nat_T, int_T, @{typ bisim_iterator}] orf is_fp_iterator_type
|
blanchet@34121
|
425 |
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
|
blanchet@34121
|
426 |
fun is_word_type (Type (@{type_name word}, _)) = true
|
blanchet@34121
|
427 |
| is_word_type _ = false
|
blanchet@33192
|
428 |
val is_record_type = not o null o Record.dest_recTs
|
blanchet@33192
|
429 |
(* theory -> typ -> bool *)
|
blanchet@33192
|
430 |
fun is_frac_type thy (Type (s, [])) =
|
blanchet@33574
|
431 |
not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
|
blanchet@33192
|
432 |
| is_frac_type _ _ = false
|
blanchet@33192
|
433 |
fun is_number_type thy = is_integer_type orf is_frac_type thy
|
blanchet@33192
|
434 |
|
blanchet@33192
|
435 |
(* bool -> styp -> typ *)
|
blanchet@33192
|
436 |
fun iterator_type_for_const gfp (s, T) =
|
blanchet@33192
|
437 |
Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
|
blanchet@33192
|
438 |
binder_types T)
|
blanchet@33192
|
439 |
(* typ -> styp *)
|
blanchet@33192
|
440 |
fun const_for_iterator_type (Type (s, Ts)) = (after_name_sep s, Ts ---> bool_T)
|
blanchet@33192
|
441 |
| const_for_iterator_type T =
|
blanchet@33224
|
442 |
raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
|
blanchet@33192
|
443 |
|
blanchet@33192
|
444 |
(* int -> typ -> typ * typ *)
|
blanchet@33192
|
445 |
fun strip_n_binders 0 T = ([], T)
|
blanchet@33192
|
446 |
| strip_n_binders n (Type ("fun", [T1, T2])) =
|
blanchet@33192
|
447 |
strip_n_binders (n - 1) T2 |>> cons T1
|
blanchet@33192
|
448 |
| strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
|
blanchet@33192
|
449 |
strip_n_binders n (Type ("fun", Ts))
|
blanchet@33224
|
450 |
| strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
|
blanchet@33192
|
451 |
(* typ -> typ *)
|
blanchet@33192
|
452 |
val nth_range_type = snd oo strip_n_binders
|
blanchet@33192
|
453 |
|
blanchet@33192
|
454 |
(* typ -> int *)
|
blanchet@33192
|
455 |
fun num_factors_in_type (Type ("*", [T1, T2])) =
|
blanchet@33192
|
456 |
fold (Integer.add o num_factors_in_type) [T1, T2] 0
|
blanchet@33192
|
457 |
| num_factors_in_type _ = 1
|
blanchet@33192
|
458 |
fun num_binder_types (Type ("fun", [_, T2])) = 1 + num_binder_types T2
|
blanchet@33192
|
459 |
| num_binder_types _ = 0
|
blanchet@33192
|
460 |
(* typ -> typ list *)
|
blanchet@33192
|
461 |
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
|
blanchet@33192
|
462 |
fun maybe_curried_binder_types T =
|
blanchet@33192
|
463 |
(if is_pair_type (body_type T) then binder_types else curried_binder_types) T
|
blanchet@33192
|
464 |
|
blanchet@33192
|
465 |
(* typ -> term list -> term *)
|
blanchet@33192
|
466 |
fun mk_flat_tuple _ [t] = t
|
blanchet@33192
|
467 |
| mk_flat_tuple (Type ("*", [T1, T2])) (t :: ts) =
|
blanchet@33192
|
468 |
HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
|
blanchet@33224
|
469 |
| mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
|
blanchet@33192
|
470 |
(* int -> term -> term list *)
|
blanchet@33192
|
471 |
fun dest_n_tuple 1 t = [t]
|
blanchet@33192
|
472 |
| dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
|
blanchet@33192
|
473 |
|
blanchet@33192
|
474 |
(* int -> typ -> typ list *)
|
blanchet@33192
|
475 |
fun dest_n_tuple_type 1 T = [T]
|
blanchet@33192
|
476 |
| dest_n_tuple_type n (Type (_, [T1, T2])) =
|
blanchet@33192
|
477 |
T1 :: dest_n_tuple_type (n - 1) T2
|
blanchet@33224
|
478 |
| dest_n_tuple_type _ T =
|
blanchet@33224
|
479 |
raise TYPE ("Nitpick_HOL.dest_n_tuple_type", [T], [])
|
blanchet@33192
|
480 |
|
blanchet@34118
|
481 |
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
|
blanchet@34118
|
482 |
e.g., by adding a field to "Datatype_Aux.info". *)
|
blanchet@34118
|
483 |
(* string -> bool *)
|
blanchet@34118
|
484 |
val is_basic_datatype =
|
blanchet@34118
|
485 |
member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
|
blanchet@34118
|
486 |
@{type_name nat}, @{type_name int},
|
blanchet@34118
|
487 |
"Code_Numeral.code_numeral"]
|
blanchet@34118
|
488 |
|
blanchet@33192
|
489 |
(* theory -> typ -> typ -> typ -> typ *)
|
blanchet@33192
|
490 |
fun instantiate_type thy T1 T1' T2 =
|
blanchet@33192
|
491 |
Same.commit (Envir.subst_type_same
|
blanchet@33192
|
492 |
(Sign.typ_match thy (Logic.varifyT T1, T1') Vartab.empty))
|
blanchet@33192
|
493 |
(Logic.varifyT T2)
|
blanchet@33192
|
494 |
handle Type.TYPE_MATCH =>
|
blanchet@33224
|
495 |
raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
|
blanchet@33192
|
496 |
|
blanchet@33192
|
497 |
(* theory -> typ -> typ -> styp *)
|
blanchet@33192
|
498 |
fun repair_constr_type thy body_T' T =
|
blanchet@33192
|
499 |
instantiate_type thy (body_type T) body_T' T
|
blanchet@33192
|
500 |
|
blanchet@33192
|
501 |
(* string -> (string * string) list -> theory -> theory *)
|
blanchet@33192
|
502 |
fun register_frac_type frac_s ersaetze thy =
|
blanchet@33192
|
503 |
let
|
blanchet@33574
|
504 |
val {frac_types, codatatypes} = Data.get thy
|
blanchet@33192
|
505 |
val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
|
blanchet@33574
|
506 |
in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
|
blanchet@33192
|
507 |
(* string -> theory -> theory *)
|
blanchet@33192
|
508 |
fun unregister_frac_type frac_s = register_frac_type frac_s []
|
blanchet@33192
|
509 |
|
blanchet@33192
|
510 |
(* typ -> string -> styp list -> theory -> theory *)
|
blanchet@33192
|
511 |
fun register_codatatype co_T case_name constr_xs thy =
|
blanchet@33192
|
512 |
let
|
blanchet@33574
|
513 |
val {frac_types, codatatypes} = Data.get thy
|
blanchet@33192
|
514 |
val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
|
blanchet@33192
|
515 |
val (co_s, co_Ts) = dest_Type co_T
|
blanchet@33192
|
516 |
val _ =
|
blanchet@34923
|
517 |
if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
|
blanchet@34923
|
518 |
co_s <> "fun" andalso not (is_basic_datatype co_s) then
|
blanchet@34118
|
519 |
()
|
blanchet@34118
|
520 |
else
|
blanchet@34118
|
521 |
raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
|
blanchet@33192
|
522 |
val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
|
blanchet@33192
|
523 |
codatatypes
|
blanchet@33574
|
524 |
in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
|
blanchet@33192
|
525 |
(* typ -> theory -> theory *)
|
blanchet@33192
|
526 |
fun unregister_codatatype co_T = register_codatatype co_T "" []
|
blanchet@33192
|
527 |
|
blanchet@33192
|
528 |
type typedef_info =
|
blanchet@33192
|
529 |
{rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
|
blanchet@33192
|
530 |
set_def: thm option, prop_of_Rep: thm, set_name: string,
|
blanchet@33876
|
531 |
Abs_inverse: thm option, Rep_inverse: thm option}
|
blanchet@33192
|
532 |
|
blanchet@33192
|
533 |
(* theory -> string -> typedef_info *)
|
blanchet@33192
|
534 |
fun typedef_info thy s =
|
blanchet@33192
|
535 |
if is_frac_type thy (Type (s, [])) then
|
blanchet@33192
|
536 |
SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
|
blanchet@33192
|
537 |
Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
|
blanchet@33192
|
538 |
set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
|
blanchet@33192
|
539 |
|> Logic.varify,
|
blanchet@33876
|
540 |
set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
|
blanchet@33192
|
541 |
else case Typedef.get_info thy s of
|
blanchet@33876
|
542 |
SOME {abs_type, rep_type, Abs_name, Rep_name, set_def, Rep, Abs_inverse,
|
blanchet@33876
|
543 |
Rep_inverse, ...} =>
|
blanchet@33192
|
544 |
SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
|
blanchet@33192
|
545 |
Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
|
blanchet@33876
|
546 |
set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
|
blanchet@33876
|
547 |
Rep_inverse = SOME Rep_inverse}
|
blanchet@33192
|
548 |
| NONE => NONE
|
blanchet@33192
|
549 |
|
blanchet@33192
|
550 |
(* theory -> string -> bool *)
|
blanchet@33192
|
551 |
val is_typedef = is_some oo typedef_info
|
blanchet@33192
|
552 |
val is_real_datatype = is_some oo Datatype.get_info
|
blanchet@33192
|
553 |
(* theory -> typ -> bool *)
|
blanchet@34969
|
554 |
fun is_quot_type _ (Type ("IntEx.my_int", _)) = true (* FIXME *)
|
blanchet@34985
|
555 |
| is_quot_type _ (Type ("FSet.fset", _)) = true (* FIXME *)
|
blanchet@34923
|
556 |
| is_quot_type _ _ = false
|
blanchet@33192
|
557 |
fun is_codatatype thy (T as Type (s, _)) =
|
blanchet@33574
|
558 |
not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
|
blanchet@33192
|
559 |
|> Option.map snd |> these))
|
blanchet@33192
|
560 |
| is_codatatype _ _ = false
|
blanchet@33192
|
561 |
fun is_pure_typedef thy (T as Type (s, _)) =
|
blanchet@33192
|
562 |
is_typedef thy s andalso
|
blanchet@34923
|
563 |
not (is_real_datatype thy s orelse is_quot_type thy T orelse
|
blanchet@34923
|
564 |
is_codatatype thy T orelse is_record_type T orelse is_integer_type T)
|
blanchet@33192
|
565 |
| is_pure_typedef _ _ = false
|
blanchet@33192
|
566 |
fun is_univ_typedef thy (Type (s, _)) =
|
blanchet@33192
|
567 |
(case typedef_info thy s of
|
blanchet@33192
|
568 |
SOME {set_def, prop_of_Rep, ...} =>
|
blanchet@33192
|
569 |
(case set_def of
|
blanchet@33192
|
570 |
SOME thm =>
|
blanchet@33192
|
571 |
try (fst o dest_Const o snd o Logic.dest_equals o prop_of) thm
|
blanchet@33192
|
572 |
| NONE =>
|
blanchet@33192
|
573 |
try (fst o dest_Const o snd o HOLogic.dest_mem
|
blanchet@33864
|
574 |
o HOLogic.dest_Trueprop) prop_of_Rep) = SOME @{const_name top}
|
blanchet@33192
|
575 |
| NONE => false)
|
blanchet@33192
|
576 |
| is_univ_typedef _ _ = false
|
blanchet@33192
|
577 |
fun is_datatype thy (T as Type (s, _)) =
|
blanchet@34923
|
578 |
(is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind} orelse
|
blanchet@34923
|
579 |
is_quot_type thy T) andalso
|
blanchet@34923
|
580 |
not (is_basic_datatype s)
|
blanchet@33192
|
581 |
| is_datatype _ _ = false
|
blanchet@33192
|
582 |
|
blanchet@33192
|
583 |
(* theory -> typ -> (string * typ) list * (string * typ) *)
|
blanchet@33192
|
584 |
fun all_record_fields thy T =
|
blanchet@33192
|
585 |
let val (recs, more) = Record.get_extT_fields thy T in
|
blanchet@33192
|
586 |
recs @ more :: all_record_fields thy (snd more)
|
blanchet@33192
|
587 |
end
|
blanchet@33192
|
588 |
handle TYPE _ => []
|
blanchet@33192
|
589 |
(* styp -> bool *)
|
blanchet@33192
|
590 |
fun is_record_constr (x as (s, T)) =
|
blanchet@33192
|
591 |
String.isSuffix Record.extN s andalso
|
blanchet@33192
|
592 |
let val dataT = body_type T in
|
blanchet@33192
|
593 |
is_record_type dataT andalso
|
blanchet@33192
|
594 |
s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
|
blanchet@33192
|
595 |
end
|
blanchet@33192
|
596 |
(* theory -> typ -> int *)
|
blanchet@33192
|
597 |
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
|
blanchet@33192
|
598 |
(* theory -> string -> typ -> int *)
|
blanchet@33192
|
599 |
fun no_of_record_field thy s T1 =
|
blanchet@34118
|
600 |
find_index (curry (op =) s o fst)
|
blanchet@34118
|
601 |
(Record.get_extT_fields thy T1 ||> single |> op @)
|
blanchet@33192
|
602 |
(* theory -> styp -> bool *)
|
blanchet@33192
|
603 |
fun is_record_get thy (s, Type ("fun", [T1, _])) =
|
blanchet@34118
|
604 |
exists (curry (op =) s o fst) (all_record_fields thy T1)
|
blanchet@33192
|
605 |
| is_record_get _ _ = false
|
blanchet@33192
|
606 |
fun is_record_update thy (s, T) =
|
blanchet@33192
|
607 |
String.isSuffix Record.updateN s andalso
|
blanchet@34118
|
608 |
exists (curry (op =) (unsuffix Record.updateN s) o fst)
|
blanchet@33192
|
609 |
(all_record_fields thy (body_type T))
|
blanchet@33192
|
610 |
handle TYPE _ => false
|
blanchet@33192
|
611 |
fun is_abs_fun thy (s, Type ("fun", [_, Type (s', _)])) =
|
blanchet@33192
|
612 |
(case typedef_info thy s' of
|
blanchet@33192
|
613 |
SOME {Abs_name, ...} => s = Abs_name
|
blanchet@33192
|
614 |
| NONE => false)
|
blanchet@33192
|
615 |
| is_abs_fun _ _ = false
|
blanchet@33192
|
616 |
fun is_rep_fun thy (s, Type ("fun", [Type (s', _), _])) =
|
blanchet@33192
|
617 |
(case typedef_info thy s' of
|
blanchet@33192
|
618 |
SOME {Rep_name, ...} => s = Rep_name
|
blanchet@33192
|
619 |
| NONE => false)
|
blanchet@33192
|
620 |
| is_rep_fun _ _ = false
|
blanchet@34923
|
621 |
(* Proof.context -> styp -> bool *)
|
blanchet@34969
|
622 |
fun is_quot_abs_fun _ ("IntEx.abs_my_int", _) = true (* FIXME *)
|
blanchet@34985
|
623 |
| is_quot_abs_fun _ ("FSet.abs_fset", _) = true (* FIXME *)
|
blanchet@34923
|
624 |
| is_quot_abs_fun _ _ = false
|
blanchet@34969
|
625 |
fun is_quot_rep_fun _ ("IntEx.rep_my_int", _) = true (* FIXME *)
|
blanchet@34985
|
626 |
| is_quot_rep_fun _ ("FSet.rep_fset", _) = true (* FIXME *)
|
blanchet@34923
|
627 |
| is_quot_rep_fun _ _ = false
|
blanchet@33192
|
628 |
|
blanchet@33192
|
629 |
(* theory -> styp -> styp *)
|
blanchet@33192
|
630 |
fun mate_of_rep_fun thy (x as (_, Type ("fun", [T1 as Type (s', _), T2]))) =
|
blanchet@33192
|
631 |
(case typedef_info thy s' of
|
blanchet@33192
|
632 |
SOME {Abs_name, ...} => (Abs_name, Type ("fun", [T2, T1]))
|
blanchet@33224
|
633 |
| NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
|
blanchet@33224
|
634 |
| mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
|
blanchet@34923
|
635 |
(* theory -> typ -> typ *)
|
blanchet@34923
|
636 |
fun rep_type_for_quot_type _ (Type ("IntEx.my_int", [])) = @{typ "nat * nat"}
|
blanchet@34985
|
637 |
| rep_type_for_quot_type _ (Type ("FSet.fset", [T])) =
|
blanchet@34985
|
638 |
Type (@{type_name list}, [T])
|
blanchet@34923
|
639 |
| rep_type_for_quot_type _ T =
|
blanchet@34923
|
640 |
raise TYPE ("Nitpick_HOL.rep_type_for_quot_type", [T], [])
|
blanchet@34923
|
641 |
(* theory -> typ -> term *)
|
blanchet@34923
|
642 |
fun equiv_relation_for_quot_type _ (Type ("IntEx.my_int", [])) =
|
blanchet@34923
|
643 |
Const ("IntEx.intrel", @{typ "(nat * nat) => (nat * nat) => bool"})
|
blanchet@34985
|
644 |
| equiv_relation_for_quot_type _ (Type ("FSet.fset", [T])) =
|
blanchet@34985
|
645 |
Const ("FSet.list_eq",
|
blanchet@34985
|
646 |
Type (@{type_name list}, [T]) --> Type (@{type_name list}, [T])
|
blanchet@34985
|
647 |
--> bool_T)
|
blanchet@34923
|
648 |
| equiv_relation_for_quot_type _ T =
|
blanchet@34923
|
649 |
raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
|
blanchet@33192
|
650 |
|
blanchet@33192
|
651 |
(* theory -> styp -> bool *)
|
blanchet@33192
|
652 |
fun is_coconstr thy (s, T) =
|
blanchet@33192
|
653 |
let
|
blanchet@33574
|
654 |
val {codatatypes, ...} = Data.get thy
|
blanchet@33192
|
655 |
val co_T = body_type T
|
blanchet@33192
|
656 |
val co_s = dest_Type co_T |> fst
|
blanchet@33192
|
657 |
in
|
blanchet@33192
|
658 |
exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
|
blanchet@33192
|
659 |
(AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
|
blanchet@33192
|
660 |
end
|
blanchet@33192
|
661 |
handle TYPE ("dest_Type", _, _) => false
|
blanchet@33192
|
662 |
fun is_constr_like thy (s, T) =
|
blanchet@34969
|
663 |
member (op =) [@{const_name FunBox}, @{const_name PairBox},
|
blanchet@34969
|
664 |
@{const_name Quot}, @{const_name Zero_Rep},
|
blanchet@34969
|
665 |
@{const_name Suc_Rep}] s orelse
|
blanchet@34121
|
666 |
let val (x as (s, T)) = (s, unbit_and_unbox_type T) in
|
blanchet@34923
|
667 |
Refute.is_IDT_constructor thy x orelse is_record_constr x orelse
|
blanchet@34923
|
668 |
(is_abs_fun thy x andalso is_pure_typedef thy (range_type T)) orelse
|
blanchet@34923
|
669 |
x = (@{const_name zero_nat_inst.zero_nat}, nat_T) orelse
|
blanchet@34923
|
670 |
is_coconstr thy x
|
blanchet@33192
|
671 |
end
|
blanchet@33572
|
672 |
fun is_stale_constr thy (x as (_, T)) =
|
blanchet@34923
|
673 |
is_codatatype thy (body_type T) andalso is_constr_like thy x andalso
|
blanchet@34923
|
674 |
not (is_coconstr thy x)
|
blanchet@33192
|
675 |
fun is_constr thy (x as (_, T)) =
|
blanchet@34923
|
676 |
is_constr_like thy x andalso
|
blanchet@34923
|
677 |
not (is_basic_datatype (fst (dest_Type (unbit_type (body_type T))))) andalso
|
blanchet@34923
|
678 |
not (is_stale_constr thy x)
|
blanchet@33192
|
679 |
(* string -> bool *)
|
blanchet@33192
|
680 |
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
|
blanchet@33192
|
681 |
val is_sel_like_and_no_discr =
|
blanchet@33192
|
682 |
String.isPrefix sel_prefix
|
blanchet@33192
|
683 |
orf (member (op =) [@{const_name fst}, @{const_name snd}])
|
blanchet@33192
|
684 |
|
blanchet@33192
|
685 |
datatype boxability =
|
blanchet@33192
|
686 |
InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
|
blanchet@33192
|
687 |
|
blanchet@33192
|
688 |
(* boxability -> boxability *)
|
blanchet@33192
|
689 |
fun in_fun_lhs_for InConstr = InSel
|
blanchet@33192
|
690 |
| in_fun_lhs_for _ = InFunLHS
|
blanchet@33192
|
691 |
fun in_fun_rhs_for InConstr = InConstr
|
blanchet@33192
|
692 |
| in_fun_rhs_for InSel = InSel
|
blanchet@33192
|
693 |
| in_fun_rhs_for InFunRHS1 = InFunRHS2
|
blanchet@33192
|
694 |
| in_fun_rhs_for _ = InFunRHS1
|
blanchet@33192
|
695 |
|
blanchet@33192
|
696 |
(* extended_context -> boxability -> typ -> bool *)
|
blanchet@33192
|
697 |
fun is_boxing_worth_it (ext_ctxt : extended_context) boxy T =
|
blanchet@33192
|
698 |
case T of
|
blanchet@33192
|
699 |
Type ("fun", _) =>
|
blanchet@34923
|
700 |
(boxy = InPair orelse boxy = InFunLHS) andalso
|
blanchet@34923
|
701 |
not (is_boolean_type (body_type T))
|
blanchet@33192
|
702 |
| Type ("*", Ts) =>
|
blanchet@34923
|
703 |
boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
|
blanchet@34923
|
704 |
((boxy = InExpr orelse boxy = InFunLHS) andalso
|
blanchet@34923
|
705 |
exists (is_boxing_worth_it ext_ctxt InPair)
|
blanchet@34923
|
706 |
(map (box_type ext_ctxt InPair) Ts))
|
blanchet@33192
|
707 |
| _ => false
|
blanchet@33192
|
708 |
(* extended_context -> boxability -> string * typ list -> string *)
|
blanchet@33192
|
709 |
and should_box_type (ext_ctxt as {thy, boxes, ...}) boxy (z as (s, Ts)) =
|
blanchet@33192
|
710 |
case triple_lookup (type_match thy) boxes (Type z) of
|
blanchet@33192
|
711 |
SOME (SOME box_me) => box_me
|
blanchet@33192
|
712 |
| _ => is_boxing_worth_it ext_ctxt boxy (Type z)
|
blanchet@33192
|
713 |
(* extended_context -> boxability -> typ -> typ *)
|
blanchet@33192
|
714 |
and box_type ext_ctxt boxy T =
|
blanchet@33192
|
715 |
case T of
|
blanchet@33192
|
716 |
Type (z as ("fun", [T1, T2])) =>
|
blanchet@34923
|
717 |
if boxy <> InConstr andalso boxy <> InSel andalso
|
blanchet@34923
|
718 |
should_box_type ext_ctxt boxy z then
|
blanchet@33192
|
719 |
Type (@{type_name fun_box},
|
blanchet@33192
|
720 |
[box_type ext_ctxt InFunLHS T1, box_type ext_ctxt InFunRHS1 T2])
|
blanchet@33192
|
721 |
else
|
blanchet@33192
|
722 |
box_type ext_ctxt (in_fun_lhs_for boxy) T1
|
blanchet@33192
|
723 |
--> box_type ext_ctxt (in_fun_rhs_for boxy) T2
|
blanchet@33192
|
724 |
| Type (z as ("*", Ts)) =>
|
blanchet@34969
|
725 |
if boxy <> InConstr andalso boxy <> InSel
|
blanchet@34969
|
726 |
andalso should_box_type ext_ctxt boxy z then
|
blanchet@33192
|
727 |
Type (@{type_name pair_box}, map (box_type ext_ctxt InSel) Ts)
|
blanchet@33192
|
728 |
else
|
blanchet@33192
|
729 |
Type ("*", map (box_type ext_ctxt
|
blanchet@34118
|
730 |
(if boxy = InConstr orelse boxy = InSel then boxy
|
blanchet@34118
|
731 |
else InPair)) Ts)
|
blanchet@33192
|
732 |
| _ => T
|
blanchet@33192
|
733 |
|
blanchet@33192
|
734 |
(* styp -> styp *)
|
blanchet@33192
|
735 |
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
|
blanchet@33192
|
736 |
|
blanchet@33192
|
737 |
(* typ -> int *)
|
blanchet@33192
|
738 |
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
|
blanchet@33192
|
739 |
(* string -> int -> string *)
|
blanchet@33192
|
740 |
fun nth_sel_name_for_constr_name s n =
|
blanchet@33192
|
741 |
if s = @{const_name Pair} then
|
blanchet@33192
|
742 |
if n = 0 then @{const_name fst} else @{const_name snd}
|
blanchet@33192
|
743 |
else
|
blanchet@33192
|
744 |
sel_prefix_for n ^ s
|
blanchet@33192
|
745 |
(* styp -> int -> styp *)
|
blanchet@33192
|
746 |
fun nth_sel_for_constr x ~1 = discr_for_constr x
|
blanchet@33192
|
747 |
| nth_sel_for_constr (s, T) n =
|
blanchet@33192
|
748 |
(nth_sel_name_for_constr_name s n,
|
blanchet@33192
|
749 |
body_type T --> nth (maybe_curried_binder_types T) n)
|
blanchet@33192
|
750 |
(* extended_context -> styp -> int -> styp *)
|
blanchet@33192
|
751 |
fun boxed_nth_sel_for_constr ext_ctxt =
|
blanchet@33192
|
752 |
apsnd (box_type ext_ctxt InSel) oo nth_sel_for_constr
|
blanchet@33192
|
753 |
|
blanchet@33192
|
754 |
(* string -> int *)
|
blanchet@33192
|
755 |
fun sel_no_from_name s =
|
blanchet@33192
|
756 |
if String.isPrefix discr_prefix s then
|
blanchet@33192
|
757 |
~1
|
blanchet@33192
|
758 |
else if String.isPrefix sel_prefix s then
|
blanchet@33192
|
759 |
s |> unprefix sel_prefix |> Int.fromString |> the
|
blanchet@33192
|
760 |
else if s = @{const_name snd} then
|
blanchet@33192
|
761 |
1
|
blanchet@33192
|
762 |
else
|
blanchet@33192
|
763 |
0
|
blanchet@33192
|
764 |
|
blanchet@33192
|
765 |
(* typ list -> term -> int -> term *)
|
blanchet@33192
|
766 |
fun eta_expand _ t 0 = t
|
blanchet@33192
|
767 |
| eta_expand Ts (Abs (s, T, t')) n =
|
blanchet@33192
|
768 |
Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
|
blanchet@33192
|
769 |
| eta_expand Ts t n =
|
blanchet@33192
|
770 |
fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
|
blanchet@33192
|
771 |
(List.take (binder_types (fastype_of1 (Ts, t)), n))
|
blanchet@33192
|
772 |
(list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
|
blanchet@33192
|
773 |
|
blanchet@33192
|
774 |
(* term -> term *)
|
blanchet@33192
|
775 |
fun extensionalize t =
|
blanchet@33192
|
776 |
case t of
|
blanchet@33192
|
777 |
(t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
|
blanchet@33192
|
778 |
| Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
|
blanchet@33192
|
779 |
let val v = Var ((s, maxidx_of_term t + 1), T) in
|
blanchet@33192
|
780 |
extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
|
blanchet@33192
|
781 |
end
|
blanchet@33192
|
782 |
| _ => t
|
blanchet@33192
|
783 |
|
blanchet@33192
|
784 |
(* typ -> term list -> term *)
|
blanchet@33192
|
785 |
fun distinctness_formula T =
|
blanchet@33192
|
786 |
all_distinct_unordered_pairs_of
|
blanchet@33192
|
787 |
#> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
|
blanchet@33192
|
788 |
#> List.foldr (s_conj o swap) @{const True}
|
blanchet@33192
|
789 |
|
blanchet@33192
|
790 |
(* typ -> term *)
|
blanchet@33192
|
791 |
fun zero_const T = Const (@{const_name zero_nat_inst.zero_nat}, T)
|
blanchet@33192
|
792 |
fun suc_const T = Const (@{const_name Suc}, T --> T)
|
blanchet@33192
|
793 |
|
blanchet@34969
|
794 |
(* extended_context -> typ -> styp list *)
|
blanchet@34969
|
795 |
fun uncached_datatype_constrs ({thy, stds, ...} : extended_context)
|
blanchet@34969
|
796 |
(T as Type (s, Ts)) =
|
blanchet@33574
|
797 |
(case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
|
blanchet@34969
|
798 |
SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
|
blanchet@33572
|
799 |
| _ =>
|
blanchet@33572
|
800 |
if is_datatype thy T then
|
blanchet@33572
|
801 |
case Datatype.get_info thy s of
|
blanchet@33572
|
802 |
SOME {index, descr, ...} =>
|
blanchet@33572
|
803 |
let
|
blanchet@33572
|
804 |
val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
|
blanchet@33572
|
805 |
in
|
blanchet@33572
|
806 |
map (fn (s', Us) =>
|
blanchet@33572
|
807 |
(s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us
|
blanchet@33572
|
808 |
---> T)) constrs
|
blanchet@34969
|
809 |
|> (triple_lookup (type_match thy) stds T |> the |> not) ?
|
blanchet@34969
|
810 |
cons (@{const_name NonStd}, @{typ \<xi>} --> T)
|
blanchet@33572
|
811 |
end
|
blanchet@33572
|
812 |
| NONE =>
|
blanchet@33572
|
813 |
if is_record_type T then
|
blanchet@33572
|
814 |
let
|
blanchet@33572
|
815 |
val s' = unsuffix Record.ext_typeN s ^ Record.extN
|
blanchet@33572
|
816 |
val T' = (Record.get_extT_fields thy T
|
blanchet@33572
|
817 |
|> apsnd single |> uncurry append |> map snd) ---> T
|
blanchet@33572
|
818 |
in [(s', T')] end
|
blanchet@34923
|
819 |
else if is_quot_type thy T then
|
blanchet@34923
|
820 |
[(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
|
blanchet@33572
|
821 |
else case typedef_info thy s of
|
blanchet@33572
|
822 |
SOME {abs_type, rep_type, Abs_name, ...} =>
|
blanchet@33572
|
823 |
[(Abs_name, instantiate_type thy abs_type T rep_type --> T)]
|
blanchet@33572
|
824 |
| NONE =>
|
blanchet@33572
|
825 |
if T = @{typ ind} then
|
blanchet@33572
|
826 |
[dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
|
blanchet@33572
|
827 |
else
|
blanchet@33572
|
828 |
[]
|
blanchet@33572
|
829 |
else
|
blanchet@33572
|
830 |
[])
|
blanchet@33571
|
831 |
| uncached_datatype_constrs _ _ = []
|
blanchet@33192
|
832 |
(* extended_context -> typ -> styp list *)
|
blanchet@34969
|
833 |
fun datatype_constrs (ext_ctxt as {constr_cache, ...}) T =
|
blanchet@33571
|
834 |
case AList.lookup (op =) (!constr_cache) T of
|
blanchet@33571
|
835 |
SOME xs => xs
|
blanchet@33571
|
836 |
| NONE =>
|
blanchet@34969
|
837 |
let val xs = uncached_datatype_constrs ext_ctxt T in
|
blanchet@33571
|
838 |
(Unsynchronized.change constr_cache (cons (T, xs)); xs)
|
blanchet@33571
|
839 |
end
|
blanchet@33571
|
840 |
fun boxed_datatype_constrs ext_ctxt =
|
blanchet@33571
|
841 |
map (apsnd (box_type ext_ctxt InConstr)) o datatype_constrs ext_ctxt
|
blanchet@33571
|
842 |
(* extended_context -> typ -> int *)
|
blanchet@33192
|
843 |
val num_datatype_constrs = length oo datatype_constrs
|
blanchet@33192
|
844 |
|
blanchet@33192
|
845 |
(* string -> string *)
|
blanchet@33192
|
846 |
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
|
blanchet@33192
|
847 |
| constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
|
blanchet@33192
|
848 |
| constr_name_for_sel_like s' = original_name s'
|
blanchet@33192
|
849 |
(* extended_context -> styp -> styp *)
|
blanchet@33192
|
850 |
fun boxed_constr_for_sel ext_ctxt (s', T') =
|
blanchet@33192
|
851 |
let val s = constr_name_for_sel_like s' in
|
blanchet@33192
|
852 |
AList.lookup (op =) (boxed_datatype_constrs ext_ctxt (domain_type T')) s
|
blanchet@33192
|
853 |
|> the |> pair s
|
blanchet@33192
|
854 |
end
|
blanchet@34969
|
855 |
|
blanchet@33571
|
856 |
(* extended_context -> styp -> term *)
|
blanchet@33571
|
857 |
fun discr_term_for_constr ext_ctxt (x as (s, T)) =
|
blanchet@33192
|
858 |
let val dataT = body_type T in
|
blanchet@33192
|
859 |
if s = @{const_name Suc} then
|
blanchet@33192
|
860 |
Abs (Name.uu, dataT,
|
blanchet@33192
|
861 |
@{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
|
blanchet@33571
|
862 |
else if num_datatype_constrs ext_ctxt dataT >= 2 then
|
blanchet@33192
|
863 |
Const (discr_for_constr x)
|
blanchet@33192
|
864 |
else
|
blanchet@33192
|
865 |
Abs (Name.uu, dataT, @{const True})
|
blanchet@33192
|
866 |
end
|
blanchet@33571
|
867 |
(* extended_context -> styp -> term -> term *)
|
blanchet@33571
|
868 |
fun discriminate_value (ext_ctxt as {thy, ...}) (x as (_, T)) t =
|
blanchet@33192
|
869 |
case strip_comb t of
|
blanchet@33192
|
870 |
(Const x', args) =>
|
blanchet@33192
|
871 |
if x = x' then @{const True}
|
blanchet@33192
|
872 |
else if is_constr_like thy x' then @{const False}
|
blanchet@33571
|
873 |
else betapply (discr_term_for_constr ext_ctxt x, t)
|
blanchet@33571
|
874 |
| _ => betapply (discr_term_for_constr ext_ctxt x, t)
|
blanchet@33192
|
875 |
|
blanchet@33192
|
876 |
(* styp -> term -> term *)
|
blanchet@33192
|
877 |
fun nth_arg_sel_term_for_constr (x as (s, T)) n =
|
blanchet@33192
|
878 |
let val (arg_Ts, dataT) = strip_type T in
|
blanchet@33192
|
879 |
if dataT = nat_T then
|
blanchet@33192
|
880 |
@{term "%n::nat. minus_nat_inst.minus_nat n one_nat_inst.one_nat"}
|
blanchet@33192
|
881 |
else if is_pair_type dataT then
|
blanchet@33192
|
882 |
Const (nth_sel_for_constr x n)
|
blanchet@33192
|
883 |
else
|
blanchet@33192
|
884 |
let
|
blanchet@33192
|
885 |
(* int -> typ -> int * term *)
|
blanchet@33192
|
886 |
fun aux m (Type ("*", [T1, T2])) =
|
blanchet@33192
|
887 |
let
|
blanchet@33192
|
888 |
val (m, t1) = aux m T1
|
blanchet@33192
|
889 |
val (m, t2) = aux m T2
|
blanchet@33192
|
890 |
in (m, HOLogic.mk_prod (t1, t2)) end
|
blanchet@33192
|
891 |
| aux m T =
|
blanchet@33192
|
892 |
(m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
|
blanchet@33192
|
893 |
$ Bound 0)
|
blanchet@33192
|
894 |
val m = fold (Integer.add o num_factors_in_type)
|
blanchet@33192
|
895 |
(List.take (arg_Ts, n)) 0
|
blanchet@33192
|
896 |
in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
|
blanchet@33192
|
897 |
end
|
blanchet@33192
|
898 |
(* theory -> styp -> term -> int -> typ -> term *)
|
blanchet@33192
|
899 |
fun select_nth_constr_arg thy x t n res_T =
|
blanchet@33192
|
900 |
case strip_comb t of
|
blanchet@33192
|
901 |
(Const x', args) =>
|
blanchet@33192
|
902 |
if x = x' then nth args n
|
blanchet@33192
|
903 |
else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
|
blanchet@33192
|
904 |
else betapply (nth_arg_sel_term_for_constr x n, t)
|
blanchet@33192
|
905 |
| _ => betapply (nth_arg_sel_term_for_constr x n, t)
|
blanchet@33192
|
906 |
|
blanchet@33192
|
907 |
(* theory -> styp -> term list -> term *)
|
blanchet@33192
|
908 |
fun construct_value _ x [] = Const x
|
blanchet@33192
|
909 |
| construct_value thy (x as (s, _)) args =
|
blanchet@33192
|
910 |
let val args = map Envir.eta_contract args in
|
blanchet@33192
|
911 |
case hd args of
|
blanchet@33192
|
912 |
Const (x' as (s', _)) $ t =>
|
blanchet@34923
|
913 |
if is_sel_like_and_no_discr s' andalso
|
blanchet@34923
|
914 |
constr_name_for_sel_like s' = s andalso
|
blanchet@34923
|
915 |
forall (fn (n, t') => select_nth_constr_arg thy x t n dummyT = t')
|
blanchet@34923
|
916 |
(index_seq 0 (length args) ~~ args) then
|
blanchet@33192
|
917 |
t
|
blanchet@33192
|
918 |
else
|
blanchet@33192
|
919 |
list_comb (Const x, args)
|
blanchet@33192
|
920 |
| _ => list_comb (Const x, args)
|
blanchet@33192
|
921 |
end
|
blanchet@33192
|
922 |
|
blanchet@33571
|
923 |
(* extended_context -> typ -> term -> term *)
|
blanchet@33571
|
924 |
fun constr_expand (ext_ctxt as {thy, ...}) T t =
|
blanchet@33192
|
925 |
(case head_of t of
|
blanchet@33192
|
926 |
Const x => if is_constr_like thy x then t else raise SAME ()
|
blanchet@33192
|
927 |
| _ => raise SAME ())
|
blanchet@33192
|
928 |
handle SAME () =>
|
blanchet@33192
|
929 |
let
|
blanchet@33192
|
930 |
val x' as (_, T') =
|
blanchet@33192
|
931 |
if is_pair_type T then
|
blanchet@33192
|
932 |
let val (T1, T2) = HOLogic.dest_prodT T in
|
blanchet@34121
|
933 |
(@{const_name Pair}, T1 --> T2 --> T)
|
blanchet@33192
|
934 |
end
|
blanchet@33192
|
935 |
else
|
blanchet@34969
|
936 |
datatype_constrs ext_ctxt T |> hd
|
blanchet@33192
|
937 |
val arg_Ts = binder_types T'
|
blanchet@33192
|
938 |
in
|
blanchet@33192
|
939 |
list_comb (Const x', map2 (select_nth_constr_arg thy x' t)
|
blanchet@33192
|
940 |
(index_seq 0 (length arg_Ts)) arg_Ts)
|
blanchet@33192
|
941 |
end
|
blanchet@33192
|
942 |
|
blanchet@33192
|
943 |
(* (typ * int) list -> typ -> int *)
|
blanchet@34120
|
944 |
fun card_of_type assigns (Type ("fun", [T1, T2])) =
|
blanchet@34120
|
945 |
reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
|
blanchet@34120
|
946 |
| card_of_type assigns (Type ("*", [T1, T2])) =
|
blanchet@34120
|
947 |
card_of_type assigns T1 * card_of_type assigns T2
|
blanchet@33192
|
948 |
| card_of_type _ (Type (@{type_name itself}, _)) = 1
|
blanchet@33192
|
949 |
| card_of_type _ @{typ prop} = 2
|
blanchet@33192
|
950 |
| card_of_type _ @{typ bool} = 2
|
blanchet@33192
|
951 |
| card_of_type _ @{typ unit} = 1
|
blanchet@34120
|
952 |
| card_of_type assigns T =
|
blanchet@34120
|
953 |
case AList.lookup (op =) assigns T of
|
blanchet@33192
|
954 |
SOME k => k
|
blanchet@33192
|
955 |
| NONE => if T = @{typ bisim_iterator} then 0
|
blanchet@33224
|
956 |
else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
|
blanchet@33192
|
957 |
(* int -> (typ * int) list -> typ -> int *)
|
blanchet@34120
|
958 |
fun bounded_card_of_type max default_card assigns (Type ("fun", [T1, T2])) =
|
blanchet@33192
|
959 |
let
|
blanchet@34120
|
960 |
val k1 = bounded_card_of_type max default_card assigns T1
|
blanchet@34120
|
961 |
val k2 = bounded_card_of_type max default_card assigns T2
|
blanchet@33192
|
962 |
in
|
blanchet@33192
|
963 |
if k1 = max orelse k2 = max then max
|
blanchet@33192
|
964 |
else Int.min (max, reasonable_power k2 k1)
|
blanchet@33192
|
965 |
end
|
blanchet@34120
|
966 |
| bounded_card_of_type max default_card assigns (Type ("*", [T1, T2])) =
|
blanchet@33192
|
967 |
let
|
blanchet@34120
|
968 |
val k1 = bounded_card_of_type max default_card assigns T1
|
blanchet@34120
|
969 |
val k2 = bounded_card_of_type max default_card assigns T2
|
blanchet@33192
|
970 |
in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
|
blanchet@34120
|
971 |
| bounded_card_of_type max default_card assigns T =
|
blanchet@33192
|
972 |
Int.min (max, if default_card = ~1 then
|
blanchet@34120
|
973 |
card_of_type assigns T
|
blanchet@33192
|
974 |
else
|
blanchet@34120
|
975 |
card_of_type assigns T
|
blanchet@33224
|
976 |
handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
|
blanchet@33192
|
977 |
default_card)
|
blanchet@33571
|
978 |
(* extended_context -> int -> (typ * int) list -> typ -> int *)
|
blanchet@34120
|
979 |
fun bounded_exact_card_of_type ext_ctxt max default_card assigns T =
|
blanchet@33192
|
980 |
let
|
blanchet@33192
|
981 |
(* typ list -> typ -> int *)
|
blanchet@33192
|
982 |
fun aux avoid T =
|
blanchet@34118
|
983 |
(if member (op =) avoid T then
|
blanchet@33192
|
984 |
0
|
blanchet@33192
|
985 |
else case T of
|
blanchet@33192
|
986 |
Type ("fun", [T1, T2]) =>
|
blanchet@33192
|
987 |
let
|
blanchet@33192
|
988 |
val k1 = aux avoid T1
|
blanchet@33192
|
989 |
val k2 = aux avoid T2
|
blanchet@33192
|
990 |
in
|
blanchet@33192
|
991 |
if k1 = 0 orelse k2 = 0 then 0
|
blanchet@33192
|
992 |
else if k1 >= max orelse k2 >= max then max
|
blanchet@33192
|
993 |
else Int.min (max, reasonable_power k2 k1)
|
blanchet@33192
|
994 |
end
|
blanchet@33192
|
995 |
| Type ("*", [T1, T2]) =>
|
blanchet@33192
|
996 |
let
|
blanchet@33192
|
997 |
val k1 = aux avoid T1
|
blanchet@33192
|
998 |
val k2 = aux avoid T2
|
blanchet@33192
|
999 |
in
|
blanchet@33192
|
1000 |
if k1 = 0 orelse k2 = 0 then 0
|
blanchet@33192
|
1001 |
else if k1 >= max orelse k2 >= max then max
|
blanchet@33192
|
1002 |
else Int.min (max, k1 * k2)
|
blanchet@33192
|
1003 |
end
|
blanchet@33192
|
1004 |
| Type (@{type_name itself}, _) => 1
|
blanchet@33192
|
1005 |
| @{typ prop} => 2
|
blanchet@33192
|
1006 |
| @{typ bool} => 2
|
blanchet@33192
|
1007 |
| @{typ unit} => 1
|
blanchet@33192
|
1008 |
| Type _ =>
|
blanchet@33571
|
1009 |
(case datatype_constrs ext_ctxt T of
|
blanchet@34123
|
1010 |
[] => if is_integer_type T orelse is_bit_type T then 0
|
blanchet@34123
|
1011 |
else raise SAME ()
|
blanchet@33192
|
1012 |
| constrs =>
|
blanchet@33192
|
1013 |
let
|
blanchet@33192
|
1014 |
val constr_cards =
|
blanchet@33571
|
1015 |
datatype_constrs ext_ctxt T
|
blanchet@33192
|
1016 |
|> map (Integer.prod o map (aux (T :: avoid)) o binder_types
|
blanchet@33192
|
1017 |
o snd)
|
blanchet@33192
|
1018 |
in
|
blanchet@34118
|
1019 |
if exists (curry (op =) 0) constr_cards then 0
|
blanchet@33192
|
1020 |
else Integer.sum constr_cards
|
blanchet@33192
|
1021 |
end)
|
blanchet@33192
|
1022 |
| _ => raise SAME ())
|
blanchet@34120
|
1023 |
handle SAME () =>
|
blanchet@34120
|
1024 |
AList.lookup (op =) assigns T |> the_default default_card
|
blanchet@33192
|
1025 |
in Int.min (max, aux [] T) end
|
blanchet@33192
|
1026 |
|
blanchet@33571
|
1027 |
(* extended_context -> typ -> bool *)
|
blanchet@33571
|
1028 |
fun is_finite_type ext_ctxt =
|
blanchet@34120
|
1029 |
not_equal 0 o bounded_exact_card_of_type ext_ctxt 1 2 []
|
blanchet@33192
|
1030 |
|
blanchet@33192
|
1031 |
(* term -> bool *)
|
blanchet@33192
|
1032 |
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
|
blanchet@33192
|
1033 |
| is_ground_term (Const _) = true
|
blanchet@33192
|
1034 |
| is_ground_term _ = false
|
blanchet@33192
|
1035 |
|
blanchet@33192
|
1036 |
(* term -> word -> word *)
|
blanchet@33192
|
1037 |
fun hashw_term (t1 $ t2) = Polyhash.hashw (hashw_term t1, hashw_term t2)
|
blanchet@33192
|
1038 |
| hashw_term (Const (s, _)) = Polyhash.hashw_string (s, 0w0)
|
blanchet@33192
|
1039 |
| hashw_term _ = 0w0
|
blanchet@33192
|
1040 |
(* term -> int *)
|
blanchet@33192
|
1041 |
val hash_term = Word.toInt o hashw_term
|
blanchet@33192
|
1042 |
|
blanchet@33192
|
1043 |
(* term list -> (indexname * typ) list *)
|
blanchet@33192
|
1044 |
fun special_bounds ts =
|
blanchet@33192
|
1045 |
fold Term.add_vars ts [] |> sort (TermOrd.fast_indexname_ord o pairself fst)
|
blanchet@33192
|
1046 |
|
blanchet@33192
|
1047 |
(* indexname * typ -> term -> term *)
|
blanchet@33192
|
1048 |
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
|
blanchet@33192
|
1049 |
|
blanchet@33562
|
1050 |
(* theory -> string -> bool *)
|
blanchet@33562
|
1051 |
fun is_funky_typedef_name thy s =
|
blanchet@34118
|
1052 |
member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
|
blanchet@34923
|
1053 |
@{type_name int}] s orelse
|
blanchet@34923
|
1054 |
is_frac_type thy (Type (s, []))
|
blanchet@33562
|
1055 |
(* theory -> term -> bool *)
|
blanchet@33562
|
1056 |
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
|
blanchet@33562
|
1057 |
| is_funky_typedef _ _ = false
|
blanchet@33192
|
1058 |
(* term -> bool *)
|
blanchet@33192
|
1059 |
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
|
blanchet@33192
|
1060 |
$ Const (@{const_name TYPE}, _)) = true
|
blanchet@33192
|
1061 |
| is_arity_type_axiom _ = false
|
blanchet@33192
|
1062 |
(* theory -> bool -> term -> bool *)
|
blanchet@33197
|
1063 |
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
|
blanchet@33197
|
1064 |
is_typedef_axiom thy boring t2
|
blanchet@33197
|
1065 |
| is_typedef_axiom thy boring
|
blanchet@33192
|
1066 |
(@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
|
blanchet@33197
|
1067 |
$ Const (_, Type ("fun", [Type (s, _), _])) $ Const _ $ _)) =
|
blanchet@33562
|
1068 |
boring <> is_funky_typedef_name thy s andalso is_typedef thy s
|
blanchet@33192
|
1069 |
| is_typedef_axiom _ _ _ = false
|
blanchet@33192
|
1070 |
|
blanchet@33192
|
1071 |
(* Distinguishes between (1) constant definition axioms, (2) type arity and
|
blanchet@33192
|
1072 |
typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
|
blanchet@33192
|
1073 |
Typedef axioms are uninteresting to Nitpick, because it can retrieve them
|
blanchet@33192
|
1074 |
using "typedef_info". *)
|
blanchet@33192
|
1075 |
(* theory -> (string * term) list -> string list -> term list * term list *)
|
blanchet@33192
|
1076 |
fun partition_axioms_by_definitionality thy axioms def_names =
|
blanchet@33192
|
1077 |
let
|
blanchet@33192
|
1078 |
val axioms = sort (fast_string_ord o pairself fst) axioms
|
blanchet@33192
|
1079 |
val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
|
blanchet@33192
|
1080 |
val nondefs =
|
blanchet@33192
|
1081 |
OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
|
blanchet@33192
|
1082 |
|> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
|
blanchet@33192
|
1083 |
in pairself (map snd) (defs, nondefs) end
|
blanchet@33192
|
1084 |
|
blanchet@33197
|
1085 |
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
|
blanchet@33197
|
1086 |
will do as long as it contains all the "axioms" and "axiomatization"
|
blanchet@33192
|
1087 |
commands. *)
|
blanchet@33192
|
1088 |
(* theory -> bool *)
|
blanchet@33192
|
1089 |
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
|
blanchet@33192
|
1090 |
|
blanchet@33192
|
1091 |
(* term -> bool *)
|
blanchet@33192
|
1092 |
val is_plain_definition =
|
blanchet@33192
|
1093 |
let
|
blanchet@33192
|
1094 |
(* term -> bool *)
|
blanchet@33192
|
1095 |
fun do_lhs t1 =
|
blanchet@33192
|
1096 |
case strip_comb t1 of
|
blanchet@34923
|
1097 |
(Const _, args) =>
|
blanchet@34923
|
1098 |
forall is_Var args andalso not (has_duplicates (op =) args)
|
blanchet@33192
|
1099 |
| _ => false
|
blanchet@33192
|
1100 |
fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
|
blanchet@33192
|
1101 |
| do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
|
blanchet@33192
|
1102 |
do_lhs t1
|
blanchet@33192
|
1103 |
| do_eq _ = false
|
blanchet@33192
|
1104 |
in do_eq end
|
blanchet@33192
|
1105 |
|
blanchet@33192
|
1106 |
(* theory -> term list * term list * term list *)
|
blanchet@33192
|
1107 |
fun all_axioms_of thy =
|
blanchet@33192
|
1108 |
let
|
blanchet@33192
|
1109 |
(* theory list -> term list *)
|
blanchet@33192
|
1110 |
val axioms_of_thys = maps Thm.axioms_of #> map (apsnd prop_of)
|
blanchet@33192
|
1111 |
val specs = Defs.all_specifications_of (Theory.defs_of thy)
|
wenzelm@33701
|
1112 |
val def_names = specs |> maps snd |> map_filter #def
|
blanchet@33197
|
1113 |
|> OrdList.make fast_string_ord
|
blanchet@33192
|
1114 |
val thys = thy :: Theory.ancestors_of thy
|
blanchet@33192
|
1115 |
val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
|
blanchet@33192
|
1116 |
val built_in_axioms = axioms_of_thys built_in_thys
|
blanchet@33192
|
1117 |
val user_axioms = axioms_of_thys user_thys
|
blanchet@33192
|
1118 |
val (built_in_defs, built_in_nondefs) =
|
blanchet@33192
|
1119 |
partition_axioms_by_definitionality thy built_in_axioms def_names
|
blanchet@33197
|
1120 |
||> filter (is_typedef_axiom thy false)
|
blanchet@33192
|
1121 |
val (user_defs, user_nondefs) =
|
blanchet@33192
|
1122 |
partition_axioms_by_definitionality thy user_axioms def_names
|
blanchet@33197
|
1123 |
val (built_in_nondefs, user_nondefs) =
|
blanchet@33197
|
1124 |
List.partition (is_typedef_axiom thy false) user_nondefs
|
blanchet@33197
|
1125 |
|>> append built_in_nondefs
|
blanchet@34118
|
1126 |
val defs =
|
blanchet@34118
|
1127 |
(thy |> PureThy.all_thms_of
|
blanchet@34118
|
1128 |
|> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
|
blanchet@34118
|
1129 |
|> map (prop_of o snd) |> filter is_plain_definition) @
|
blanchet@34118
|
1130 |
user_defs @ built_in_defs
|
blanchet@33192
|
1131 |
in (defs, built_in_nondefs, user_nondefs) end
|
blanchet@33192
|
1132 |
|
blanchet@33192
|
1133 |
(* bool -> styp -> int option *)
|
blanchet@33192
|
1134 |
fun arity_of_built_in_const fast_descrs (s, T) =
|
blanchet@33192
|
1135 |
if s = @{const_name If} then
|
blanchet@33192
|
1136 |
if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
|
blanchet@33192
|
1137 |
else case AList.lookup (op =)
|
blanchet@33192
|
1138 |
(built_in_consts
|
blanchet@33192
|
1139 |
|> fast_descrs ? append built_in_descr_consts) s of
|
blanchet@33192
|
1140 |
SOME n => SOME n
|
blanchet@33192
|
1141 |
| NONE =>
|
blanchet@33192
|
1142 |
case AList.lookup (op =) built_in_typed_consts (s, T) of
|
blanchet@33192
|
1143 |
SOME n => SOME n
|
blanchet@33192
|
1144 |
| NONE =>
|
blanchet@33192
|
1145 |
if is_fun_type T andalso is_set_type (domain_type T) then
|
blanchet@33192
|
1146 |
AList.lookup (op =) built_in_set_consts s
|
blanchet@33192
|
1147 |
else
|
blanchet@33192
|
1148 |
NONE
|
blanchet@33192
|
1149 |
(* bool -> styp -> bool *)
|
blanchet@33192
|
1150 |
val is_built_in_const = is_some oo arity_of_built_in_const
|
blanchet@33192
|
1151 |
|
blanchet@33192
|
1152 |
(* This function is designed to work for both real definition axioms and
|
blanchet@33192
|
1153 |
simplification rules (equational specifications). *)
|
blanchet@33192
|
1154 |
(* term -> term *)
|
blanchet@33192
|
1155 |
fun term_under_def t =
|
blanchet@33192
|
1156 |
case t of
|
blanchet@33192
|
1157 |
@{const "==>"} $ _ $ t2 => term_under_def t2
|
blanchet@33192
|
1158 |
| Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
|
blanchet@33192
|
1159 |
| @{const Trueprop} $ t1 => term_under_def t1
|
blanchet@33192
|
1160 |
| Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
|
blanchet@33192
|
1161 |
| Abs (_, _, t') => term_under_def t'
|
blanchet@33192
|
1162 |
| t1 $ _ => term_under_def t1
|
blanchet@33192
|
1163 |
| _ => t
|
blanchet@33192
|
1164 |
|
blanchet@33192
|
1165 |
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
|
blanchet@33192
|
1166 |
traversal of the term, without which the wrong occurrence of a constant could
|
blanchet@33192
|
1167 |
be matched in the face of overloading. *)
|
blanchet@33192
|
1168 |
(* theory -> bool -> const_table -> styp -> term list *)
|
blanchet@33192
|
1169 |
fun def_props_for_const thy fast_descrs table (x as (s, _)) =
|
blanchet@33192
|
1170 |
if is_built_in_const fast_descrs x then
|
blanchet@33192
|
1171 |
[]
|
blanchet@33192
|
1172 |
else
|
blanchet@33192
|
1173 |
these (Symtab.lookup table s)
|
blanchet@33192
|
1174 |
|> map_filter (try (Refute.specialize_type thy x))
|
blanchet@34118
|
1175 |
|> filter (curry (op =) (Const x) o term_under_def)
|
blanchet@33192
|
1176 |
|
blanchet@33743
|
1177 |
(* theory -> term -> term option *)
|
blanchet@33192
|
1178 |
fun normalized_rhs_of thy t =
|
blanchet@33192
|
1179 |
let
|
blanchet@33743
|
1180 |
(* term option -> term option *)
|
blanchet@33743
|
1181 |
fun aux (v as Var _) (SOME t) = SOME (lambda v t)
|
blanchet@33743
|
1182 |
| aux (c as Const (@{const_name TYPE}, T)) (SOME t) = SOME (lambda c t)
|
blanchet@33743
|
1183 |
| aux _ _ = NONE
|
blanchet@33192
|
1184 |
val (lhs, rhs) =
|
blanchet@33192
|
1185 |
case t of
|
blanchet@33192
|
1186 |
Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
|
blanchet@33192
|
1187 |
| @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
|
blanchet@33192
|
1188 |
(t1, t2)
|
blanchet@33224
|
1189 |
| _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
|
blanchet@33192
|
1190 |
val args = strip_comb lhs |> snd
|
blanchet@33743
|
1191 |
in fold_rev aux args (SOME rhs) end
|
blanchet@33192
|
1192 |
|
blanchet@33192
|
1193 |
(* theory -> const_table -> styp -> term option *)
|
blanchet@33192
|
1194 |
fun def_of_const thy table (x as (s, _)) =
|
blanchet@33192
|
1195 |
if is_built_in_const false x orelse original_name s <> s then
|
blanchet@33192
|
1196 |
NONE
|
blanchet@33192
|
1197 |
else
|
blanchet@33192
|
1198 |
x |> def_props_for_const thy false table |> List.last
|
blanchet@33743
|
1199 |
|> normalized_rhs_of thy |> Option.map (prefix_abs_vars s)
|
blanchet@33192
|
1200 |
handle List.Empty => NONE
|
blanchet@33192
|
1201 |
|
blanchet@33192
|
1202 |
datatype fixpoint_kind = Lfp | Gfp | NoFp
|
blanchet@33192
|
1203 |
|
blanchet@33192
|
1204 |
(* term -> fixpoint_kind *)
|
blanchet@33192
|
1205 |
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
|
blanchet@33192
|
1206 |
| fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
|
blanchet@33192
|
1207 |
| fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
|
blanchet@33192
|
1208 |
| fixpoint_kind_of_rhs _ = NoFp
|
blanchet@33192
|
1209 |
|
blanchet@33192
|
1210 |
(* theory -> const_table -> term -> bool *)
|
blanchet@33192
|
1211 |
fun is_mutually_inductive_pred_def thy table t =
|
blanchet@33192
|
1212 |
let
|
blanchet@33192
|
1213 |
(* term -> bool *)
|
blanchet@33192
|
1214 |
fun is_good_arg (Bound _) = true
|
blanchet@33192
|
1215 |
| is_good_arg (Const (s, _)) =
|
blanchet@34923
|
1216 |
s = @{const_name True} orelse s = @{const_name False} orelse
|
blanchet@34923
|
1217 |
s = @{const_name undefined}
|
blanchet@33192
|
1218 |
| is_good_arg _ = false
|
blanchet@33192
|
1219 |
in
|
blanchet@33192
|
1220 |
case t |> strip_abs_body |> strip_comb of
|
blanchet@33192
|
1221 |
(Const x, ts as (_ :: _)) =>
|
blanchet@33192
|
1222 |
(case def_of_const thy table x of
|
blanchet@33192
|
1223 |
SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
|
blanchet@33192
|
1224 |
| NONE => false)
|
blanchet@33192
|
1225 |
| _ => false
|
blanchet@33192
|
1226 |
end
|
blanchet@33192
|
1227 |
(* theory -> const_table -> term -> term *)
|
blanchet@33192
|
1228 |
fun unfold_mutually_inductive_preds thy table =
|
blanchet@33192
|
1229 |
map_aterms (fn t as Const x =>
|
blanchet@33192
|
1230 |
(case def_of_const thy table x of
|
blanchet@33192
|
1231 |
SOME t' =>
|
blanchet@33192
|
1232 |
let val t' = Envir.eta_contract t' in
|
blanchet@33192
|
1233 |
if is_mutually_inductive_pred_def thy table t' then t'
|
blanchet@33192
|
1234 |
else t
|
blanchet@33192
|
1235 |
end
|
blanchet@33192
|
1236 |
| NONE => t)
|
blanchet@33192
|
1237 |
| t => t)
|
blanchet@33192
|
1238 |
|
blanchet@33192
|
1239 |
(* term -> string * term *)
|
blanchet@33192
|
1240 |
fun pair_for_prop t =
|
blanchet@33192
|
1241 |
case term_under_def t of
|
blanchet@33192
|
1242 |
Const (s, _) => (s, t)
|
blanchet@33192
|
1243 |
| Free _ => raise NOT_SUPPORTED "local definitions"
|
blanchet@33224
|
1244 |
| t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
|
blanchet@33192
|
1245 |
|
blanchet@33192
|
1246 |
(* (Proof.context -> term list) -> Proof.context -> const_table *)
|
blanchet@33192
|
1247 |
fun table_for get ctxt =
|
blanchet@33192
|
1248 |
get ctxt |> map pair_for_prop |> AList.group (op =) |> Symtab.make
|
blanchet@33192
|
1249 |
|
blanchet@33192
|
1250 |
(* theory -> (string * int) list *)
|
blanchet@33192
|
1251 |
fun case_const_names thy =
|
blanchet@33192
|
1252 |
Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
|
blanchet@33192
|
1253 |
if is_basic_datatype dtype_s then
|
blanchet@33192
|
1254 |
I
|
blanchet@33192
|
1255 |
else
|
blanchet@33192
|
1256 |
cons (case_name, AList.lookup (op =) descr index
|
blanchet@33192
|
1257 |
|> the |> #3 |> length))
|
blanchet@33192
|
1258 |
(Datatype.get_all thy) [] @
|
blanchet@33574
|
1259 |
map (apsnd length o snd) (#codatatypes (Data.get thy))
|
blanchet@33192
|
1260 |
|
blanchet@33192
|
1261 |
(* Proof.context -> term list -> const_table *)
|
blanchet@33192
|
1262 |
fun const_def_table ctxt ts =
|
blanchet@34123
|
1263 |
table_for (map prop_of o Nitpick_Defs.get) ctxt
|
blanchet@33192
|
1264 |
|> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
|
blanchet@33192
|
1265 |
(map pair_for_prop ts)
|
blanchet@33192
|
1266 |
(* term list -> const_table *)
|
blanchet@33192
|
1267 |
fun const_nondef_table ts =
|
blanchet@33192
|
1268 |
fold (fn t => append (map (fn s => (s, t)) (Term.add_const_names t []))) ts []
|
blanchet@33192
|
1269 |
|> AList.group (op =) |> Symtab.make
|
blanchet@33192
|
1270 |
(* Proof.context -> const_table *)
|
blanchet@33192
|
1271 |
val const_simp_table = table_for (map prop_of o Nitpick_Simps.get)
|
blanchet@33192
|
1272 |
val const_psimp_table = table_for (map prop_of o Nitpick_Psimps.get)
|
blanchet@33192
|
1273 |
(* Proof.context -> const_table -> const_table *)
|
blanchet@33192
|
1274 |
fun inductive_intro_table ctxt def_table =
|
blanchet@33192
|
1275 |
table_for (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
|
blanchet@33192
|
1276 |
def_table o prop_of)
|
blanchet@33192
|
1277 |
o Nitpick_Intros.get) ctxt
|
blanchet@33192
|
1278 |
(* theory -> term list Inttab.table *)
|
blanchet@33192
|
1279 |
fun ground_theorem_table thy =
|
blanchet@33192
|
1280 |
fold ((fn @{const Trueprop} $ t1 =>
|
blanchet@33192
|
1281 |
is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
|
blanchet@33192
|
1282 |
| _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
|
blanchet@33192
|
1283 |
|
blanchet@33192
|
1284 |
val basic_ersatz_table =
|
blanchet@33192
|
1285 |
[(@{const_name prod_case}, @{const_name split}),
|
blanchet@33192
|
1286 |
(@{const_name card}, @{const_name card'}),
|
blanchet@33192
|
1287 |
(@{const_name setsum}, @{const_name setsum'}),
|
blanchet@33192
|
1288 |
(@{const_name fold_graph}, @{const_name fold_graph'}),
|
blanchet@33192
|
1289 |
(@{const_name wf}, @{const_name wf'}),
|
blanchet@33192
|
1290 |
(@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
|
blanchet@33192
|
1291 |
(@{const_name wfrec}, @{const_name wfrec'})]
|
blanchet@33192
|
1292 |
|
blanchet@33192
|
1293 |
(* theory -> (string * string) list *)
|
blanchet@33192
|
1294 |
fun ersatz_table thy =
|
blanchet@33574
|
1295 |
fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
|
blanchet@33192
|
1296 |
|
blanchet@33192
|
1297 |
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
|
blanchet@33192
|
1298 |
fun add_simps simp_table s eqs =
|
blanchet@33192
|
1299 |
Unsynchronized.change simp_table
|
blanchet@33192
|
1300 |
(Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
|
blanchet@33192
|
1301 |
|
blanchet@33192
|
1302 |
(* Similar to "Refute.specialize_type" but returns all matches rather than only
|
blanchet@33192
|
1303 |
the first (preorder) match. *)
|
blanchet@33192
|
1304 |
(* theory -> styp -> term -> term list *)
|
blanchet@33197
|
1305 |
fun multi_specialize_type thy slack (x as (s, T)) t =
|
blanchet@33192
|
1306 |
let
|
blanchet@33192
|
1307 |
(* term -> (typ * term) list -> (typ * term) list *)
|
blanchet@33192
|
1308 |
fun aux (Const (s', T')) ys =
|
blanchet@33192
|
1309 |
if s = s' then
|
blanchet@33197
|
1310 |
ys |> (if AList.defined (op =) ys T' then
|
blanchet@33197
|
1311 |
I
|
blanchet@33574
|
1312 |
else
|
blanchet@33197
|
1313 |
cons (T', Refute.monomorphic_term
|
blanchet@33197
|
1314 |
(Sign.typ_match thy (T', T) Vartab.empty) t)
|
blanchet@33197
|
1315 |
handle Type.TYPE_MATCH => I
|
blanchet@33197
|
1316 |
| Refute.REFUTE _ =>
|
blanchet@33197
|
1317 |
if slack then
|
blanchet@33197
|
1318 |
I
|
blanchet@33197
|
1319 |
else
|
blanchet@33197
|
1320 |
raise NOT_SUPPORTED ("too much polymorphism in \
|
blanchet@33197
|
1321 |
\axiom involving " ^ quote s))
|
blanchet@33192
|
1322 |
else
|
blanchet@33192
|
1323 |
ys
|
blanchet@33192
|
1324 |
| aux _ ys = ys
|
blanchet@33192
|
1325 |
in map snd (fold_aterms aux t []) end
|
blanchet@33192
|
1326 |
|
blanchet@33197
|
1327 |
(* theory -> bool -> const_table -> styp -> term list *)
|
blanchet@33197
|
1328 |
fun nondef_props_for_const thy slack table (x as (s, _)) =
|
blanchet@33197
|
1329 |
these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
|
blanchet@33192
|
1330 |
|
blanchet@34923
|
1331 |
(* theory -> styp -> term list *)
|
blanchet@34923
|
1332 |
fun inverse_axioms_for_rep_fun thy (x as (_, T)) =
|
blanchet@34923
|
1333 |
let val abs_T = domain_type T in
|
blanchet@34923
|
1334 |
typedef_info thy (fst (dest_Type abs_T)) |> the
|
blanchet@34923
|
1335 |
|> pairf #Abs_inverse #Rep_inverse
|
blanchet@34923
|
1336 |
|> pairself (Refute.specialize_type thy x o prop_of o the)
|
blanchet@34923
|
1337 |
||> single |> op ::
|
blanchet@34923
|
1338 |
end
|
blanchet@33192
|
1339 |
(* theory -> styp list -> term list *)
|
blanchet@34923
|
1340 |
fun optimized_typedef_axioms thy (abs_z as (abs_s, abs_Ts)) =
|
blanchet@34923
|
1341 |
let val abs_T = Type abs_z in
|
blanchet@33192
|
1342 |
if is_univ_typedef thy abs_T then
|
blanchet@33192
|
1343 |
[]
|
blanchet@33192
|
1344 |
else case typedef_info thy abs_s of
|
blanchet@33192
|
1345 |
SOME {abs_type, rep_type, Abs_name, Rep_name, prop_of_Rep, set_name,
|
blanchet@33192
|
1346 |
...} =>
|
blanchet@33192
|
1347 |
let
|
blanchet@33192
|
1348 |
val rep_T = instantiate_type thy abs_type abs_T rep_type
|
blanchet@33192
|
1349 |
val rep_t = Const (Rep_name, abs_T --> rep_T)
|
blanchet@33192
|
1350 |
val set_t = Const (set_name, rep_T --> bool_T)
|
blanchet@33192
|
1351 |
val set_t' =
|
blanchet@33192
|
1352 |
prop_of_Rep |> HOLogic.dest_Trueprop
|
blanchet@33192
|
1353 |
|> Refute.specialize_type thy (dest_Const rep_t)
|
blanchet@33192
|
1354 |
|> HOLogic.dest_mem |> snd
|
blanchet@33192
|
1355 |
in
|
blanchet@33192
|
1356 |
[HOLogic.all_const abs_T
|
blanchet@33192
|
1357 |
$ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
|
blanchet@33192
|
1358 |
|> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
|
blanchet@33192
|
1359 |
|> map HOLogic.mk_Trueprop
|
blanchet@33192
|
1360 |
end
|
blanchet@33192
|
1361 |
| NONE => []
|
blanchet@33192
|
1362 |
end
|
blanchet@34923
|
1363 |
fun optimized_quot_type_axioms thy abs_z =
|
blanchet@34923
|
1364 |
let
|
blanchet@34923
|
1365 |
val abs_T = Type abs_z
|
blanchet@34923
|
1366 |
val rep_T = rep_type_for_quot_type thy abs_T
|
blanchet@34923
|
1367 |
val equiv_rel = equiv_relation_for_quot_type thy abs_T
|
blanchet@34923
|
1368 |
val a_var = Var (("a", 0), abs_T)
|
blanchet@34923
|
1369 |
val x_var = Var (("x", 0), rep_T)
|
blanchet@34923
|
1370 |
val y_var = Var (("y", 0), rep_T)
|
blanchet@34923
|
1371 |
val x = (@{const_name Quot}, rep_T --> abs_T)
|
blanchet@34923
|
1372 |
val sel_a_t = select_nth_constr_arg thy x a_var 0 rep_T
|
blanchet@34923
|
1373 |
val normal_t = Const (@{const_name quot_normal}, rep_T --> rep_T)
|
blanchet@34923
|
1374 |
val normal_x = normal_t $ x_var
|
blanchet@34923
|
1375 |
val normal_y = normal_t $ y_var
|
blanchet@34923
|
1376 |
val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
|
blanchet@34923
|
1377 |
in
|
blanchet@34969
|
1378 |
[Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
|
blanchet@34923
|
1379 |
Logic.list_implies
|
blanchet@34969
|
1380 |
([@{const Not} $ (is_unknown_t $ normal_x),
|
blanchet@34923
|
1381 |
@{const Not} $ (is_unknown_t $ normal_y),
|
blanchet@34923
|
1382 |
equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
|
blanchet@34923
|
1383 |
Logic.mk_equals (normal_x, normal_y)),
|
blanchet@34923
|
1384 |
@{const "==>"}
|
blanchet@34923
|
1385 |
$ (HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)))
|
blanchet@34923
|
1386 |
$ (HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
|
blanchet@33864
|
1387 |
end
|
blanchet@33192
|
1388 |
|
blanchet@33192
|
1389 |
(* theory -> int * styp -> term *)
|
blanchet@33192
|
1390 |
fun constr_case_body thy (j, (x as (_, T))) =
|
blanchet@33192
|
1391 |
let val arg_Ts = binder_types T in
|
blanchet@33192
|
1392 |
list_comb (Bound j, map2 (select_nth_constr_arg thy x (Bound 0))
|
blanchet@33192
|
1393 |
(index_seq 0 (length arg_Ts)) arg_Ts)
|
blanchet@33192
|
1394 |
end
|
blanchet@33571
|
1395 |
(* extended_context -> typ -> int * styp -> term -> term *)
|
blanchet@33571
|
1396 |
fun add_constr_case (ext_ctxt as {thy, ...}) res_T (j, x) res_t =
|
blanchet@34121
|
1397 |
Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
|
blanchet@33571
|
1398 |
$ discriminate_value ext_ctxt x (Bound 0) $ constr_case_body thy (j, x)
|
blanchet@33571
|
1399 |
$ res_t
|
blanchet@33571
|
1400 |
(* extended_context -> typ -> typ -> term *)
|
blanchet@33571
|
1401 |
fun optimized_case_def (ext_ctxt as {thy, ...}) dataT res_T =
|
blanchet@33192
|
1402 |
let
|
blanchet@33571
|
1403 |
val xs = datatype_constrs ext_ctxt dataT
|
blanchet@34969
|
1404 |
val xs' = filter_out (fn (s, _) => s = @{const_name NonStd}) xs
|
blanchet@34969
|
1405 |
val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs'
|
blanchet@33192
|
1406 |
in
|
blanchet@34969
|
1407 |
(if length xs = length xs' then
|
blanchet@34969
|
1408 |
let
|
blanchet@34969
|
1409 |
val (xs'', x) = split_last xs'
|
blanchet@34969
|
1410 |
in
|
blanchet@34969
|
1411 |
constr_case_body thy (1, x)
|
blanchet@34969
|
1412 |
|> fold_rev (add_constr_case ext_ctxt res_T)
|
blanchet@34969
|
1413 |
(length xs' downto 2 ~~ xs'')
|
blanchet@34969
|
1414 |
end
|
blanchet@34969
|
1415 |
else
|
blanchet@34969
|
1416 |
Const (@{const_name undefined}, dataT --> res_T) $ Bound 0
|
blanchet@34969
|
1417 |
|> fold_rev (add_constr_case ext_ctxt res_T)
|
blanchet@34969
|
1418 |
(length xs' downto 1 ~~ xs'))
|
blanchet@33192
|
1419 |
|> fold_rev (curry absdummy) (func_Ts @ [dataT])
|
blanchet@33192
|
1420 |
end
|
blanchet@33192
|
1421 |
|
blanchet@33571
|
1422 |
(* extended_context -> string -> typ -> typ -> term -> term *)
|
blanchet@33571
|
1423 |
fun optimized_record_get (ext_ctxt as {thy, ...}) s rec_T res_T t =
|
blanchet@34969
|
1424 |
let val constr_x = hd (datatype_constrs ext_ctxt rec_T) in
|
blanchet@33192
|
1425 |
case no_of_record_field thy s rec_T of
|
blanchet@33192
|
1426 |
~1 => (case rec_T of
|
blanchet@33192
|
1427 |
Type (_, Ts as _ :: _) =>
|
blanchet@33192
|
1428 |
let
|
blanchet@33192
|
1429 |
val rec_T' = List.last Ts
|
blanchet@33192
|
1430 |
val j = num_record_fields thy rec_T - 1
|
blanchet@33192
|
1431 |
in
|
blanchet@33192
|
1432 |
select_nth_constr_arg thy constr_x t j res_T
|
blanchet@33571
|
1433 |
|> optimized_record_get ext_ctxt s rec_T' res_T
|
blanchet@33192
|
1434 |
end
|
blanchet@33224
|
1435 |
| _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
|
blanchet@33224
|
1436 |
[]))
|
blanchet@33192
|
1437 |
| j => select_nth_constr_arg thy constr_x t j res_T
|
blanchet@33192
|
1438 |
end
|
blanchet@33571
|
1439 |
(* extended_context -> string -> typ -> term -> term -> term *)
|
blanchet@33571
|
1440 |
fun optimized_record_update (ext_ctxt as {thy, ...}) s rec_T fun_t rec_t =
|
blanchet@33192
|
1441 |
let
|
blanchet@34969
|
1442 |
val constr_x as (_, constr_T) = hd (datatype_constrs ext_ctxt rec_T)
|
blanchet@33192
|
1443 |
val Ts = binder_types constr_T
|
blanchet@33192
|
1444 |
val n = length Ts
|
blanchet@33192
|
1445 |
val special_j = no_of_record_field thy s rec_T
|
blanchet@33192
|
1446 |
val ts = map2 (fn j => fn T =>
|
blanchet@33192
|
1447 |
let
|
blanchet@33192
|
1448 |
val t = select_nth_constr_arg thy constr_x rec_t j T
|
blanchet@33192
|
1449 |
in
|
blanchet@33192
|
1450 |
if j = special_j then
|
blanchet@33192
|
1451 |
betapply (fun_t, t)
|
blanchet@33192
|
1452 |
else if j = n - 1 andalso special_j = ~1 then
|
blanchet@33571
|
1453 |
optimized_record_update ext_ctxt s
|
blanchet@33192
|
1454 |
(rec_T |> dest_Type |> snd |> List.last) fun_t t
|
blanchet@33192
|
1455 |
else
|
blanchet@33192
|
1456 |
t
|
blanchet@33192
|
1457 |
end) (index_seq 0 n) Ts
|
blanchet@33192
|
1458 |
in list_comb (Const constr_x, ts) end
|
blanchet@33192
|
1459 |
|
blanchet@33192
|
1460 |
(* Constants "c" whose definition is of the form "c == c'", where "c'" is also a
|
blanchet@33192
|
1461 |
constant, are said to be trivial. For those, we ignore the simplification
|
blanchet@33192
|
1462 |
rules and use the definition instead, to ensure that built-in symbols like
|
blanchet@33192
|
1463 |
"ord_nat_inst.less_eq_nat" are picked up correctly. *)
|
blanchet@33192
|
1464 |
(* theory -> const_table -> styp -> bool *)
|
blanchet@33192
|
1465 |
fun has_trivial_definition thy table x =
|
blanchet@33192
|
1466 |
case def_of_const thy table x of SOME (Const _) => true | _ => false
|
blanchet@33192
|
1467 |
|
blanchet@33192
|
1468 |
(* theory -> const_table -> string * typ -> fixpoint_kind *)
|
blanchet@33192
|
1469 |
fun fixpoint_kind_of_const thy table x =
|
blanchet@33192
|
1470 |
if is_built_in_const false x then
|
blanchet@33192
|
1471 |
NoFp
|
blanchet@33192
|
1472 |
else
|
blanchet@33192
|
1473 |
fixpoint_kind_of_rhs (the (def_of_const thy table x))
|
blanchet@33192
|
1474 |
handle Option.Option => NoFp
|
blanchet@33192
|
1475 |
|
blanchet@33192
|
1476 |
(* extended_context -> styp -> bool *)
|
blanchet@33192
|
1477 |
fun is_real_inductive_pred ({thy, fast_descrs, def_table, intro_table, ...}
|
blanchet@33192
|
1478 |
: extended_context) x =
|
blanchet@34923
|
1479 |
not (null (def_props_for_const thy fast_descrs intro_table x)) andalso
|
blanchet@34923
|
1480 |
fixpoint_kind_of_const thy def_table x <> NoFp
|
blanchet@33192
|
1481 |
fun is_real_equational_fun ({thy, fast_descrs, simp_table, psimp_table, ...}
|
blanchet@33192
|
1482 |
: extended_context) x =
|
blanchet@33192
|
1483 |
exists (fn table => not (null (def_props_for_const thy fast_descrs table x)))
|
blanchet@33192
|
1484 |
[!simp_table, psimp_table]
|
blanchet@33192
|
1485 |
fun is_inductive_pred ext_ctxt =
|
blanchet@33192
|
1486 |
is_real_inductive_pred ext_ctxt andf (not o is_real_equational_fun ext_ctxt)
|
blanchet@33192
|
1487 |
fun is_equational_fun (ext_ctxt as {thy, def_table, ...}) =
|
blanchet@33192
|
1488 |
(is_real_equational_fun ext_ctxt orf is_real_inductive_pred ext_ctxt
|
blanchet@33192
|
1489 |
orf (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
|
blanchet@33192
|
1490 |
andf (not o has_trivial_definition thy def_table)
|
blanchet@33192
|
1491 |
|
blanchet@33192
|
1492 |
(* term * term -> term *)
|
blanchet@33192
|
1493 |
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
|
blanchet@33192
|
1494 |
| s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
|
blanchet@33192
|
1495 |
| s_betapply p = betapply p
|
blanchet@33192
|
1496 |
(* term * term list -> term *)
|
blanchet@33192
|
1497 |
val s_betapplys = Library.foldl s_betapply
|
blanchet@33192
|
1498 |
|
blanchet@33192
|
1499 |
(* term -> term *)
|
blanchet@33192
|
1500 |
fun lhs_of_equation t =
|
blanchet@33192
|
1501 |
case t of
|
blanchet@33192
|
1502 |
Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
|
blanchet@33192
|
1503 |
| Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
|
blanchet@33192
|
1504 |
| @{const "==>"} $ _ $ t2 => lhs_of_equation t2
|
blanchet@33192
|
1505 |
| @{const Trueprop} $ t1 => lhs_of_equation t1
|
blanchet@33192
|
1506 |
| Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
|
blanchet@33192
|
1507 |
| Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
|
blanchet@33192
|
1508 |
| @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
|
blanchet@33192
|
1509 |
| _ => NONE
|
blanchet@33192
|
1510 |
(* theory -> term -> bool *)
|
blanchet@33192
|
1511 |
fun is_constr_pattern _ (Bound _) = true
|
blanchet@33864
|
1512 |
| is_constr_pattern _ (Var _) = true
|
blanchet@33192
|
1513 |
| is_constr_pattern thy t =
|
blanchet@33192
|
1514 |
case strip_comb t of
|
blanchet@33192
|
1515 |
(Const (x as (s, _)), args) =>
|
blanchet@33192
|
1516 |
is_constr_like thy x andalso forall (is_constr_pattern thy) args
|
blanchet@33192
|
1517 |
| _ => false
|
blanchet@33192
|
1518 |
fun is_constr_pattern_lhs thy t =
|
blanchet@33192
|
1519 |
forall (is_constr_pattern thy) (snd (strip_comb t))
|
blanchet@33192
|
1520 |
fun is_constr_pattern_formula thy t =
|
blanchet@33192
|
1521 |
case lhs_of_equation t of
|
blanchet@33192
|
1522 |
SOME t' => is_constr_pattern_lhs thy t'
|
blanchet@33192
|
1523 |
| NONE => false
|
blanchet@33192
|
1524 |
|
blanchet@33747
|
1525 |
val unfold_max_depth = 255
|
blanchet@33747
|
1526 |
val axioms_max_depth = 255
|
blanchet@33192
|
1527 |
|
blanchet@33192
|
1528 |
(* extended_context -> term -> term *)
|
blanchet@33192
|
1529 |
fun unfold_defs_in_term (ext_ctxt as {thy, destroy_constrs, fast_descrs,
|
blanchet@33192
|
1530 |
case_names, def_table, ground_thm_table,
|
blanchet@33192
|
1531 |
ersatz_table, ...}) =
|
blanchet@33192
|
1532 |
let
|
blanchet@33192
|
1533 |
(* int -> typ list -> term -> term *)
|
blanchet@33192
|
1534 |
fun do_term depth Ts t =
|
blanchet@33192
|
1535 |
case t of
|
blanchet@33192
|
1536 |
(t0 as Const (@{const_name Int.number_class.number_of},
|
blanchet@33192
|
1537 |
Type ("fun", [_, ran_T]))) $ t1 =>
|
blanchet@33192
|
1538 |
((if is_number_type thy ran_T then
|
blanchet@33192
|
1539 |
let
|
blanchet@33192
|
1540 |
val j = t1 |> HOLogic.dest_numeral
|
blanchet@33882
|
1541 |
|> ran_T = nat_T ? Integer.max 0
|
blanchet@33192
|
1542 |
val s = numeral_prefix ^ signed_string_of_int j
|
blanchet@33192
|
1543 |
in
|
blanchet@33192
|
1544 |
if is_integer_type ran_T then
|
blanchet@33192
|
1545 |
Const (s, ran_T)
|
blanchet@33192
|
1546 |
else
|
blanchet@33192
|
1547 |
do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
|
blanchet@33192
|
1548 |
$ Const (s, int_T))
|
blanchet@33192
|
1549 |
end
|
blanchet@33192
|
1550 |
handle TERM _ => raise SAME ()
|
blanchet@33192
|
1551 |
else
|
blanchet@33192
|
1552 |
raise SAME ())
|
blanchet@33192
|
1553 |
handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
|
blanchet@33864
|
1554 |
| Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
|
blanchet@33192
|
1555 |
do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
|
blanchet@33192
|
1556 |
| (t0 as Const (x as (@{const_name Sigma}, T))) $ t1
|
blanchet@33192
|
1557 |
$ (t2 as Abs (_, _, t2')) =>
|
blanchet@33192
|
1558 |
betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
|
blanchet@33192
|
1559 |
map (do_term depth Ts) [t1, t2])
|
blanchet@33192
|
1560 |
| Const (x as (@{const_name distinct},
|
blanchet@33192
|
1561 |
Type ("fun", [Type (@{type_name list}, [T']), _])))
|
blanchet@33192
|
1562 |
$ (t1 as _ $ _) =>
|
blanchet@33192
|
1563 |
(t1 |> HOLogic.dest_list |> distinctness_formula T'
|
blanchet@33192
|
1564 |
handle TERM _ => do_const depth Ts t x [t1])
|
blanchet@33192
|
1565 |
| (t0 as Const (x as (@{const_name If}, _))) $ t1 $ t2 $ t3 =>
|
blanchet@34923
|
1566 |
if is_ground_term t1 andalso
|
blanchet@34923
|
1567 |
exists (Pattern.matches thy o rpair t1)
|
blanchet@34923
|
1568 |
(Inttab.lookup_list ground_thm_table (hash_term t1)) then
|
blanchet@33192
|
1569 |
do_term depth Ts t2
|
blanchet@33192
|
1570 |
else
|
blanchet@33192
|
1571 |
do_const depth Ts t x [t1, t2, t3]
|
blanchet@33192
|
1572 |
| Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
|
blanchet@33192
|
1573 |
| Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
|
blanchet@33192
|
1574 |
| Const x $ t1 => do_const depth Ts t x [t1]
|
blanchet@33192
|
1575 |
| Const x => do_const depth Ts t x []
|
blanchet@33192
|
1576 |
| t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
|
blanchet@33192
|
1577 |
| Free _ => t
|
blanchet@33192
|
1578 |
| Var _ => t
|
blanchet@33192
|
1579 |
| Bound _ => t
|
blanchet@33192
|
1580 |
| Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
|
blanchet@33192
|
1581 |
(* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
|
blanchet@33192
|
1582 |
and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
|
blanchet@33192
|
1583 |
(Abs (Name.uu, body_type T,
|
blanchet@33192
|
1584 |
select_nth_constr_arg thy x (Bound 0) n res_T), [])
|
blanchet@33192
|
1585 |
| select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
|
blanchet@33192
|
1586 |
(select_nth_constr_arg thy x (do_term depth Ts t) n res_T, ts)
|
blanchet@33192
|
1587 |
(* int -> typ list -> term -> styp -> term list -> term *)
|
blanchet@33192
|
1588 |
and do_const depth Ts t (x as (s, T)) ts =
|
blanchet@33192
|
1589 |
case AList.lookup (op =) ersatz_table s of
|
blanchet@33192
|
1590 |
SOME s' =>
|
blanchet@33192
|
1591 |
do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
|
blanchet@33192
|
1592 |
| NONE =>
|
blanchet@33192
|
1593 |
let
|
blanchet@33192
|
1594 |
val (const, ts) =
|
blanchet@33192
|
1595 |
if is_built_in_const fast_descrs x then
|
blanchet@33877
|
1596 |
(Const x, ts)
|
blanchet@33192
|
1597 |
else case AList.lookup (op =) case_names s of
|
blanchet@33192
|
1598 |
SOME n =>
|
blanchet@33192
|
1599 |
let
|
blanchet@33192
|
1600 |
val (dataT, res_T) = nth_range_type n T
|
blanchet@33705
|
1601 |
|> pairf domain_type range_type
|
blanchet@33192
|
1602 |
in
|
blanchet@33571
|
1603 |
(optimized_case_def ext_ctxt dataT res_T
|
blanchet@33192
|
1604 |
|> do_term (depth + 1) Ts, ts)
|
blanchet@33192
|
1605 |
end
|
blanchet@33192
|
1606 |
| _ =>
|
blanchet@33192
|
1607 |
if is_constr thy x then
|
blanchet@33192
|
1608 |
(Const x, ts)
|
blanchet@33572
|
1609 |
else if is_stale_constr thy x then
|
blanchet@34923
|
1610 |
raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
|
blanchet@33572
|
1611 |
\(\"" ^ s ^ "\")")
|
blanchet@34923
|
1612 |
else if is_quot_abs_fun thy x then
|
blanchet@34923
|
1613 |
let
|
blanchet@34923
|
1614 |
val rep_T = domain_type T
|
blanchet@34923
|
1615 |
val abs_T = range_type T
|
blanchet@34923
|
1616 |
in
|
blanchet@34923
|
1617 |
(Abs (Name.uu, rep_T,
|
blanchet@34923
|
1618 |
Const (@{const_name Quot}, rep_T --> abs_T)
|
blanchet@34923
|
1619 |
$ (Const (@{const_name quot_normal},
|
blanchet@34923
|
1620 |
rep_T --> rep_T) $ Bound 0)), ts)
|
blanchet@34923
|
1621 |
end
|
blanchet@34923
|
1622 |
else if is_quot_rep_fun thy x then
|
blanchet@34923
|
1623 |
let
|
blanchet@34923
|
1624 |
val abs_T = domain_type T
|
blanchet@34923
|
1625 |
val rep_T = range_type T
|
blanchet@34923
|
1626 |
val x' = (@{const_name Quot}, rep_T --> abs_T)
|
blanchet@34923
|
1627 |
in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
|
blanchet@33192
|
1628 |
else if is_record_get thy x then
|
blanchet@33192
|
1629 |
case length ts of
|
blanchet@33192
|
1630 |
0 => (do_term depth Ts (eta_expand Ts t 1), [])
|
blanchet@33571
|
1631 |
| _ => (optimized_record_get ext_ctxt s (domain_type T)
|
blanchet@34969
|
1632 |
(range_type T) (do_term depth Ts (hd ts)), tl ts)
|
blanchet@33192
|
1633 |
else if is_record_update thy x then
|
blanchet@33192
|
1634 |
case length ts of
|
blanchet@33571
|
1635 |
2 => (optimized_record_update ext_ctxt
|
blanchet@33571
|
1636 |
(unsuffix Record.updateN s) (nth_range_type 2 T)
|
blanchet@33571
|
1637 |
(do_term depth Ts (hd ts))
|
blanchet@33571
|
1638 |
(do_term depth Ts (nth ts 1)), [])
|
blanchet@33192
|
1639 |
| n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
|
blanchet@33192
|
1640 |
else if is_rep_fun thy x then
|
blanchet@33192
|
1641 |
let val x' = mate_of_rep_fun thy x in
|
blanchet@33192
|
1642 |
if is_constr thy x' then
|
blanchet@33192
|
1643 |
select_nth_constr_arg_with_args depth Ts x' ts 0
|
blanchet@33192
|
1644 |
(range_type T)
|
blanchet@33192
|
1645 |
else
|
blanchet@33192
|
1646 |
(Const x, ts)
|
blanchet@33192
|
1647 |
end
|
blanchet@33192
|
1648 |
else if is_equational_fun ext_ctxt x then
|
blanchet@33192
|
1649 |
(Const x, ts)
|
blanchet@33192
|
1650 |
else case def_of_const thy def_table x of
|
blanchet@33192
|
1651 |
SOME def =>
|
blanchet@33192
|
1652 |
if depth > unfold_max_depth then
|
blanchet@34121
|
1653 |
raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
|
blanchet@34121
|
1654 |
"too many nested definitions (" ^
|
blanchet@34121
|
1655 |
string_of_int depth ^ ") while expanding " ^
|
blanchet@34121
|
1656 |
quote s)
|
blanchet@33192
|
1657 |
else if s = @{const_name wfrec'} then
|
blanchet@33192
|
1658 |
(do_term (depth + 1) Ts (betapplys (def, ts)), [])
|
blanchet@33192
|
1659 |
else
|
blanchet@33192
|
1660 |
(do_term (depth + 1) Ts def, ts)
|
blanchet@33192
|
1661 |
| NONE => (Const x, ts)
|
blanchet@33192
|
1662 |
in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
|
blanchet@33192
|
1663 |
in do_term 0 [] end
|
blanchet@33192
|
1664 |
|
blanchet@33571
|
1665 |
(* extended_context -> typ -> term list *)
|
blanchet@33571
|
1666 |
fun codatatype_bisim_axioms (ext_ctxt as {thy, ...}) T =
|
blanchet@33192
|
1667 |
let
|
blanchet@33571
|
1668 |
val xs = datatype_constrs ext_ctxt T
|
blanchet@33192
|
1669 |
val set_T = T --> bool_T
|
blanchet@33192
|
1670 |
val iter_T = @{typ bisim_iterator}
|
blanchet@34121
|
1671 |
val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
|
blanchet@33192
|
1672 |
val bisim_max = @{const bisim_iterator_max}
|
blanchet@33192
|
1673 |
val n_var = Var (("n", 0), iter_T)
|
blanchet@33192
|
1674 |
val n_var_minus_1 =
|
blanchet@33192
|
1675 |
Const (@{const_name Tha}, (iter_T --> bool_T) --> iter_T)
|
blanchet@33192
|
1676 |
$ Abs ("m", iter_T, HOLogic.eq_const iter_T
|
blanchet@33192
|
1677 |
$ (suc_const iter_T $ Bound 0) $ n_var)
|
blanchet@33192
|
1678 |
val x_var = Var (("x", 0), T)
|
blanchet@33192
|
1679 |
val y_var = Var (("y", 0), T)
|
blanchet@33192
|
1680 |
(* styp -> int -> typ -> term *)
|
blanchet@33192
|
1681 |
fun nth_sub_bisim x n nth_T =
|
blanchet@33192
|
1682 |
(if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
|
blanchet@33192
|
1683 |
else HOLogic.eq_const nth_T)
|
blanchet@33192
|
1684 |
$ select_nth_constr_arg thy x x_var n nth_T
|
blanchet@33192
|
1685 |
$ select_nth_constr_arg thy x y_var n nth_T
|
blanchet@33192
|
1686 |
(* styp -> term *)
|
blanchet@33192
|
1687 |
fun case_func (x as (_, T)) =
|
blanchet@33192
|
1688 |
let
|
blanchet@33192
|
1689 |
val arg_Ts = binder_types T
|
blanchet@33192
|
1690 |
val core_t =
|
blanchet@33571
|
1691 |
discriminate_value ext_ctxt x y_var ::
|
blanchet@33192
|
1692 |
map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
|
blanchet@33192
|
1693 |
|> foldr1 s_conj
|
blanchet@33192
|
1694 |
in List.foldr absdummy core_t arg_Ts end
|
blanchet@33192
|
1695 |
in
|
blanchet@33192
|
1696 |
[HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
|
blanchet@33192
|
1697 |
$ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
|
blanchet@33571
|
1698 |
$ (betapplys (optimized_case_def ext_ctxt T bool_T,
|
blanchet@33192
|
1699 |
map case_func xs @ [x_var]))),
|
blanchet@33192
|
1700 |
HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
|
blanchet@34121
|
1701 |
$ (Const (@{const_name insert}, T --> set_T --> set_T)
|
blanchet@33192
|
1702 |
$ x_var $ Const (@{const_name bot_fun_inst.bot_fun}, set_T))]
|
blanchet@33192
|
1703 |
|> map HOLogic.mk_Trueprop
|
blanchet@33192
|
1704 |
end
|
blanchet@33192
|
1705 |
|
blanchet@33192
|
1706 |
exception NO_TRIPLE of unit
|
blanchet@33192
|
1707 |
|
blanchet@33192
|
1708 |
(* theory -> styp -> term -> term list * term list * term *)
|
blanchet@33192
|
1709 |
fun triple_for_intro_rule thy x t =
|
blanchet@33192
|
1710 |
let
|
blanchet@33192
|
1711 |
val prems = Logic.strip_imp_prems t |> map (ObjectLogic.atomize_term thy)
|
blanchet@33192
|
1712 |
val concl = Logic.strip_imp_concl t |> ObjectLogic.atomize_term thy
|
blanchet@34118
|
1713 |
val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
|
blanchet@33192
|
1714 |
(* term -> bool *)
|
blanchet@34118
|
1715 |
val is_good_head = curry (op =) (Const x) o head_of
|
blanchet@33192
|
1716 |
in
|
blanchet@33192
|
1717 |
if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
|
blanchet@33192
|
1718 |
end
|
blanchet@33192
|
1719 |
|
blanchet@33192
|
1720 |
(* term -> term *)
|
blanchet@33192
|
1721 |
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
|
blanchet@33192
|
1722 |
|
blanchet@33192
|
1723 |
(* indexname * typ -> term list -> term -> term -> term *)
|
blanchet@33192
|
1724 |
fun wf_constraint_for rel side concl main =
|
blanchet@33192
|
1725 |
let
|
blanchet@33192
|
1726 |
val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
|
blanchet@33192
|
1727 |
tuple_for_args concl), Var rel)
|
blanchet@33192
|
1728 |
val t = List.foldl HOLogic.mk_imp core side
|
blanchet@33192
|
1729 |
val vars = filter (not_equal rel) (Term.add_vars t [])
|
blanchet@33192
|
1730 |
in
|
blanchet@33192
|
1731 |
Library.foldl (fn (t', ((x, j), T)) =>
|
blanchet@33192
|
1732 |
HOLogic.all_const T
|
blanchet@33192
|
1733 |
$ Abs (x, T, abstract_over (Var ((x, j), T), t')))
|
blanchet@33192
|
1734 |
(t, vars)
|
blanchet@33192
|
1735 |
end
|
blanchet@33192
|
1736 |
|
blanchet@33192
|
1737 |
(* indexname * typ -> term list * term list * term -> term *)
|
blanchet@33192
|
1738 |
fun wf_constraint_for_triple rel (side, main, concl) =
|
blanchet@33192
|
1739 |
map (wf_constraint_for rel side concl) main |> foldr1 s_conj
|
blanchet@33192
|
1740 |
|
blanchet@33192
|
1741 |
(* Proof.context -> Time.time option -> thm
|
blanchet@33192
|
1742 |
-> (Proof.context -> tactic -> tactic) -> bool *)
|
blanchet@33192
|
1743 |
fun terminates_by ctxt timeout goal tac =
|
blanchet@33192
|
1744 |
can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
|
blanchet@33192
|
1745 |
#> SINGLE (DETERM_TIMEOUT timeout
|
blanchet@33192
|
1746 |
(tac ctxt (auto_tac (clasimpset_of ctxt))))
|
blanchet@33192
|
1747 |
#> the #> Goal.finish ctxt) goal
|
blanchet@33192
|
1748 |
|
blanchet@33548
|
1749 |
val max_cached_wfs = 100
|
blanchet@33192
|
1750 |
val cached_timeout = Unsynchronized.ref (SOME Time.zeroTime)
|
blanchet@33192
|
1751 |
val cached_wf_props : (term * bool) list Unsynchronized.ref =
|
blanchet@33192
|
1752 |
Unsynchronized.ref []
|
blanchet@33192
|
1753 |
|
krauss@33351
|
1754 |
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
|
blanchet@33192
|
1755 |
ScnpReconstruct.sizechange_tac]
|
blanchet@33192
|
1756 |
|
blanchet@33192
|
1757 |
(* extended_context -> const_table -> styp -> bool *)
|
blanchet@33571
|
1758 |
fun uncached_is_well_founded_inductive_pred
|
blanchet@33192
|
1759 |
({thy, ctxt, debug, fast_descrs, tac_timeout, intro_table, ...}
|
blanchet@33192
|
1760 |
: extended_context) (x as (_, T)) =
|
blanchet@33192
|
1761 |
case def_props_for_const thy fast_descrs intro_table x of
|
blanchet@33571
|
1762 |
[] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
|
blanchet@33224
|
1763 |
[Const x])
|
blanchet@33192
|
1764 |
| intro_ts =>
|
blanchet@33192
|
1765 |
(case map (triple_for_intro_rule thy x) intro_ts
|
blanchet@33192
|
1766 |
|> filter_out (null o #2) of
|
blanchet@33192
|
1767 |
[] => true
|
blanchet@33192
|
1768 |
| triples =>
|
blanchet@33192
|
1769 |
let
|
blanchet@33192
|
1770 |
val binders_T = HOLogic.mk_tupleT (binder_types T)
|
blanchet@33192
|
1771 |
val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
|
blanchet@33882
|
1772 |
val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
|
blanchet@33192
|
1773 |
val rel = (("R", j), rel_T)
|
blanchet@33192
|
1774 |
val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
|
blanchet@33192
|
1775 |
map (wf_constraint_for_triple rel) triples
|
blanchet@33192
|
1776 |
|> foldr1 s_conj |> HOLogic.mk_Trueprop
|
blanchet@33192
|
1777 |
val _ = if debug then
|
blanchet@33192
|
1778 |
priority ("Wellfoundedness goal: " ^
|
blanchet@33192
|
1779 |
Syntax.string_of_term ctxt prop ^ ".")
|
blanchet@33192
|
1780 |
else
|
blanchet@33192
|
1781 |
()
|
blanchet@33192
|
1782 |
in
|
blanchet@34923
|
1783 |
if tac_timeout = (!cached_timeout) andalso
|
blanchet@34923
|
1784 |
length (!cached_wf_props) < max_cached_wfs then
|
blanchet@33548
|
1785 |
()
|
blanchet@33548
|
1786 |
else
|
blanchet@33548
|
1787 |
(cached_wf_props := []; cached_timeout := tac_timeout);
|
blanchet@33192
|
1788 |
case AList.lookup (op =) (!cached_wf_props) prop of
|
blanchet@33192
|
1789 |
SOME wf => wf
|
blanchet@33192
|
1790 |
| NONE =>
|
blanchet@33192
|
1791 |
let
|
blanchet@33192
|
1792 |
val goal = prop |> cterm_of thy |> Goal.init
|
blanchet@33705
|
1793 |
val wf = exists (terminates_by ctxt tac_timeout goal)
|
blanchet@33705
|
1794 |
termination_tacs
|
blanchet@33192
|
1795 |
in Unsynchronized.change cached_wf_props (cons (prop, wf)); wf end
|
blanchet@33192
|
1796 |
end)
|
blanchet@33192
|
1797 |
handle List.Empty => false
|
blanchet@33192
|
1798 |
| NO_TRIPLE () => false
|
blanchet@33192
|
1799 |
|
blanchet@33192
|
1800 |
(* The type constraint below is a workaround for a Poly/ML bug. *)
|
blanchet@33192
|
1801 |
|
blanchet@33192
|
1802 |
(* extended_context -> styp -> bool *)
|
blanchet@33192
|
1803 |
fun is_well_founded_inductive_pred
|
blanchet@33192
|
1804 |
(ext_ctxt as {thy, wfs, def_table, wf_cache, ...} : extended_context)
|
blanchet@33192
|
1805 |
(x as (s, _)) =
|
blanchet@33192
|
1806 |
case triple_lookup (const_match thy) wfs x of
|
blanchet@33192
|
1807 |
SOME (SOME b) => b
|
blanchet@34923
|
1808 |
| _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
|
blanchet@34923
|
1809 |
case AList.lookup (op =) (!wf_cache) x of
|
blanchet@33192
|
1810 |
SOME (_, wf) => wf
|
blanchet@33192
|
1811 |
| NONE =>
|
blanchet@33192
|
1812 |
let
|
blanchet@33192
|
1813 |
val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
|
blanchet@33571
|
1814 |
val wf = uncached_is_well_founded_inductive_pred ext_ctxt x
|
blanchet@33192
|
1815 |
in
|
blanchet@33192
|
1816 |
Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
|
blanchet@33192
|
1817 |
end
|
blanchet@33192
|
1818 |
|
blanchet@33192
|
1819 |
(* typ list -> typ -> typ -> term -> term *)
|
blanchet@33192
|
1820 |
fun ap_curry [_] _ _ t = t
|
blanchet@33192
|
1821 |
| ap_curry arg_Ts tuple_T body_T t =
|
blanchet@33192
|
1822 |
let val n = length arg_Ts in
|
blanchet@33192
|
1823 |
list_abs (map (pair "c") arg_Ts,
|
blanchet@33192
|
1824 |
incr_boundvars n t
|
blanchet@33192
|
1825 |
$ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
|
blanchet@33192
|
1826 |
end
|
blanchet@33192
|
1827 |
|
blanchet@33192
|
1828 |
(* int -> term -> int *)
|
blanchet@33192
|
1829 |
fun num_occs_of_bound_in_term j (t1 $ t2) =
|
blanchet@33192
|
1830 |
op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
|
blanchet@33192
|
1831 |
| num_occs_of_bound_in_term j (Abs (s, T, t')) =
|
blanchet@33192
|
1832 |
num_occs_of_bound_in_term (j + 1) t'
|
blanchet@33192
|
1833 |
| num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
|
blanchet@33192
|
1834 |
| num_occs_of_bound_in_term _ _ = 0
|
blanchet@33192
|
1835 |
|
blanchet@33192
|
1836 |
(* term -> bool *)
|
blanchet@33192
|
1837 |
val is_linear_inductive_pred_def =
|
blanchet@33192
|
1838 |
let
|
blanchet@33192
|
1839 |
(* int -> term -> bool *)
|
blanchet@33192
|
1840 |
fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
|
blanchet@33192
|
1841 |
do_disjunct (j + 1) t2
|
blanchet@33192
|
1842 |
| do_disjunct j t =
|
blanchet@33192
|
1843 |
case num_occs_of_bound_in_term j t of
|
blanchet@33192
|
1844 |
0 => true
|
blanchet@34118
|
1845 |
| 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts t)
|
blanchet@33192
|
1846 |
| _ => false
|
blanchet@33192
|
1847 |
(* term -> bool *)
|
blanchet@33192
|
1848 |
fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
|
blanchet@33192
|
1849 |
let val (xs, body) = strip_abs t2 in
|
blanchet@33192
|
1850 |
case length xs of
|
blanchet@33192
|
1851 |
1 => false
|
blanchet@33192
|
1852 |
| n => forall (do_disjunct (n - 1)) (disjuncts body)
|
blanchet@33192
|
1853 |
end
|
blanchet@33192
|
1854 |
| do_lfp_def _ = false
|
blanchet@33192
|
1855 |
in do_lfp_def o strip_abs_body end
|
blanchet@33192
|
1856 |
|
blanchet@33851
|
1857 |
(* int -> int list list *)
|
blanchet@33851
|
1858 |
fun n_ptuple_paths 0 = []
|
blanchet@33851
|
1859 |
| n_ptuple_paths 1 = []
|
blanchet@33851
|
1860 |
| n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
|
blanchet@33851
|
1861 |
(* int -> typ -> typ -> term -> term *)
|
blanchet@33851
|
1862 |
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
|
blanchet@33192
|
1863 |
|
blanchet@33192
|
1864 |
(* term -> term * term *)
|
blanchet@33192
|
1865 |
val linear_pred_base_and_step_rhss =
|
blanchet@33192
|
1866 |
let
|
blanchet@33192
|
1867 |
(* term -> term *)
|
blanchet@33192
|
1868 |
fun aux (Const (@{const_name lfp}, _) $ t2) =
|
blanchet@33192
|
1869 |
let
|
blanchet@33192
|
1870 |
val (xs, body) = strip_abs t2
|
blanchet@33192
|
1871 |
val arg_Ts = map snd (tl xs)
|
blanchet@33192
|
1872 |
val tuple_T = HOLogic.mk_tupleT arg_Ts
|
blanchet@33192
|
1873 |
val j = length arg_Ts
|
blanchet@33192
|
1874 |
(* int -> term -> term *)
|
blanchet@33192
|
1875 |
fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
|
blanchet@33192
|
1876 |
Const (@{const_name Ex}, T1)
|
blanchet@33192
|
1877 |
$ Abs (s2, T2, repair_rec (j + 1) t2')
|
blanchet@33192
|
1878 |
| repair_rec j (@{const "op &"} $ t1 $ t2) =
|
blanchet@33192
|
1879 |
@{const "op &"} $ repair_rec j t1 $ repair_rec j t2
|
blanchet@33192
|
1880 |
| repair_rec j t =
|
blanchet@33192
|
1881 |
let val (head, args) = strip_comb t in
|
blanchet@33192
|
1882 |
if head = Bound j then
|
blanchet@33192
|
1883 |
HOLogic.eq_const tuple_T $ Bound j
|
blanchet@33192
|
1884 |
$ mk_flat_tuple tuple_T args
|
blanchet@33192
|
1885 |
else
|
blanchet@33192
|
1886 |
t
|
blanchet@33192
|
1887 |
end
|
blanchet@33192
|
1888 |
val (nonrecs, recs) =
|
blanchet@34118
|
1889 |
List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
|
blanchet@33192
|
1890 |
(disjuncts body)
|
blanchet@33192
|
1891 |
val base_body = nonrecs |> List.foldl s_disj @{const False}
|
blanchet@33192
|
1892 |
val step_body = recs |> map (repair_rec j)
|
blanchet@33192
|
1893 |
|> List.foldl s_disj @{const False}
|
blanchet@33192
|
1894 |
in
|
blanchet@33192
|
1895 |
(list_abs (tl xs, incr_bv (~1, j, base_body))
|
blanchet@33851
|
1896 |
|> ap_n_split (length arg_Ts) tuple_T bool_T,
|
blanchet@33192
|
1897 |
Abs ("y", tuple_T, list_abs (tl xs, step_body)
|
blanchet@33851
|
1898 |
|> ap_n_split (length arg_Ts) tuple_T bool_T))
|
blanchet@33192
|
1899 |
end
|
blanchet@33192
|
1900 |
| aux t =
|
blanchet@33224
|
1901 |
raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
|
blanchet@33192
|
1902 |
in aux end
|
blanchet@33192
|
1903 |
|
blanchet@33192
|
1904 |
(* extended_context -> styp -> term -> term *)
|
blanchet@33851
|
1905 |
fun starred_linear_pred_const (ext_ctxt as {simp_table, ...}) (x as (s, T))
|
blanchet@33851
|
1906 |
def =
|
blanchet@33192
|
1907 |
let
|
blanchet@33192
|
1908 |
val j = maxidx_of_term def + 1
|
blanchet@33192
|
1909 |
val (outer, fp_app) = strip_abs def
|
blanchet@33192
|
1910 |
val outer_bounds = map Bound (length outer - 1 downto 0)
|
blanchet@33192
|
1911 |
val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
|
blanchet@33192
|
1912 |
val fp_app = subst_bounds (rev outer_vars, fp_app)
|
blanchet@33192
|
1913 |
val (outer_Ts, rest_T) = strip_n_binders (length outer) T
|
blanchet@33192
|
1914 |
val tuple_arg_Ts = strip_type rest_T |> fst
|
blanchet@33192
|
1915 |
val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
|
blanchet@33192
|
1916 |
val set_T = tuple_T --> bool_T
|
blanchet@33192
|
1917 |
val curried_T = tuple_T --> set_T
|
blanchet@33192
|
1918 |
val uncurried_T = Type ("*", [tuple_T, tuple_T]) --> bool_T
|
blanchet@33192
|
1919 |
val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
|
blanchet@33192
|
1920 |
val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
|
blanchet@33192
|
1921 |
val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
|
blanchet@33192
|
1922 |
|> HOLogic.mk_Trueprop
|
blanchet@33192
|
1923 |
val _ = add_simps simp_table base_s [base_eq]
|
blanchet@33192
|
1924 |
val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
|
blanchet@33192
|
1925 |
val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
|
blanchet@33192
|
1926 |
|> HOLogic.mk_Trueprop
|
blanchet@33192
|
1927 |
val _ = add_simps simp_table step_s [step_eq]
|
blanchet@33192
|
1928 |
in
|
blanchet@33192
|
1929 |
list_abs (outer,
|
blanchet@33192
|
1930 |
Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
|
blanchet@33192
|
1931 |
$ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
|
blanchet@33192
|
1932 |
$ (Const (@{const_name split}, curried_T --> uncurried_T)
|
blanchet@33192
|
1933 |
$ list_comb (Const step_x, outer_bounds)))
|
blanchet@33192
|
1934 |
$ list_comb (Const base_x, outer_bounds)
|
blanchet@33192
|
1935 |
|> ap_curry tuple_arg_Ts tuple_T bool_T)
|
blanchet@33192
|
1936 |
|> unfold_defs_in_term ext_ctxt
|
blanchet@33192
|
1937 |
end
|
blanchet@33192
|
1938 |
|
blanchet@33192
|
1939 |
(* extended_context -> bool -> styp -> term *)
|
blanchet@33192
|
1940 |
fun unrolled_inductive_pred_const (ext_ctxt as {thy, star_linear_preds,
|
blanchet@33192
|
1941 |
def_table, simp_table, ...})
|
blanchet@33192
|
1942 |
gfp (x as (s, T)) =
|
blanchet@33192
|
1943 |
let
|
blanchet@33192
|
1944 |
val iter_T = iterator_type_for_const gfp x
|
blanchet@33192
|
1945 |
val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
|
blanchet@33192
|
1946 |
val unrolled_const = Const x' $ zero_const iter_T
|
blanchet@33192
|
1947 |
val def = the (def_of_const thy def_table x)
|
blanchet@33192
|
1948 |
in
|
blanchet@33192
|
1949 |
if is_equational_fun ext_ctxt x' then
|
blanchet@33192
|
1950 |
unrolled_const (* already done *)
|
blanchet@34923
|
1951 |
else if not gfp andalso is_linear_inductive_pred_def def andalso
|
blanchet@34923
|
1952 |
star_linear_preds then
|
blanchet@33851
|
1953 |
starred_linear_pred_const ext_ctxt x def
|
blanchet@33192
|
1954 |
else
|
blanchet@33192
|
1955 |
let
|
blanchet@33192
|
1956 |
val j = maxidx_of_term def + 1
|
blanchet@33192
|
1957 |
val (outer, fp_app) = strip_abs def
|
blanchet@33192
|
1958 |
val outer_bounds = map Bound (length outer - 1 downto 0)
|
blanchet@33192
|
1959 |
val cur = Var ((iter_var_prefix, j + 1), iter_T)
|
blanchet@33192
|
1960 |
val next = suc_const iter_T $ cur
|
blanchet@33192
|
1961 |
val rhs = case fp_app of
|
blanchet@33192
|
1962 |
Const _ $ t =>
|
blanchet@33192
|
1963 |
betapply (t, list_comb (Const x', next :: outer_bounds))
|
blanchet@33224
|
1964 |
| _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_\
|
blanchet@33224
|
1965 |
\const", [fp_app])
|
blanchet@33192
|
1966 |
val (inner, naked_rhs) = strip_abs rhs
|
blanchet@33192
|
1967 |
val all = outer @ inner
|
blanchet@33192
|
1968 |
val bounds = map Bound (length all - 1 downto 0)
|
blanchet@33192
|
1969 |
val vars = map (fn (s, T) => Var ((s, j), T)) all
|
blanchet@33192
|
1970 |
val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
|
blanchet@33192
|
1971 |
|> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
|
blanchet@33192
|
1972 |
val _ = add_simps simp_table s' [eq]
|
blanchet@33192
|
1973 |
in unrolled_const end
|
blanchet@33192
|
1974 |
end
|
blanchet@33192
|
1975 |
|
blanchet@33192
|
1976 |
(* extended_context -> styp -> term *)
|
blanchet@33192
|
1977 |
fun raw_inductive_pred_axiom ({thy, def_table, ...} : extended_context) x =
|
blanchet@33192
|
1978 |
let
|
blanchet@33192
|
1979 |
val def = the (def_of_const thy def_table x)
|
blanchet@33192
|
1980 |
val (outer, fp_app) = strip_abs def
|
blanchet@33192
|
1981 |
val outer_bounds = map Bound (length outer - 1 downto 0)
|
blanchet@33192
|
1982 |
val rhs = case fp_app of
|
blanchet@33192
|
1983 |
Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
|
blanchet@33224
|
1984 |
| _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom",
|
blanchet@33192
|
1985 |
[fp_app])
|
blanchet@33192
|
1986 |
val (inner, naked_rhs) = strip_abs rhs
|
blanchet@33192
|
1987 |
val all = outer @ inner
|
blanchet@33192
|
1988 |
val bounds = map Bound (length all - 1 downto 0)
|
blanchet@33192
|
1989 |
val j = maxidx_of_term def + 1
|
blanchet@33192
|
1990 |
val vars = map (fn (s, T) => Var ((s, j), T)) all
|
blanchet@33192
|
1991 |
in
|
blanchet@33192
|
1992 |
HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
|
blanchet@33192
|
1993 |
|> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
|
blanchet@33192
|
1994 |
end
|
blanchet@33192
|
1995 |
fun inductive_pred_axiom ext_ctxt (x as (s, T)) =
|
blanchet@33192
|
1996 |
if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
|
blanchet@33192
|
1997 |
let val x' = (after_name_sep s, T) in
|
blanchet@33192
|
1998 |
raw_inductive_pred_axiom ext_ctxt x' |> subst_atomic [(Const x', Const x)]
|
blanchet@33192
|
1999 |
end
|
blanchet@33192
|
2000 |
else
|
blanchet@33192
|
2001 |
raw_inductive_pred_axiom ext_ctxt x
|
blanchet@33192
|
2002 |
|
blanchet@33192
|
2003 |
(* extended_context -> styp -> term list *)
|
blanchet@33192
|
2004 |
fun raw_equational_fun_axioms (ext_ctxt as {thy, fast_descrs, simp_table,
|
blanchet@33192
|
2005 |
psimp_table, ...}) (x as (s, _)) =
|
blanchet@33547
|
2006 |
case def_props_for_const thy fast_descrs (!simp_table) x of
|
blanchet@33192
|
2007 |
[] => (case def_props_for_const thy fast_descrs psimp_table x of
|
blanchet@33192
|
2008 |
[] => [inductive_pred_axiom ext_ctxt x]
|
blanchet@33192
|
2009 |
| psimps => psimps)
|
blanchet@33192
|
2010 |
| simps => simps
|
blanchet@33192
|
2011 |
|
blanchet@33192
|
2012 |
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
|
blanchet@33192
|
2013 |
|
blanchet@33192
|
2014 |
(* term list -> term list *)
|
blanchet@33547
|
2015 |
fun merge_type_vars_in_terms ts =
|
blanchet@33192
|
2016 |
let
|
blanchet@33192
|
2017 |
(* typ -> (sort * string) list -> (sort * string) list *)
|
blanchet@33192
|
2018 |
fun add_type (TFree (s, S)) table =
|
blanchet@33192
|
2019 |
(case AList.lookup (op =) table S of
|
blanchet@33192
|
2020 |
SOME s' =>
|
blanchet@33192
|
2021 |
if string_ord (s', s) = LESS then AList.update (op =) (S, s') table
|
blanchet@33192
|
2022 |
else table
|
blanchet@33192
|
2023 |
| NONE => (S, s) :: table)
|
blanchet@33192
|
2024 |
| add_type _ table = table
|
blanchet@33192
|
2025 |
val table = fold (fold_types (fold_atyps add_type)) ts []
|
blanchet@33192
|
2026 |
(* typ -> typ *)
|
blanchet@33192
|
2027 |
fun coalesce (TFree (s, S)) = TFree (AList.lookup (op =) table S |> the, S)
|
blanchet@33192
|
2028 |
| coalesce T = T
|
blanchet@33192
|
2029 |
in map (map_types (map_atyps coalesce)) ts end
|
blanchet@33192
|
2030 |
|
blanchet@33192
|
2031 |
(* extended_context -> typ -> typ list -> typ list *)
|
blanchet@33192
|
2032 |
fun add_ground_types ext_ctxt T accum =
|
blanchet@33192
|
2033 |
case T of
|
blanchet@33192
|
2034 |
Type ("fun", Ts) => fold (add_ground_types ext_ctxt) Ts accum
|
blanchet@33192
|
2035 |
| Type ("*", Ts) => fold (add_ground_types ext_ctxt) Ts accum
|
blanchet@33192
|
2036 |
| Type (@{type_name itself}, [T1]) => add_ground_types ext_ctxt T1 accum
|
blanchet@33192
|
2037 |
| Type (_, Ts) =>
|
blanchet@34118
|
2038 |
if member (op =) (@{typ prop} :: @{typ bool} :: @{typ unit} :: accum) T then
|
blanchet@33192
|
2039 |
accum
|
blanchet@33192
|
2040 |
else
|
blanchet@33192
|
2041 |
T :: accum
|
blanchet@33192
|
2042 |
|> fold (add_ground_types ext_ctxt)
|
blanchet@33192
|
2043 |
(case boxed_datatype_constrs ext_ctxt T of
|
blanchet@33192
|
2044 |
[] => Ts
|
blanchet@33192
|
2045 |
| xs => map snd xs)
|
blanchet@33192
|
2046 |
| _ => insert (op =) T accum
|
blanchet@33192
|
2047 |
(* extended_context -> typ -> typ list *)
|
blanchet@33192
|
2048 |
fun ground_types_in_type ext_ctxt T = add_ground_types ext_ctxt T []
|
blanchet@33192
|
2049 |
(* extended_context -> term list -> typ list *)
|
blanchet@33192
|
2050 |
fun ground_types_in_terms ext_ctxt ts =
|
blanchet@33192
|
2051 |
fold (fold_types (add_ground_types ext_ctxt)) ts []
|
blanchet@33192
|
2052 |
|
blanchet@33192
|
2053 |
(* typ list -> int -> term -> bool *)
|
blanchet@33192
|
2054 |
fun has_heavy_bounds_or_vars Ts level t =
|
blanchet@33192
|
2055 |
let
|
blanchet@33192
|
2056 |
(* typ list -> bool *)
|
blanchet@33192
|
2057 |
fun aux [] = false
|
blanchet@33192
|
2058 |
| aux [T] = is_fun_type T orelse is_pair_type T
|
blanchet@33192
|
2059 |
| aux _ = true
|
blanchet@33192
|
2060 |
in aux (map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t)) end
|
blanchet@33192
|
2061 |
|
blanchet@33192
|
2062 |
(* typ list -> int -> int -> int -> term -> term *)
|
blanchet@33192
|
2063 |
fun fresh_value_var Ts k n j t =
|
blanchet@33192
|
2064 |
Var ((val_var_prefix ^ nat_subscript (n - j), k), fastype_of1 (Ts, t))
|
blanchet@33192
|
2065 |
|
blanchet@33192
|
2066 |
(* theory -> typ list -> bool -> int -> int -> term -> term list -> term list
|
blanchet@33192
|
2067 |
-> term * term list *)
|
blanchet@33192
|
2068 |
fun pull_out_constr_comb thy Ts relax k level t args seen =
|
blanchet@33192
|
2069 |
let val t_comb = list_comb (t, args) in
|
blanchet@33192
|
2070 |
case t of
|
blanchet@33192
|
2071 |
Const x =>
|
blanchet@34923
|
2072 |
if not relax andalso is_constr thy x andalso
|
blanchet@34923
|
2073 |
not (is_fun_type (fastype_of1 (Ts, t_comb))) andalso
|
blanchet@34923
|
2074 |
has_heavy_bounds_or_vars Ts level t_comb andalso
|
blanchet@34923
|
2075 |
not (loose_bvar (t_comb, level)) then
|
blanchet@33192
|
2076 |
let
|
blanchet@34118
|
2077 |
val (j, seen) = case find_index (curry (op =) t_comb) seen of
|
blanchet@33192
|
2078 |
~1 => (0, t_comb :: seen)
|
blanchet@33192
|
2079 |
| j => (j, seen)
|
blanchet@33192
|
2080 |
in (fresh_value_var Ts k (length seen) j t_comb, seen) end
|
blanchet@33192
|
2081 |
else
|
blanchet@33192
|
2082 |
(t_comb, seen)
|
blanchet@33192
|
2083 |
| _ => (t_comb, seen)
|
blanchet@33192
|
2084 |
end
|
blanchet@33192
|
2085 |
|
blanchet@33192
|
2086 |
(* (term -> term) -> typ list -> int -> term list -> term list *)
|
blanchet@33192
|
2087 |
fun equations_for_pulled_out_constrs mk_eq Ts k seen =
|
blanchet@33192
|
2088 |
let val n = length seen in
|
blanchet@33192
|
2089 |
map2 (fn j => fn t => mk_eq (fresh_value_var Ts k n j t, t))
|
blanchet@33192
|
2090 |
(index_seq 0 n) seen
|
blanchet@33192
|
2091 |
end
|
blanchet@33192
|
2092 |
|
blanchet@33192
|
2093 |
(* theory -> bool -> term -> term *)
|
blanchet@33192
|
2094 |
fun pull_out_universal_constrs thy def t =
|
blanchet@33192
|
2095 |
let
|
blanchet@33192
|
2096 |
val k = maxidx_of_term t + 1
|
blanchet@33192
|
2097 |
(* typ list -> bool -> term -> term list -> term list -> term * term list *)
|
blanchet@33192
|
2098 |
fun do_term Ts def t args seen =
|
blanchet@33192
|
2099 |
case t of
|
blanchet@33192
|
2100 |
(t0 as Const (@{const_name "=="}, _)) $ t1 $ t2 =>
|
blanchet@33978
|
2101 |
do_eq_or_imp Ts true def t0 t1 t2 seen
|
blanchet@33978
|
2102 |
| (t0 as @{const "==>"}) $ t1 $ t2 =>
|
blanchet@34969
|
2103 |
if def then (t, []) else do_eq_or_imp Ts false def t0 t1 t2 seen
|
blanchet@33192
|
2104 |
| (t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2 =>
|
blanchet@33978
|
2105 |
do_eq_or_imp Ts true def t0 t1 t2 seen
|
blanchet@33978
|
2106 |
| (t0 as @{const "op -->"}) $ t1 $ t2 =>
|
blanchet@33978
|
2107 |
do_eq_or_imp Ts false def t0 t1 t2 seen
|
blanchet@33192
|
2108 |
| Abs (s, T, t') =>
|
blanchet@33192
|
2109 |
let val (t', seen) = do_term (T :: Ts) def t' [] seen in
|
blanchet@33192
|
2110 |
(list_comb (Abs (s, T, t'), args), seen)
|
blanchet@33192
|
2111 |
end
|
blanchet@33192
|
2112 |
| t1 $ t2 =>
|
blanchet@33192
|
2113 |
let val (t2, seen) = do_term Ts def t2 [] seen in
|
blanchet@33192
|
2114 |
do_term Ts def t1 (t2 :: args) seen
|
blanchet@33192
|
2115 |
end
|
blanchet@33192
|
2116 |
| _ => pull_out_constr_comb thy Ts def k 0 t args seen
|
blanchet@33978
|
2117 |
(* typ list -> bool -> bool -> term -> term -> term -> term list
|
blanchet@33192
|
2118 |
-> term * term list *)
|
blanchet@33978
|
2119 |
and do_eq_or_imp Ts eq def t0 t1 t2 seen =
|
blanchet@33192
|
2120 |
let
|
blanchet@33978
|
2121 |
val (t2, seen) = if eq andalso def then (t2, seen)
|
blanchet@33978
|
2122 |
else do_term Ts false t2 [] seen
|
blanchet@33192
|
2123 |
val (t1, seen) = do_term Ts false t1 [] seen
|
blanchet@33192
|
2124 |
in (t0 $ t1 $ t2, seen) end
|
blanchet@33192
|
2125 |
val (concl, seen) = do_term [] def t [] []
|
blanchet@33192
|
2126 |
in
|
blanchet@33192
|
2127 |
Logic.list_implies (equations_for_pulled_out_constrs Logic.mk_equals [] k
|
blanchet@33192
|
2128 |
seen, concl)
|
blanchet@33192
|
2129 |
end
|
blanchet@33192
|
2130 |
|
blanchet@33571
|
2131 |
(* extended_context -> bool -> term -> term *)
|
blanchet@33571
|
2132 |
fun destroy_pulled_out_constrs (ext_ctxt as {thy, ...}) axiom t =
|
blanchet@33192
|
2133 |
let
|
blanchet@33192
|
2134 |
(* styp -> int *)
|
blanchet@33192
|
2135 |
val num_occs_of_var =
|
blanchet@33192
|
2136 |
fold_aterms (fn Var z => (fn f => fn z' => f z' |> z = z' ? Integer.add 1)
|
blanchet@33192
|
2137 |
| _ => I) t (K 0)
|
blanchet@33192
|
2138 |
(* bool -> term -> term *)
|
blanchet@33192
|
2139 |
fun aux careful ((t0 as Const (@{const_name "=="}, _)) $ t1 $ t2) =
|
blanchet@33192
|
2140 |
aux_eq careful true t0 t1 t2
|
blanchet@33192
|
2141 |
| aux careful ((t0 as @{const "==>"}) $ t1 $ t2) =
|
blanchet@33192
|
2142 |
t0 $ aux false t1 $ aux careful t2
|
blanchet@33192
|
2143 |
| aux careful ((t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2) =
|
blanchet@33192
|
2144 |
aux_eq careful true t0 t1 t2
|
blanchet@33192
|
2145 |
| aux careful ((t0 as @{const "op -->"}) $ t1 $ t2) =
|
blanchet@33192
|
2146 |
t0 $ aux false t1 $ aux careful t2
|
blanchet@33192
|
2147 |
| aux careful (Abs (s, T, t')) = Abs (s, T, aux careful t')
|
blanchet@33192
|
2148 |
| aux careful (t1 $ t2) = aux careful t1 $ aux careful t2
|
blanchet@33192
|
2149 |
| aux _ t = t
|
blanchet@33192
|
2150 |
(* bool -> bool -> term -> term -> term -> term *)
|
blanchet@33192
|
2151 |
and aux_eq careful pass1 t0 t1 t2 =
|
blanchet@34969
|
2152 |
((if careful then
|
blanchet@34969
|
2153 |
raise SAME ()
|
blanchet@34969
|
2154 |
else if axiom andalso is_Var t2 andalso
|
blanchet@34969
|
2155 |
num_occs_of_var (dest_Var t2) = 1 then
|
blanchet@34969
|
2156 |
@{const True}
|
blanchet@34969
|
2157 |
else case strip_comb t2 of
|
blanchet@34969
|
2158 |
(* The first case is not as general as it could be. *)
|
blanchet@34969
|
2159 |
(Const (@{const_name PairBox}, _),
|
blanchet@34969
|
2160 |
[Const (@{const_name fst}, _) $ Var z1,
|
blanchet@34969
|
2161 |
Const (@{const_name snd}, _) $ Var z2]) =>
|
blanchet@34969
|
2162 |
if z1 = z2 andalso num_occs_of_var z1 = 2 then @{const True}
|
blanchet@34969
|
2163 |
else raise SAME ()
|
blanchet@34969
|
2164 |
| (Const (x as (s, T)), args) =>
|
blanchet@34969
|
2165 |
let val arg_Ts = binder_types T in
|
blanchet@34969
|
2166 |
if length arg_Ts = length args andalso
|
blanchet@34969
|
2167 |
(is_constr thy x orelse s = @{const_name Pair} orelse
|
blanchet@34969
|
2168 |
x = (@{const_name Suc}, nat_T --> nat_T)) andalso
|
blanchet@34969
|
2169 |
(not careful orelse not (is_Var t1) orelse
|
blanchet@34969
|
2170 |
String.isPrefix val_var_prefix (fst (fst (dest_Var t1)))) then
|
blanchet@34969
|
2171 |
discriminate_value ext_ctxt x t1 ::
|
blanchet@34969
|
2172 |
map3 (sel_eq x t1) (index_seq 0 (length args)) arg_Ts args
|
blanchet@34969
|
2173 |
|> foldr1 s_conj
|
blanchet@34969
|
2174 |
else
|
blanchet@34969
|
2175 |
raise SAME ()
|
blanchet@34969
|
2176 |
end
|
blanchet@34969
|
2177 |
| _ => raise SAME ())
|
blanchet@34969
|
2178 |
|> body_type (type_of t0) = prop_T ? HOLogic.mk_Trueprop)
|
blanchet@33192
|
2179 |
handle SAME () => if pass1 then aux_eq careful false t0 t2 t1
|
blanchet@33192
|
2180 |
else t0 $ aux false t2 $ aux false t1
|
blanchet@33192
|
2181 |
(* styp -> term -> int -> typ -> term -> term *)
|
blanchet@33192
|
2182 |
and sel_eq x t n nth_T nth_t =
|
blanchet@33192
|
2183 |
HOLogic.eq_const nth_T $ nth_t $ select_nth_constr_arg thy x t n nth_T
|
blanchet@33192
|
2184 |
|> aux false
|
blanchet@33192
|
2185 |
in aux axiom t end
|
blanchet@33192
|
2186 |
|
blanchet@33192
|
2187 |
(* theory -> term -> term *)
|
blanchet@33192
|
2188 |
fun simplify_constrs_and_sels thy t =
|
blanchet@33192
|
2189 |
let
|
blanchet@33192
|
2190 |
(* term -> int -> term *)
|
blanchet@33192
|
2191 |
fun is_nth_sel_on t' n (Const (s, _) $ t) =
|
blanchet@34923
|
2192 |
(t = t' andalso is_sel_like_and_no_discr s andalso
|
blanchet@34923
|
2193 |
sel_no_from_name s = n)
|
blanchet@33192
|
2194 |
| is_nth_sel_on _ _ _ = false
|
blanchet@33192
|
2195 |
(* term -> term list -> term *)
|
blanchet@33192
|
2196 |
fun do_term (Const (@{const_name Rep_Frac}, _)
|
blanchet@33192
|
2197 |
$ (Const (@{const_name Abs_Frac}, _) $ t1)) [] = do_term t1 []
|
blanchet@33192
|
2198 |
| do_term (Const (@{const_name Abs_Frac}, _)
|
blanchet@33192
|
2199 |
$ (Const (@{const_name Rep_Frac}, _) $ t1)) [] = do_term t1 []
|
blanchet@33192
|
2200 |
| do_term (t1 $ t2) args = do_term t1 (do_term t2 [] :: args)
|
blanchet@33192
|
2201 |
| do_term (t as Const (x as (s, T))) (args as _ :: _) =
|
blanchet@33192
|
2202 |
((if is_constr_like thy x then
|
blanchet@33192
|
2203 |
if length args = num_binder_types T then
|
blanchet@33192
|
2204 |
case hd args of
|
blanchet@33192
|
2205 |
Const (x' as (_, T')) $ t' =>
|
blanchet@34923
|
2206 |
if domain_type T' = body_type T andalso
|
blanchet@34923
|
2207 |
forall (uncurry (is_nth_sel_on t'))
|
blanchet@34923
|
2208 |
(index_seq 0 (length args) ~~ args) then
|
blanchet@33192
|
2209 |
t'
|
blanchet@33192
|
2210 |
else
|
blanchet@33192
|
2211 |
raise SAME ()
|
blanchet@33192
|
2212 |
| _ => raise SAME ()
|
blanchet@33192
|
2213 |
else
|
blanchet@33192
|
2214 |
raise SAME ()
|
blanchet@33192
|
2215 |
else if is_sel_like_and_no_discr s then
|
blanchet@33192
|
2216 |
case strip_comb (hd args) of
|
blanchet@33192
|
2217 |
(Const (x' as (s', T')), ts') =>
|
blanchet@34923
|
2218 |
if is_constr_like thy x' andalso
|
blanchet@34923
|
2219 |
constr_name_for_sel_like s = s' andalso
|
blanchet@34923
|
2220 |
not (exists is_pair_type (binder_types T')) then
|
blanchet@33192
|
2221 |
list_comb (nth ts' (sel_no_from_name s), tl args)
|
blanchet@33192
|
2222 |
else
|
blanchet@33192
|
2223 |
raise SAME ()
|
blanchet@33192
|
2224 |
| _ => raise SAME ()
|
blanchet@33192
|
2225 |
else
|
blanchet@33192
|
2226 |
raise SAME ())
|
blanchet@33192
|
2227 |
handle SAME () => betapplys (t, args))
|
blanchet@33192
|
2228 |
| do_term (Abs (s, T, t')) args =
|
blanchet@33192
|
2229 |
betapplys (Abs (s, T, do_term t' []), args)
|
blanchet@33192
|
2230 |
| do_term t args = betapplys (t, args)
|
blanchet@33192
|
2231 |
in do_term t [] end
|
blanchet@33192
|
2232 |
|
blanchet@33192
|
2233 |
(* term -> term *)
|
blanchet@33192
|
2234 |
fun curry_assms (@{const "==>"} $ (@{const Trueprop}
|
blanchet@33192
|
2235 |
$ (@{const "op &"} $ t1 $ t2)) $ t3) =
|
blanchet@33192
|
2236 |
curry_assms (Logic.list_implies ([t1, t2] |> map HOLogic.mk_Trueprop, t3))
|
blanchet@33192
|
2237 |
| curry_assms (@{const "==>"} $ t1 $ t2) =
|
blanchet@33192
|
2238 |
@{const "==>"} $ curry_assms t1 $ curry_assms t2
|
blanchet@33192
|
2239 |
| curry_assms t = t
|
blanchet@33192
|
2240 |
|
blanchet@33192
|
2241 |
(* term -> term *)
|
blanchet@33192
|
2242 |
val destroy_universal_equalities =
|
blanchet@33192
|
2243 |
let
|
blanchet@33192
|
2244 |
(* term list -> (indexname * typ) list -> term -> term *)
|
blanchet@33192
|
2245 |
fun aux prems zs t =
|
blanchet@33192
|
2246 |
case t of
|
blanchet@33192
|
2247 |
@{const "==>"} $ t1 $ t2 => aux_implies prems zs t1 t2
|
blanchet@33192
|
2248 |
| _ => Logic.list_implies (rev prems, t)
|
blanchet@33192
|
2249 |
(* term list -> (indexname * typ) list -> term -> term -> term *)
|
blanchet@33192
|
2250 |
and aux_implies prems zs t1 t2 =
|
blanchet@33192
|
2251 |
case t1 of
|
blanchet@33192
|
2252 |
Const (@{const_name "=="}, _) $ Var z $ t' => aux_eq prems zs z t' t1 t2
|
blanchet@33192
|
2253 |
| @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ Var z $ t') =>
|
blanchet@33192
|
2254 |
aux_eq prems zs z t' t1 t2
|
blanchet@33192
|
2255 |
| @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t' $ Var z) =>
|
blanchet@33192
|
2256 |
aux_eq prems zs z t' t1 t2
|
blanchet@33192
|
2257 |
| _ => aux (t1 :: prems) (Term.add_vars t1 zs) t2
|
blanchet@33192
|
2258 |
(* term list -> (indexname * typ) list -> indexname * typ -> term -> term
|
blanchet@33192
|
2259 |
-> term -> term *)
|
blanchet@33192
|
2260 |
and aux_eq prems zs z t' t1 t2 =
|
blanchet@34923
|
2261 |
if not (member (op =) zs z) andalso
|
blanchet@34923
|
2262 |
not (exists_subterm (curry (op =) (Var z)) t') then
|
blanchet@33192
|
2263 |
aux prems zs (subst_free [(Var z, t')] t2)
|
blanchet@33192
|
2264 |
else
|
blanchet@33192
|
2265 |
aux (t1 :: prems) (Term.add_vars t1 zs) t2
|
blanchet@33192
|
2266 |
in aux [] [] end
|
blanchet@33192
|
2267 |
|
blanchet@33192
|
2268 |
(* theory -> term -> term *)
|
blanchet@33192
|
2269 |
fun pull_out_existential_constrs thy t =
|
blanchet@33192
|
2270 |
let
|
blanchet@33192
|
2271 |
val k = maxidx_of_term t + 1
|
blanchet@33192
|
2272 |
(* typ list -> int -> term -> term list -> term list -> term * term list *)
|
blanchet@33192
|
2273 |
fun aux Ts num_exists t args seen =
|
blanchet@33192
|
2274 |
case t of
|
blanchet@33192
|
2275 |
(t0 as Const (@{const_name Ex}, _)) $ Abs (s1, T1, t1) =>
|
blanchet@33192
|
2276 |
let
|
blanchet@33192
|
2277 |
val (t1, seen') = aux (T1 :: Ts) (num_exists + 1) t1 [] []
|
blanchet@33192
|
2278 |
val n = length seen'
|
blanchet@33192
|
2279 |
(* unit -> term list *)
|
blanchet@33192
|
2280 |
fun vars () = map2 (fresh_value_var Ts k n) (index_seq 0 n) seen'
|
blanchet@33192
|
2281 |
in
|
blanchet@33192
|
2282 |
(equations_for_pulled_out_constrs HOLogic.mk_eq Ts k seen'
|
blanchet@33192
|
2283 |
|> List.foldl s_conj t1 |> fold mk_exists (vars ())
|
blanchet@33192
|
2284 |
|> curry3 Abs s1 T1 |> curry (op $) t0, seen)
|
blanchet@33192
|
2285 |
end
|
blanchet@33192
|
2286 |
| t1 $ t2 =>
|
blanchet@33192
|
2287 |
let val (t2, seen) = aux Ts num_exists t2 [] seen in
|
blanchet@33192
|
2288 |
aux Ts num_exists t1 (t2 :: args) seen
|
blanchet@33192
|
2289 |
end
|
blanchet@33192
|
2290 |
| Abs (s, T, t') =>
|
blanchet@33192
|
2291 |
let
|
blanchet@33192
|
2292 |
val (t', seen) = aux (T :: Ts) 0 t' [] (map (incr_boundvars 1) seen)
|
blanchet@33192
|
2293 |
in (list_comb (Abs (s, T, t'), args), map (incr_boundvars ~1) seen) end
|
blanchet@33192
|
2294 |
| _ =>
|
blanchet@33192
|
2295 |
if num_exists > 0 then
|
blanchet@33192
|
2296 |
pull_out_constr_comb thy Ts false k num_exists t args seen
|
blanchet@33192
|
2297 |
else
|
blanchet@33192
|
2298 |
(list_comb (t, args), seen)
|
blanchet@33192
|
2299 |
in aux [] 0 t [] [] |> fst end
|
blanchet@33192
|
2300 |
|
blanchet@33192
|
2301 |
(* theory -> int -> term list -> term list -> (term * term list) option *)
|
blanchet@33192
|
2302 |
fun find_bound_assign _ _ _ [] = NONE
|
blanchet@33192
|
2303 |
| find_bound_assign thy j seen (t :: ts) =
|
blanchet@33192
|
2304 |
let
|
blanchet@33192
|
2305 |
(* bool -> term -> term -> (term * term list) option *)
|
blanchet@33192
|
2306 |
fun aux pass1 t1 t2 =
|
blanchet@33192
|
2307 |
(if loose_bvar1 (t2, j) then
|
blanchet@33192
|
2308 |
if pass1 then aux false t2 t1 else raise SAME ()
|
blanchet@33192
|
2309 |
else case t1 of
|
blanchet@33192
|
2310 |
Bound j' => if j' = j then SOME (t2, ts @ seen) else raise SAME ()
|
blanchet@33192
|
2311 |
| Const (s, Type ("fun", [T1, T2])) $ Bound j' =>
|
blanchet@33192
|
2312 |
if j' = j andalso s = sel_prefix_for 0 ^ @{const_name FunBox} then
|
blanchet@33192
|
2313 |
SOME (construct_value thy (@{const_name FunBox}, T2 --> T1) [t2],
|
blanchet@33192
|
2314 |
ts @ seen)
|
blanchet@33192
|
2315 |
else
|
blanchet@33192
|
2316 |
raise SAME ()
|
blanchet@33192
|
2317 |
| _ => raise SAME ())
|
blanchet@33192
|
2318 |
handle SAME () => find_bound_assign thy j (t :: seen) ts
|
blanchet@33192
|
2319 |
in
|
blanchet@33192
|
2320 |
case t of
|
blanchet@33192
|
2321 |
Const (@{const_name "op ="}, _) $ t1 $ t2 => aux true t1 t2
|
blanchet@33192
|
2322 |
| _ => find_bound_assign thy j (t :: seen) ts
|
blanchet@33192
|
2323 |
end
|
blanchet@33192
|
2324 |
|
blanchet@33192
|
2325 |
(* int -> term -> term -> term *)
|
blanchet@33192
|
2326 |
fun subst_one_bound j arg t =
|
blanchet@33192
|
2327 |
let
|
blanchet@33192
|
2328 |
fun aux (Bound i, lev) =
|
blanchet@33192
|
2329 |
if i < lev then raise SAME ()
|
blanchet@33192
|
2330 |
else if i = lev then incr_boundvars (lev - j) arg
|
blanchet@33192
|
2331 |
else Bound (i - 1)
|
blanchet@33192
|
2332 |
| aux (Abs (a, T, body), lev) = Abs (a, T, aux (body, lev + 1))
|
blanchet@33192
|
2333 |
| aux (f $ t, lev) =
|
blanchet@33192
|
2334 |
(aux (f, lev) $ (aux (t, lev) handle SAME () => t)
|
blanchet@33192
|
2335 |
handle SAME () => f $ aux (t, lev))
|
blanchet@33192
|
2336 |
| aux _ = raise SAME ()
|
blanchet@33192
|
2337 |
in aux (t, j) handle SAME () => t end
|
blanchet@33192
|
2338 |
|
blanchet@33192
|
2339 |
(* theory -> term -> term *)
|
blanchet@33192
|
2340 |
fun destroy_existential_equalities thy =
|
blanchet@33192
|
2341 |
let
|
blanchet@33192
|
2342 |
(* string list -> typ list -> term list -> term *)
|
blanchet@33192
|
2343 |
fun kill [] [] ts = foldr1 s_conj ts
|
blanchet@33192
|
2344 |
| kill (s :: ss) (T :: Ts) ts =
|
blanchet@33192
|
2345 |
(case find_bound_assign thy (length ss) [] ts of
|
blanchet@33192
|
2346 |
SOME (_, []) => @{const True}
|
blanchet@33192
|
2347 |
| SOME (arg_t, ts) =>
|
blanchet@33192
|
2348 |
kill ss Ts (map (subst_one_bound (length ss)
|
blanchet@33192
|
2349 |
(incr_bv (~1, length ss + 1, arg_t))) ts)
|
blanchet@33192
|
2350 |
| NONE =>
|
blanchet@33192
|
2351 |
Const (@{const_name Ex}, (T --> bool_T) --> bool_T)
|
blanchet@33192
|
2352 |
$ Abs (s, T, kill ss Ts ts))
|
blanchet@33192
|
2353 |
| kill _ _ _ = raise UnequalLengths
|
blanchet@33192
|
2354 |
(* string list -> typ list -> term -> term *)
|
blanchet@33192
|
2355 |
fun gather ss Ts ((t0 as Const (@{const_name Ex}, _)) $ Abs (s1, T1, t1)) =
|
blanchet@33192
|
2356 |
gather (ss @ [s1]) (Ts @ [T1]) t1
|
blanchet@33192
|
2357 |
| gather [] [] (Abs (s, T, t1)) = Abs (s, T, gather [] [] t1)
|
blanchet@33192
|
2358 |
| gather [] [] (t1 $ t2) = gather [] [] t1 $ gather [] [] t2
|
blanchet@33192
|
2359 |
| gather [] [] t = t
|
blanchet@33192
|
2360 |
| gather ss Ts t = kill ss Ts (conjuncts (gather [] [] t))
|
blanchet@33192
|
2361 |
in gather [] [] end
|
blanchet@33192
|
2362 |
|
blanchet@33192
|
2363 |
(* term -> term *)
|
blanchet@33192
|
2364 |
fun distribute_quantifiers t =
|
blanchet@33192
|
2365 |
case t of
|
blanchet@33192
|
2366 |
(t0 as Const (@{const_name All}, T0)) $ Abs (s, T1, t1) =>
|
blanchet@33192
|
2367 |
(case t1 of
|
blanchet@33192
|
2368 |
(t10 as @{const "op &"}) $ t11 $ t12 =>
|
blanchet@33192
|
2369 |
t10 $ distribute_quantifiers (t0 $ Abs (s, T1, t11))
|
blanchet@33192
|
2370 |
$ distribute_quantifiers (t0 $ Abs (s, T1, t12))
|
blanchet@33192
|
2371 |
| (t10 as @{const Not}) $ t11 =>
|
blanchet@33192
|
2372 |
t10 $ distribute_quantifiers (Const (@{const_name Ex}, T0)
|
blanchet@33192
|
2373 |
$ Abs (s, T1, t11))
|
blanchet@33192
|
2374 |
| t1 =>
|
blanchet@33192
|
2375 |
if not (loose_bvar1 (t1, 0)) then
|
blanchet@33192
|
2376 |
distribute_quantifiers (incr_boundvars ~1 t1)
|
blanchet@33192
|
2377 |
else
|
blanchet@33192
|
2378 |
t0 $ Abs (s, T1, distribute_quantifiers t1))
|
blanchet@33192
|
2379 |
| (t0 as Const (@{const_name Ex}, T0)) $ Abs (s, T1, t1) =>
|
blanchet@33192
|
2380 |
(case distribute_quantifiers t1 of
|
blanchet@33192
|
2381 |
(t10 as @{const "op |"}) $ t11 $ t12 =>
|
blanchet@33192
|
2382 |
t10 $ distribute_quantifiers (t0 $ Abs (s, T1, t11))
|
blanchet@33192
|
2383 |
$ distribute_quantifiers (t0 $ Abs (s, T1, t12))
|
blanchet@33192
|
2384 |
| (t10 as @{const "op -->"}) $ t11 $ t12 =>
|
blanchet@33192
|
2385 |
t10 $ distribute_quantifiers (Const (@{const_name All}, T0)
|
blanchet@33192
|
2386 |
$ Abs (s, T1, t11))
|
blanchet@33192
|
2387 |
$ distribute_quantifiers (t0 $ Abs (s, T1, t12))
|
blanchet@33192
|
2388 |
| (t10 as @{const Not}) $ t11 =>
|
blanchet@33192
|
2389 |
t10 $ distribute_quantifiers (Const (@{const_name All}, T0)
|
blanchet@33192
|
2390 |
$ Abs (s, T1, t11))
|
blanchet@33192
|
2391 |
| t1 =>
|
blanchet@33192
|
2392 |
if not (loose_bvar1 (t1, 0)) then
|
blanchet@33192
|
2393 |
distribute_quantifiers (incr_boundvars ~1 t1)
|
blanchet@33192
|
2394 |
else
|
blanchet@33192
|
2395 |
t0 $ Abs (s, T1, distribute_quantifiers t1))
|
blanchet@33192
|
2396 |
| t1 $ t2 => distribute_quantifiers t1 $ distribute_quantifiers t2
|
blanchet@33192
|
2397 |
| Abs (s, T, t') => Abs (s, T, distribute_quantifiers t')
|
blanchet@33192
|
2398 |
| _ => t
|
blanchet@33192
|
2399 |
|
blanchet@33192
|
2400 |
(* int -> int -> (int -> int) -> term -> term *)
|
blanchet@33192
|
2401 |
fun renumber_bounds j n f t =
|
blanchet@33192
|
2402 |
case t of
|
blanchet@33192
|
2403 |
t1 $ t2 => renumber_bounds j n f t1 $ renumber_bounds j n f t2
|
blanchet@33192
|
2404 |
| Abs (s, T, t') => Abs (s, T, renumber_bounds (j + 1) n f t')
|
blanchet@33192
|
2405 |
| Bound j' =>
|
blanchet@33192
|
2406 |
Bound (if j' >= j andalso j' < j + n then f (j' - j) + j else j')
|
blanchet@33192
|
2407 |
| _ => t
|
blanchet@33192
|
2408 |
|
blanchet@34985
|
2409 |
val quantifier_cluster_threshold = 7
|
blanchet@33192
|
2410 |
|
blanchet@33192
|
2411 |
(* theory -> term -> term *)
|
blanchet@33192
|
2412 |
fun push_quantifiers_inward thy =
|
blanchet@33192
|
2413 |
let
|
blanchet@33192
|
2414 |
(* string -> string list -> typ list -> term -> term *)
|
blanchet@33192
|
2415 |
fun aux quant_s ss Ts t =
|
blanchet@33192
|
2416 |
(case t of
|
blanchet@33192
|
2417 |
(t0 as Const (s0, _)) $ Abs (s1, T1, t1 as _ $ _) =>
|
blanchet@34985
|
2418 |
if s0 = quant_s then
|
blanchet@33192
|
2419 |
aux s0 (s1 :: ss) (T1 :: Ts) t1
|
blanchet@34923
|
2420 |
else if quant_s = "" andalso
|
blanchet@34923
|
2421 |
(s0 = @{const_name All} orelse s0 = @{const_name Ex}) then
|
blanchet@33192
|
2422 |
aux s0 [s1] [T1] t1
|
blanchet@33192
|
2423 |
else
|
blanchet@33192
|
2424 |
raise SAME ()
|
blanchet@33192
|
2425 |
| _ => raise SAME ())
|
blanchet@33192
|
2426 |
handle SAME () =>
|
blanchet@33192
|
2427 |
case t of
|
blanchet@33192
|
2428 |
t1 $ t2 =>
|
blanchet@33192
|
2429 |
if quant_s = "" then
|
blanchet@33192
|
2430 |
aux "" [] [] t1 $ aux "" [] [] t2
|
blanchet@33192
|
2431 |
else
|
blanchet@33192
|
2432 |
let
|
blanchet@33192
|
2433 |
val typical_card = 4
|
blanchet@33192
|
2434 |
(* ('a -> ''b list) -> 'a list -> ''b list *)
|
blanchet@33192
|
2435 |
fun big_union proj ps =
|
blanchet@33192
|
2436 |
fold (fold (insert (op =)) o proj) ps []
|
blanchet@33192
|
2437 |
val (ts, connective) = strip_any_connective t
|
blanchet@33192
|
2438 |
val T_costs =
|
blanchet@33192
|
2439 |
map (bounded_card_of_type 65536 typical_card []) Ts
|
blanchet@33192
|
2440 |
val t_costs = map size_of_term ts
|
blanchet@33192
|
2441 |
val num_Ts = length Ts
|
blanchet@33192
|
2442 |
(* int -> int *)
|
blanchet@33192
|
2443 |
val flip = curry (op -) (num_Ts - 1)
|
blanchet@33192
|
2444 |
val t_boundss = map (map flip o loose_bnos) ts
|
blanchet@34985
|
2445 |
(* (int list * int) list -> int list
|
blanchet@34985
|
2446 |
-> (int list * int) list *)
|
blanchet@34985
|
2447 |
fun merge costly_boundss [] = costly_boundss
|
blanchet@34985
|
2448 |
| merge costly_boundss (j :: js) =
|
blanchet@33192
|
2449 |
let
|
blanchet@33192
|
2450 |
val (yeas, nays) =
|
blanchet@34118
|
2451 |
List.partition (fn (bounds, _) =>
|
blanchet@34118
|
2452 |
member (op =) bounds j)
|
blanchet@34985
|
2453 |
costly_boundss
|
blanchet@33192
|
2454 |
val yeas_bounds = big_union fst yeas
|
blanchet@33192
|
2455 |
val yeas_cost = Integer.sum (map snd yeas)
|
blanchet@33192
|
2456 |
* nth T_costs j
|
blanchet@34985
|
2457 |
in merge ((yeas_bounds, yeas_cost) :: nays) js end
|
blanchet@34985
|
2458 |
(* (int list * int) list -> int list -> int *)
|
blanchet@34985
|
2459 |
val cost = Integer.sum o map snd oo merge
|
blanchet@34985
|
2460 |
(* Inspired by Claessen & Sörensson's polynomial binary
|
blanchet@34985
|
2461 |
splitting heuristic (p. 5 of their MODEL 2003 paper). *)
|
blanchet@34985
|
2462 |
(* (int list * int) list -> int list -> int list *)
|
blanchet@34985
|
2463 |
fun heuristically_best_permutation _ [] = []
|
blanchet@34985
|
2464 |
| heuristically_best_permutation costly_boundss js =
|
blanchet@34985
|
2465 |
let
|
blanchet@34985
|
2466 |
val (costly_boundss, (j, js)) =
|
blanchet@34985
|
2467 |
js |> map (`(merge costly_boundss o single))
|
blanchet@34985
|
2468 |
|> sort (int_ord
|
blanchet@34985
|
2469 |
o pairself (Integer.sum o map snd o fst))
|
blanchet@34985
|
2470 |
|> split_list |>> hd ||> pairf hd tl
|
blanchet@34985
|
2471 |
in
|
blanchet@34985
|
2472 |
j :: heuristically_best_permutation costly_boundss js
|
blanchet@34985
|
2473 |
end
|
blanchet@34985
|
2474 |
val js =
|
blanchet@34985
|
2475 |
if length Ts <= quantifier_cluster_threshold then
|
blanchet@34985
|
2476 |
all_permutations (index_seq 0 num_Ts)
|
blanchet@34985
|
2477 |
|> map (`(cost (t_boundss ~~ t_costs)))
|
blanchet@34985
|
2478 |
|> sort (int_ord o pairself fst) |> hd |> snd
|
blanchet@34985
|
2479 |
else
|
blanchet@34985
|
2480 |
heuristically_best_permutation (t_boundss ~~ t_costs)
|
blanchet@34985
|
2481 |
(index_seq 0 num_Ts)
|
blanchet@34118
|
2482 |
val back_js = map (fn j => find_index (curry (op =) j) js)
|
blanchet@33192
|
2483 |
(index_seq 0 num_Ts)
|
blanchet@33192
|
2484 |
val ts = map (renumber_bounds 0 num_Ts (nth back_js o flip))
|
blanchet@33192
|
2485 |
ts
|
blanchet@33192
|
2486 |
(* (term * int list) list -> term *)
|
blanchet@33192
|
2487 |
fun mk_connection [] =
|
blanchet@33224
|
2488 |
raise ARG ("Nitpick_HOL.push_quantifiers_inward.aux.\
|
blanchet@33192
|
2489 |
\mk_connection", "")
|
blanchet@33192
|
2490 |
| mk_connection ts_cum_bounds =
|
blanchet@33192
|
2491 |
ts_cum_bounds |> map fst
|
blanchet@33192
|
2492 |
|> foldr1 (fn (t1, t2) => connective $ t1 $ t2)
|
blanchet@33192
|
2493 |
(* (term * int list) list -> int list -> term *)
|
blanchet@33192
|
2494 |
fun build ts_cum_bounds [] = ts_cum_bounds |> mk_connection
|
blanchet@33192
|
2495 |
| build ts_cum_bounds (j :: js) =
|
blanchet@33192
|
2496 |
let
|
blanchet@33192
|
2497 |
val (yeas, nays) =
|
blanchet@34118
|
2498 |
List.partition (fn (_, bounds) =>
|
blanchet@34118
|
2499 |
member (op =) bounds j)
|
blanchet@33192
|
2500 |
ts_cum_bounds
|
blanchet@33192
|
2501 |
||> map (apfst (incr_boundvars ~1))
|
blanchet@33192
|
2502 |
in
|
blanchet@33192
|
2503 |
if null yeas then
|
blanchet@33192
|
2504 |
build nays js
|
blanchet@33192
|
2505 |
else
|
blanchet@33192
|
2506 |
let val T = nth Ts (flip j) in
|
blanchet@33192
|
2507 |
build ((Const (quant_s, (T --> bool_T) --> bool_T)
|
blanchet@33192
|
2508 |
$ Abs (nth ss (flip j), T,
|
blanchet@33192
|
2509 |
mk_connection yeas),
|
blanchet@33192
|
2510 |
big_union snd yeas) :: nays) js
|
blanchet@33192
|
2511 |
end
|
blanchet@33192
|
2512 |
end
|
blanchet@33192
|
2513 |
in build (ts ~~ t_boundss) js end
|
blanchet@33192
|
2514 |
| Abs (s, T, t') => Abs (s, T, aux "" [] [] t')
|
blanchet@33192
|
2515 |
| _ => t
|
blanchet@33192
|
2516 |
in aux "" [] [] end
|
blanchet@33192
|
2517 |
|
blanchet@33192
|
2518 |
(* polarity -> string -> bool *)
|
blanchet@33192
|
2519 |
fun is_positive_existential polar quant_s =
|
blanchet@34923
|
2520 |
(polar = Pos andalso quant_s = @{const_name Ex}) orelse
|
blanchet@34923
|
2521 |
(polar = Neg andalso quant_s <> @{const_name Ex})
|
blanchet@33192
|
2522 |
|
blanchet@33192
|
2523 |
(* extended_context -> int -> term -> term *)
|
blanchet@33192
|
2524 |
fun skolemize_term_and_more (ext_ctxt as {thy, def_table, skolems, ...})
|
blanchet@33192
|
2525 |
skolem_depth =
|
blanchet@33192
|
2526 |
let
|
blanchet@33192
|
2527 |
(* int list -> int list *)
|
blanchet@33192
|
2528 |
val incrs = map (Integer.add 1)
|
blanchet@33192
|
2529 |
(* string list -> typ list -> int list -> int -> polarity -> term -> term *)
|
blanchet@33192
|
2530 |
fun aux ss Ts js depth polar t =
|
blanchet@33192
|
2531 |
let
|
blanchet@33192
|
2532 |
(* string -> typ -> string -> typ -> term -> term *)
|
blanchet@33192
|
2533 |
fun do_quantifier quant_s quant_T abs_s abs_T t =
|
blanchet@33192
|
2534 |
if not (loose_bvar1 (t, 0)) then
|
blanchet@33192
|
2535 |
aux ss Ts js depth polar (incr_boundvars ~1 t)
|
blanchet@34923
|
2536 |
else if depth <= skolem_depth andalso
|
blanchet@34923
|
2537 |
is_positive_existential polar quant_s then
|
blanchet@33192
|
2538 |
let
|
blanchet@33192
|
2539 |
val j = length (!skolems) + 1
|
blanchet@33192
|
2540 |
val sko_s = skolem_prefix_for (length js) j ^ abs_s
|
blanchet@33192
|
2541 |
val _ = Unsynchronized.change skolems (cons (sko_s, ss))
|
blanchet@33192
|
2542 |
val sko_t = list_comb (Const (sko_s, rev Ts ---> abs_T),
|
blanchet@33192
|
2543 |
map Bound (rev js))
|
blanchet@33192
|
2544 |
val abs_t = Abs (abs_s, abs_T, aux ss Ts (incrs js) depth polar t)
|
blanchet@33192
|
2545 |
in
|
blanchet@33192
|
2546 |
if null js then betapply (abs_t, sko_t)
|
blanchet@33192
|
2547 |
else Const (@{const_name Let}, abs_T --> quant_T) $ sko_t $ abs_t
|
blanchet@33192
|
2548 |
end
|
blanchet@33192
|
2549 |
else
|
blanchet@33192
|
2550 |
Const (quant_s, quant_T)
|
blanchet@33192
|
2551 |
$ Abs (abs_s, abs_T,
|
blanchet@33192
|
2552 |
if is_higher_order_type abs_T then
|
blanchet@33192
|
2553 |
t
|
blanchet@33192
|
2554 |
else
|
blanchet@33192
|
2555 |
aux (abs_s :: ss) (abs_T :: Ts) (0 :: incrs js)
|
blanchet@33192
|
2556 |
(depth + 1) polar t)
|
blanchet@33192
|
2557 |
in
|
blanchet@33192
|
2558 |
case t of
|
blanchet@33192
|
2559 |
Const (s0 as @{const_name all}, T0) $ Abs (s1, T1, t1) =>
|
blanchet@33192
|
2560 |
do_quantifier s0 T0 s1 T1 t1
|
blanchet@33192
|
2561 |
| @{const "==>"} $ t1 $ t2 =>
|
blanchet@33192
|
2562 |
@{const "==>"} $ aux ss Ts js depth (flip_polarity polar) t1
|
blanchet@33192
|
2563 |
$ aux ss Ts js depth polar t2
|
blanchet@33192
|
2564 |
| @{const Pure.conjunction} $ t1 $ t2 =>
|
blanchet@33192
|
2565 |
@{const Pure.conjunction} $ aux ss Ts js depth polar t1
|
blanchet@33192
|
2566 |
$ aux ss Ts js depth polar t2
|
blanchet@33192
|
2567 |
| @{const Trueprop} $ t1 =>
|
blanchet@33192
|
2568 |
@{const Trueprop} $ aux ss Ts js depth polar t1
|
blanchet@33192
|
2569 |
| @{const Not} $ t1 =>
|
blanchet@33192
|
2570 |
@{const Not} $ aux ss Ts js depth (flip_polarity polar) t1
|
blanchet@33192
|
2571 |
| Const (s0 as @{const_name All}, T0) $ Abs (s1, T1, t1) =>
|
blanchet@33192
|
2572 |
do_quantifier s0 T0 s1 T1 t1
|
blanchet@33192
|
2573 |
| Const (s0 as @{const_name Ex}, T0) $ Abs (s1, T1, t1) =>
|
blanchet@33192
|
2574 |
do_quantifier s0 T0 s1 T1 t1
|
blanchet@33192
|
2575 |
| @{const "op &"} $ t1 $ t2 =>
|
blanchet@33192
|
2576 |
@{const "op &"} $ aux ss Ts js depth polar t1
|
blanchet@33192
|
2577 |
$ aux ss Ts js depth polar t2
|
blanchet@33192
|
2578 |
| @{const "op |"} $ t1 $ t2 =>
|
blanchet@33192
|
2579 |
@{const "op |"} $ aux ss Ts js depth polar t1
|
blanchet@33192
|
2580 |
$ aux ss Ts js depth polar t2
|
blanchet@33192
|
2581 |
| @{const "op -->"} $ t1 $ t2 =>
|
blanchet@33192
|
2582 |
@{const "op -->"} $ aux ss Ts js depth (flip_polarity polar) t1
|
blanchet@33192
|
2583 |
$ aux ss Ts js depth polar t2
|
blanchet@33192
|
2584 |
| (t0 as Const (@{const_name Let}, T0)) $ t1 $ t2 =>
|
blanchet@33192
|
2585 |
t0 $ t1 $ aux ss Ts js depth polar t2
|
blanchet@33192
|
2586 |
| Const (x as (s, T)) =>
|
blanchet@34923
|
2587 |
if is_inductive_pred ext_ctxt x andalso
|
blanchet@34923
|
2588 |
not (is_well_founded_inductive_pred ext_ctxt x) then
|
blanchet@33192
|
2589 |
let
|
blanchet@33192
|
2590 |
val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
|
blanchet@33192
|
2591 |
val (pref, connective, set_oper) =
|
blanchet@33192
|
2592 |
if gfp then
|
blanchet@33192
|
2593 |
(lbfp_prefix,
|
blanchet@33192
|
2594 |
@{const "op |"},
|
haftmann@35028
|
2595 |
@{const_name semilattice_sup_fun_inst.sup_fun})
|
blanchet@33192
|
2596 |
else
|
blanchet@33192
|
2597 |
(ubfp_prefix,
|
blanchet@33192
|
2598 |
@{const "op &"},
|
haftmann@35028
|
2599 |
@{const_name semilattice_inf_fun_inst.inf_fun})
|
blanchet@33192
|
2600 |
(* unit -> term *)
|
blanchet@33192
|
2601 |
fun pos () = unrolled_inductive_pred_const ext_ctxt gfp x
|
blanchet@33192
|
2602 |
|> aux ss Ts js depth polar
|
blanchet@33192
|
2603 |
fun neg () = Const (pref ^ s, T)
|
blanchet@33192
|
2604 |
in
|
blanchet@33192
|
2605 |
(case polar |> gfp ? flip_polarity of
|
blanchet@33192
|
2606 |
Pos => pos ()
|
blanchet@33192
|
2607 |
| Neg => neg ()
|
blanchet@33192
|
2608 |
| Neut =>
|
blanchet@33192
|
2609 |
if is_fun_type T then
|
blanchet@33192
|
2610 |
let
|
blanchet@33192
|
2611 |
val ((trunk_arg_Ts, rump_arg_T), body_T) =
|
blanchet@33192
|
2612 |
T |> strip_type |>> split_last
|
blanchet@33192
|
2613 |
val set_T = rump_arg_T --> body_T
|
blanchet@33192
|
2614 |
(* (unit -> term) -> term *)
|
blanchet@33192
|
2615 |
fun app f =
|
blanchet@33192
|
2616 |
list_comb (f (),
|
blanchet@33192
|
2617 |
map Bound (length trunk_arg_Ts - 1 downto 0))
|
blanchet@33192
|
2618 |
in
|
blanchet@33879
|
2619 |
List.foldr absdummy
|
blanchet@34121
|
2620 |
(Const (set_oper, set_T --> set_T --> set_T)
|
blanchet@33192
|
2621 |
$ app pos $ app neg) trunk_arg_Ts
|
blanchet@33192
|
2622 |
end
|
blanchet@33192
|
2623 |
else
|
blanchet@33192
|
2624 |
connective $ pos () $ neg ())
|
blanchet@33192
|
2625 |
end
|
blanchet@33192
|
2626 |
else
|
blanchet@33192
|
2627 |
Const x
|
blanchet@33192
|
2628 |
| t1 $ t2 =>
|
blanchet@33192
|
2629 |
betapply (aux ss Ts [] (skolem_depth + 1) polar t1,
|
blanchet@33192
|
2630 |
aux ss Ts [] depth Neut t2)
|
blanchet@33192
|
2631 |
| Abs (s, T, t1) => Abs (s, T, aux ss Ts (incrs js) depth polar t1)
|
blanchet@33192
|
2632 |
| _ => t
|
blanchet@33192
|
2633 |
end
|
blanchet@33192
|
2634 |
in aux [] [] [] 0 Pos end
|
blanchet@33192
|
2635 |
|
blanchet@33192
|
2636 |
(* extended_context -> styp -> (int * term option) list *)
|
blanchet@33192
|
2637 |
fun static_args_in_term ({ersatz_table, ...} : extended_context) x t =
|
blanchet@33192
|
2638 |
let
|
blanchet@33192
|
2639 |
(* term -> term list -> term list -> term list list *)
|
blanchet@33192
|
2640 |
fun fun_calls (Abs (_, _, t)) _ = fun_calls t []
|
blanchet@33192
|
2641 |
| fun_calls (t1 $ t2) args = fun_calls t2 [] #> fun_calls t1 (t2 :: args)
|
blanchet@33192
|
2642 |
| fun_calls t args =
|
blanchet@33192
|
2643 |
(case t of
|
blanchet@33192
|
2644 |
Const (x' as (s', T')) =>
|
blanchet@33192
|
2645 |
x = x' orelse (case AList.lookup (op =) ersatz_table s' of
|
blanchet@33192
|
2646 |
SOME s'' => x = (s'', T')
|
blanchet@33192
|
2647 |
| NONE => false)
|
blanchet@33192
|
2648 |
| _ => false) ? cons args
|
blanchet@33192
|
2649 |
(* term list list -> term list list -> term list -> term list list *)
|
blanchet@33192
|
2650 |
fun call_sets [] [] vs = [vs]
|
blanchet@33192
|
2651 |
| call_sets [] uss vs = vs :: call_sets uss [] []
|
blanchet@33192
|
2652 |
| call_sets ([] :: _) _ _ = []
|
blanchet@33192
|
2653 |
| call_sets ((t :: ts) :: tss) uss vs =
|
blanchet@33192
|
2654 |
OrdList.insert TermOrd.term_ord t vs |> call_sets tss (ts :: uss)
|
blanchet@33192
|
2655 |
val sets = call_sets (fun_calls t [] []) [] []
|
blanchet@33192
|
2656 |
val indexed_sets = sets ~~ (index_seq 0 (length sets))
|
blanchet@33192
|
2657 |
in
|
blanchet@33192
|
2658 |
fold_rev (fn (set, j) =>
|
blanchet@33192
|
2659 |
case set of
|
blanchet@33192
|
2660 |
[Var _] => AList.lookup (op =) indexed_sets set = SOME j
|
blanchet@33192
|
2661 |
? cons (j, NONE)
|
blanchet@33192
|
2662 |
| [t as Const _] => cons (j, SOME t)
|
blanchet@33192
|
2663 |
| [t as Free _] => cons (j, SOME t)
|
blanchet@33192
|
2664 |
| _ => I) indexed_sets []
|
blanchet@33192
|
2665 |
end
|
blanchet@33192
|
2666 |
(* extended_context -> styp -> term list -> (int * term option) list *)
|
blanchet@33192
|
2667 |
fun static_args_in_terms ext_ctxt x =
|
blanchet@33192
|
2668 |
map (static_args_in_term ext_ctxt x)
|
blanchet@33192
|
2669 |
#> fold1 (OrdList.inter (prod_ord int_ord (option_ord TermOrd.term_ord)))
|
blanchet@33192
|
2670 |
|
blanchet@33192
|
2671 |
(* term -> term list *)
|
blanchet@33192
|
2672 |
fun params_in_equation (@{const "==>"} $ _ $ t2) = params_in_equation t2
|
blanchet@33192
|
2673 |
| params_in_equation (@{const Trueprop} $ t1) = params_in_equation t1
|
blanchet@33192
|
2674 |
| params_in_equation (Const (@{const_name "op ="}, _) $ t1 $ _) =
|
blanchet@33192
|
2675 |
snd (strip_comb t1)
|
blanchet@33192
|
2676 |
| params_in_equation _ = []
|
blanchet@33192
|
2677 |
|
blanchet@33192
|
2678 |
(* styp -> styp -> int list -> term list -> term list -> term -> term *)
|
blanchet@33192
|
2679 |
fun specialize_fun_axiom x x' fixed_js fixed_args extra_args t =
|
blanchet@33192
|
2680 |
let
|
blanchet@33192
|
2681 |
val k = fold Integer.max (map maxidx_of_term (fixed_args @ extra_args)) 0
|
blanchet@33192
|
2682 |
+ 1
|
blanchet@33192
|
2683 |
val t = map_aterms (fn Var ((s, i), T) => Var ((s, k + i), T) | t' => t') t
|
blanchet@33192
|
2684 |
val fixed_params = filter_indices fixed_js (params_in_equation t)
|
blanchet@33192
|
2685 |
(* term list -> term -> term *)
|
blanchet@33192
|
2686 |
fun aux args (Abs (s, T, t)) = list_comb (Abs (s, T, aux [] t), args)
|
blanchet@33192
|
2687 |
| aux args (t1 $ t2) = aux (aux [] t2 :: args) t1
|
blanchet@33192
|
2688 |
| aux args t =
|
blanchet@33192
|
2689 |
if t = Const x then
|
blanchet@33192
|
2690 |
list_comb (Const x', extra_args @ filter_out_indices fixed_js args)
|
blanchet@33192
|
2691 |
else
|
blanchet@34118
|
2692 |
let val j = find_index (curry (op =) t) fixed_params in
|
blanchet@33192
|
2693 |
list_comb (if j >= 0 then nth fixed_args j else t, args)
|
blanchet@33192
|
2694 |
end
|
blanchet@33192
|
2695 |
in aux [] t end
|
blanchet@33192
|
2696 |
|
blanchet@33192
|
2697 |
(* typ list -> term -> bool *)
|
blanchet@33192
|
2698 |
fun is_eligible_arg Ts t =
|
blanchet@33192
|
2699 |
let val bad_Ts = map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t) in
|
blanchet@34923
|
2700 |
null bad_Ts orelse
|
blanchet@34923
|
2701 |
(is_higher_order_type (fastype_of1 (Ts, t)) andalso
|
blanchet@34923
|
2702 |
forall (not o is_higher_order_type) bad_Ts)
|
blanchet@33192
|
2703 |
end
|
blanchet@33192
|
2704 |
|
blanchet@33192
|
2705 |
(* (int * term option) list -> (int * term) list -> int list *)
|
blanchet@33192
|
2706 |
fun overlapping_indices [] _ = []
|
blanchet@33192
|
2707 |
| overlapping_indices _ [] = []
|
blanchet@33192
|
2708 |
| overlapping_indices (ps1 as (j1, t1) :: ps1') (ps2 as (j2, t2) :: ps2') =
|
blanchet@33192
|
2709 |
if j1 < j2 then overlapping_indices ps1' ps2
|
blanchet@33192
|
2710 |
else if j1 > j2 then overlapping_indices ps1 ps2'
|
blanchet@33192
|
2711 |
else overlapping_indices ps1' ps2' |> the_default t2 t1 = t2 ? cons j1
|
blanchet@33192
|
2712 |
|
blanchet@33192
|
2713 |
val special_depth = 20
|
blanchet@33192
|
2714 |
|
blanchet@33192
|
2715 |
(* extended_context -> int -> term -> term *)
|
blanchet@33192
|
2716 |
fun specialize_consts_in_term (ext_ctxt as {thy, specialize, simp_table,
|
blanchet@33192
|
2717 |
special_funs, ...}) depth t =
|
blanchet@33192
|
2718 |
if not specialize orelse depth > special_depth then
|
blanchet@33192
|
2719 |
t
|
blanchet@33192
|
2720 |
else
|
blanchet@33192
|
2721 |
let
|
blanchet@33192
|
2722 |
val blacklist = if depth = 0 then []
|
blanchet@33192
|
2723 |
else case term_under_def t of Const x => [x] | _ => []
|
blanchet@33192
|
2724 |
(* term list -> typ list -> term -> term *)
|
blanchet@33192
|
2725 |
fun aux args Ts (Const (x as (s, T))) =
|
blanchet@34923
|
2726 |
((if not (member (op =) blacklist x) andalso not (null args) andalso
|
blanchet@34923
|
2727 |
not (String.isPrefix special_prefix s) andalso
|
blanchet@34923
|
2728 |
is_equational_fun ext_ctxt x then
|
blanchet@33192
|
2729 |
let
|
blanchet@33192
|
2730 |
val eligible_args = filter (is_eligible_arg Ts o snd)
|
blanchet@33192
|
2731 |
(index_seq 0 (length args) ~~ args)
|
blanchet@33192
|
2732 |
val _ = not (null eligible_args) orelse raise SAME ()
|
blanchet@33192
|
2733 |
val old_axs = equational_fun_axioms ext_ctxt x
|
blanchet@33192
|
2734 |
|> map (destroy_existential_equalities thy)
|
blanchet@33192
|
2735 |
val static_params = static_args_in_terms ext_ctxt x old_axs
|
blanchet@33192
|
2736 |
val fixed_js = overlapping_indices static_params eligible_args
|
blanchet@33192
|
2737 |
val _ = not (null fixed_js) orelse raise SAME ()
|
blanchet@33192
|
2738 |
val fixed_args = filter_indices fixed_js args
|
blanchet@33192
|
2739 |
val vars = fold Term.add_vars fixed_args []
|
blanchet@33192
|
2740 |
|> sort (TermOrd.fast_indexname_ord o pairself fst)
|
blanchet@33192
|
2741 |
val bound_js = fold (fn t => fn js => add_loose_bnos (t, 0, js))
|
blanchet@33192
|
2742 |
fixed_args []
|
blanchet@33192
|
2743 |
|> sort int_ord
|
blanchet@33192
|
2744 |
val live_args = filter_out_indices fixed_js args
|
blanchet@33192
|
2745 |
val extra_args = map Var vars @ map Bound bound_js @ live_args
|
blanchet@33192
|
2746 |
val extra_Ts = map snd vars @ filter_indices bound_js Ts
|
blanchet@33192
|
2747 |
val k = maxidx_of_term t + 1
|
blanchet@33192
|
2748 |
(* int -> term *)
|
blanchet@33192
|
2749 |
fun var_for_bound_no j =
|
blanchet@33192
|
2750 |
Var ((bound_var_prefix ^
|
blanchet@34118
|
2751 |
nat_subscript (find_index (curry (op =) j) bound_js
|
blanchet@34118
|
2752 |
+ 1), k),
|
blanchet@33192
|
2753 |
nth Ts j)
|
blanchet@33192
|
2754 |
val fixed_args_in_axiom =
|
blanchet@33192
|
2755 |
map (curry subst_bounds
|
blanchet@33192
|
2756 |
(map var_for_bound_no (index_seq 0 (length Ts))))
|
blanchet@33192
|
2757 |
fixed_args
|
blanchet@33192
|
2758 |
in
|
blanchet@33192
|
2759 |
case AList.lookup (op =) (!special_funs)
|
blanchet@33192
|
2760 |
(x, fixed_js, fixed_args_in_axiom) of
|
blanchet@33192
|
2761 |
SOME x' => list_comb (Const x', extra_args)
|
blanchet@33192
|
2762 |
| NONE =>
|
blanchet@33192
|
2763 |
let
|
blanchet@33192
|
2764 |
val extra_args_in_axiom =
|
blanchet@33192
|
2765 |
map Var vars @ map var_for_bound_no bound_js
|
blanchet@33192
|
2766 |
val x' as (s', _) =
|
blanchet@33192
|
2767 |
(special_prefix_for (length (!special_funs) + 1) ^ s,
|
blanchet@33192
|
2768 |
extra_Ts @ filter_out_indices fixed_js (binder_types T)
|
blanchet@33192
|
2769 |
---> body_type T)
|
blanchet@33192
|
2770 |
val new_axs =
|
blanchet@33192
|
2771 |
map (specialize_fun_axiom x x' fixed_js
|
blanchet@33192
|
2772 |
fixed_args_in_axiom extra_args_in_axiom) old_axs
|
blanchet@33192
|
2773 |
val _ =
|
blanchet@33192
|
2774 |
Unsynchronized.change special_funs
|
blanchet@33192
|
2775 |
(cons ((x, fixed_js, fixed_args_in_axiom), x'))
|
blanchet@33192
|
2776 |
val _ = add_simps simp_table s' new_axs
|
blanchet@33192
|
2777 |
in list_comb (Const x', extra_args) end
|
blanchet@33192
|
2778 |
end
|
blanchet@33192
|
2779 |
else
|
blanchet@33192
|
2780 |
raise SAME ())
|
blanchet@33192
|
2781 |
handle SAME () => list_comb (Const x, args))
|
blanchet@33192
|
2782 |
| aux args Ts (Abs (s, T, t)) =
|
blanchet@33192
|
2783 |
list_comb (Abs (s, T, aux [] (T :: Ts) t), args)
|
blanchet@33192
|
2784 |
| aux args Ts (t1 $ t2) = aux (aux [] Ts t2 :: args) Ts t1
|
blanchet@33192
|
2785 |
| aux args _ t = list_comb (t, args)
|
blanchet@33192
|
2786 |
in aux [] [] t end
|
blanchet@33192
|
2787 |
|
blanchet@33192
|
2788 |
(* theory -> term -> int Termtab.tab -> int Termtab.tab *)
|
blanchet@33192
|
2789 |
fun add_to_uncurry_table thy t =
|
blanchet@33192
|
2790 |
let
|
blanchet@33192
|
2791 |
(* term -> term list -> int Termtab.tab -> int Termtab.tab *)
|
blanchet@33192
|
2792 |
fun aux (t1 $ t2) args table =
|
blanchet@33192
|
2793 |
let val table = aux t2 [] table in aux t1 (t2 :: args) table end
|
blanchet@33192
|
2794 |
| aux (Abs (_, _, t')) _ table = aux t' [] table
|
blanchet@33192
|
2795 |
| aux (t as Const (x as (s, _))) args table =
|
blanchet@34923
|
2796 |
if is_built_in_const true x orelse is_constr_like thy x orelse
|
blanchet@34923
|
2797 |
is_sel s orelse s = @{const_name Sigma} then
|
blanchet@33192
|
2798 |
table
|
blanchet@33192
|
2799 |
else
|
blanchet@33192
|
2800 |
Termtab.map_default (t, 65536) (curry Int.min (length args)) table
|
blanchet@33192
|
2801 |
| aux _ _ table = table
|
blanchet@33192
|
2802 |
in aux t [] end
|
blanchet@33192
|
2803 |
|
blanchet@33192
|
2804 |
(* int Termtab.tab term -> term *)
|
blanchet@33192
|
2805 |
fun uncurry_term table t =
|
blanchet@33192
|
2806 |
let
|
blanchet@33192
|
2807 |
(* term -> term list -> term *)
|
blanchet@33192
|
2808 |
fun aux (t1 $ t2) args = aux t1 (aux t2 [] :: args)
|
blanchet@33192
|
2809 |
| aux (Abs (s, T, t')) args = betapplys (Abs (s, T, aux t' []), args)
|
blanchet@33192
|
2810 |
| aux (t as Const (s, T)) args =
|
blanchet@33192
|
2811 |
(case Termtab.lookup table t of
|
blanchet@33192
|
2812 |
SOME n =>
|
blanchet@33192
|
2813 |
if n >= 2 then
|
blanchet@33192
|
2814 |
let
|
blanchet@33192
|
2815 |
val (arg_Ts, rest_T) = strip_n_binders n T
|
blanchet@33192
|
2816 |
val j =
|
blanchet@34923
|
2817 |
if hd arg_Ts = @{typ bisim_iterator} orelse
|
blanchet@34923
|
2818 |
is_fp_iterator_type (hd arg_Ts) then
|
blanchet@33192
|
2819 |
1
|
blanchet@33192
|
2820 |
else case find_index (not_equal bool_T) arg_Ts of
|
blanchet@33192
|
2821 |
~1 => n
|
blanchet@33192
|
2822 |
| j => j
|
blanchet@33192
|
2823 |
val ((before_args, tuple_args), after_args) =
|
blanchet@33192
|
2824 |
args |> chop n |>> chop j
|
blanchet@33192
|
2825 |
val ((before_arg_Ts, tuple_arg_Ts), rest_T) =
|
blanchet@33192
|
2826 |
T |> strip_n_binders n |>> chop j
|
blanchet@33192
|
2827 |
val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
|
blanchet@33192
|
2828 |
in
|
blanchet@33192
|
2829 |
if n - j < 2 then
|
blanchet@33192
|
2830 |
betapplys (t, args)
|
blanchet@33192
|
2831 |
else
|
blanchet@33192
|
2832 |
betapplys (Const (uncurry_prefix_for (n - j) j ^ s,
|
blanchet@33192
|
2833 |
before_arg_Ts ---> tuple_T --> rest_T),
|
blanchet@33192
|
2834 |
before_args @ [mk_flat_tuple tuple_T tuple_args] @
|
blanchet@33192
|
2835 |
after_args)
|
blanchet@33192
|
2836 |
end
|
blanchet@33192
|
2837 |
else
|
blanchet@33192
|
2838 |
betapplys (t, args)
|
blanchet@33192
|
2839 |
| NONE => betapplys (t, args))
|
blanchet@33192
|
2840 |
| aux t args = betapplys (t, args)
|
blanchet@33192
|
2841 |
in aux t [] end
|
blanchet@33192
|
2842 |
|
blanchet@33192
|
2843 |
(* (term -> term) -> int -> term -> term *)
|
blanchet@33192
|
2844 |
fun coerce_bound_no f j t =
|
blanchet@33192
|
2845 |
case t of
|
blanchet@33192
|
2846 |
t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
|
blanchet@33192
|
2847 |
| Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
|
blanchet@33192
|
2848 |
| Bound j' => if j' = j then f t else t
|
blanchet@33192
|
2849 |
| _ => t
|
blanchet@33192
|
2850 |
|
blanchet@33192
|
2851 |
(* extended_context -> bool -> term -> term *)
|
blanchet@33192
|
2852 |
fun box_fun_and_pair_in_term (ext_ctxt as {thy, fast_descrs, ...}) def orig_t =
|
blanchet@33192
|
2853 |
let
|
blanchet@33192
|
2854 |
(* typ -> typ *)
|
blanchet@33192
|
2855 |
fun box_relational_operator_type (Type ("fun", Ts)) =
|
blanchet@33192
|
2856 |
Type ("fun", map box_relational_operator_type Ts)
|
blanchet@33192
|
2857 |
| box_relational_operator_type (Type ("*", Ts)) =
|
blanchet@33192
|
2858 |
Type ("*", map (box_type ext_ctxt InPair) Ts)
|
blanchet@33192
|
2859 |
| box_relational_operator_type T = T
|
blanchet@33192
|
2860 |
(* typ -> typ -> term -> term *)
|
blanchet@33192
|
2861 |
fun coerce_bound_0_in_term new_T old_T =
|
blanchet@33192
|
2862 |
old_T <> new_T ? coerce_bound_no (coerce_term [new_T] old_T new_T) 0
|
blanchet@33192
|
2863 |
(* typ list -> typ -> term -> term *)
|
blanchet@33192
|
2864 |
and coerce_term Ts new_T old_T t =
|
blanchet@33192
|
2865 |
if old_T = new_T then
|
blanchet@33192
|
2866 |
t
|
blanchet@33192
|
2867 |
else
|
blanchet@33192
|
2868 |
case (new_T, old_T) of
|
blanchet@33192
|
2869 |
(Type (new_s, new_Ts as [new_T1, new_T2]),
|
blanchet@33192
|
2870 |
Type ("fun", [old_T1, old_T2])) =>
|
blanchet@33192
|
2871 |
(case eta_expand Ts t 1 of
|
blanchet@33192
|
2872 |
Abs (s, _, t') =>
|
blanchet@33192
|
2873 |
Abs (s, new_T1,
|
blanchet@33192
|
2874 |
t' |> coerce_bound_0_in_term new_T1 old_T1
|
blanchet@33192
|
2875 |
|> coerce_term (new_T1 :: Ts) new_T2 old_T2)
|
blanchet@33192
|
2876 |
|> Envir.eta_contract
|
blanchet@33192
|
2877 |
|> new_s <> "fun"
|
blanchet@33192
|
2878 |
? construct_value thy (@{const_name FunBox},
|
blanchet@33192
|
2879 |
Type ("fun", new_Ts) --> new_T) o single
|
blanchet@33224
|
2880 |
| t' => raise TERM ("Nitpick_HOL.box_fun_and_pair_in_term.\
|
blanchet@33192
|
2881 |
\coerce_term", [t']))
|
blanchet@33192
|
2882 |
| (Type (new_s, new_Ts as [new_T1, new_T2]),
|
blanchet@33192
|
2883 |
Type (old_s, old_Ts as [old_T1, old_T2])) =>
|
blanchet@34923
|
2884 |
if old_s = @{type_name fun_box} orelse
|
blanchet@34923
|
2885 |
old_s = @{type_name pair_box} orelse old_s = "*" then
|
blanchet@33571
|
2886 |
case constr_expand ext_ctxt old_T t of
|
blanchet@33192
|
2887 |
Const (@{const_name FunBox}, _) $ t1 =>
|
blanchet@33192
|
2888 |
if new_s = "fun" then
|
blanchet@33192
|
2889 |
coerce_term Ts new_T (Type ("fun", old_Ts)) t1
|
blanchet@33192
|
2890 |
else
|
blanchet@33192
|
2891 |
construct_value thy
|
blanchet@33192
|
2892 |
(@{const_name FunBox}, Type ("fun", new_Ts) --> new_T)
|
blanchet@33192
|
2893 |
[coerce_term Ts (Type ("fun", new_Ts))
|
blanchet@33192
|
2894 |
(Type ("fun", old_Ts)) t1]
|
blanchet@33192
|
2895 |
| Const _ $ t1 $ t2 =>
|
blanchet@33192
|
2896 |
construct_value thy
|
blanchet@33192
|
2897 |
(if new_s = "*" then @{const_name Pair}
|
blanchet@33192
|
2898 |
else @{const_name PairBox}, new_Ts ---> new_T)
|
blanchet@33192
|
2899 |
[coerce_term Ts new_T1 old_T1 t1,
|
blanchet@33192
|
2900 |
coerce_term Ts new_T2 old_T2 t2]
|
blanchet@33224
|
2901 |
| t' => raise TERM ("Nitpick_HOL.box_fun_and_pair_in_term.\
|
blanchet@33192
|
2902 |
\coerce_term", [t'])
|
blanchet@33192
|
2903 |
else
|
blanchet@33192
|
2904 |
raise TYPE ("coerce_term", [new_T, old_T], [t])
|
blanchet@33192
|
2905 |
| _ => raise TYPE ("coerce_term", [new_T, old_T], [t])
|
blanchet@33192
|
2906 |
(* indexname * typ -> typ * term -> typ option list -> typ option list *)
|
blanchet@33192
|
2907 |
fun add_boxed_types_for_var (z as (_, T)) (T', t') =
|
blanchet@33192
|
2908 |
case t' of
|
blanchet@33192
|
2909 |
Var z' => z' = z ? insert (op =) T'
|
blanchet@33192
|
2910 |
| Const (@{const_name Pair}, _) $ t1 $ t2 =>
|
blanchet@33192
|
2911 |
(case T' of
|
blanchet@33192
|
2912 |
Type (_, [T1, T2]) =>
|
blanchet@33192
|
2913 |
fold (add_boxed_types_for_var z) [(T1, t1), (T2, t2)]
|
blanchet@33224
|
2914 |
| _ => raise TYPE ("Nitpick_HOL.box_fun_and_pair_in_term.\
|
blanchet@33192
|
2915 |
\add_boxed_types_for_var", [T'], []))
|
blanchet@34118
|
2916 |
| _ => exists_subterm (curry (op =) (Var z)) t' ? insert (op =) T
|
blanchet@33192
|
2917 |
(* typ list -> typ list -> term -> indexname * typ -> typ *)
|
blanchet@33192
|
2918 |
fun box_var_in_def new_Ts old_Ts t (z as (_, T)) =
|
blanchet@33192
|
2919 |
case t of
|
blanchet@33192
|
2920 |
@{const Trueprop} $ t1 => box_var_in_def new_Ts old_Ts t1 z
|
blanchet@33192
|
2921 |
| Const (s0, _) $ t1 $ _ =>
|
blanchet@34118
|
2922 |
if s0 = @{const_name "=="} orelse s0 = @{const_name "op ="} then
|
blanchet@33192
|
2923 |
let
|
blanchet@33192
|
2924 |
val (t', args) = strip_comb t1
|
blanchet@33192
|
2925 |
val T' = fastype_of1 (new_Ts, do_term new_Ts old_Ts Neut t')
|
blanchet@33192
|
2926 |
in
|
blanchet@33192
|
2927 |
case fold (add_boxed_types_for_var z)
|
blanchet@33192
|
2928 |
(fst (strip_n_binders (length args) T') ~~ args) [] of
|
blanchet@33192
|
2929 |
[T''] => T''
|
blanchet@33192
|
2930 |
| _ => T
|
blanchet@33192
|
2931 |
end
|
blanchet@33192
|
2932 |
else
|
blanchet@33192
|
2933 |
T
|
blanchet@33192
|
2934 |
| _ => T
|
blanchet@33192
|
2935 |
(* typ list -> typ list -> polarity -> string -> typ -> string -> typ
|
blanchet@33192
|
2936 |
-> term -> term *)
|
blanchet@33192
|
2937 |
and do_quantifier new_Ts old_Ts polar quant_s quant_T abs_s abs_T t =
|
blanchet@33192
|
2938 |
let
|
blanchet@33192
|
2939 |
val abs_T' =
|
blanchet@33192
|
2940 |
if polar = Neut orelse is_positive_existential polar quant_s then
|
blanchet@33192
|
2941 |
box_type ext_ctxt InFunLHS abs_T
|
blanchet@33192
|
2942 |
else
|
blanchet@33192
|
2943 |
abs_T
|
blanchet@33192
|
2944 |
val body_T = body_type quant_T
|
blanchet@33192
|
2945 |
in
|
blanchet@33192
|
2946 |
Const (quant_s, (abs_T' --> body_T) --> body_T)
|
blanchet@33192
|
2947 |
$ Abs (abs_s, abs_T',
|
blanchet@33192
|
2948 |
t |> do_term (abs_T' :: new_Ts) (abs_T :: old_Ts) polar)
|
blanchet@33192
|
2949 |
end
|
blanchet@33192
|
2950 |
(* typ list -> typ list -> string -> typ -> term -> term -> term *)
|
blanchet@33192
|
2951 |
and do_equals new_Ts old_Ts s0 T0 t1 t2 =
|
blanchet@33192
|
2952 |
let
|
blanchet@33192
|
2953 |
val (t1, t2) = pairself (do_term new_Ts old_Ts Neut) (t1, t2)
|
blanchet@33192
|
2954 |
val (T1, T2) = pairself (curry fastype_of1 new_Ts) (t1, t2)
|
blanchet@33192
|
2955 |
val T = [T1, T2] |> sort TermOrd.typ_ord |> List.last
|
blanchet@33192
|
2956 |
in
|
blanchet@34121
|
2957 |
list_comb (Const (s0, T --> T --> body_type T0),
|
blanchet@33192
|
2958 |
map2 (coerce_term new_Ts T) [T1, T2] [t1, t2])
|
blanchet@33192
|
2959 |
end
|
blanchet@33192
|
2960 |
(* string -> typ -> term *)
|
blanchet@33192
|
2961 |
and do_description_operator s T =
|
blanchet@33192
|
2962 |
let val T1 = box_type ext_ctxt InFunLHS (range_type T) in
|
blanchet@33192
|
2963 |
Const (s, (T1 --> bool_T) --> T1)
|
blanchet@33192
|
2964 |
end
|
blanchet@33192
|
2965 |
(* typ list -> typ list -> polarity -> term -> term *)
|
blanchet@33192
|
2966 |
and do_term new_Ts old_Ts polar t =
|
blanchet@33192
|
2967 |
case t of
|
blanchet@33192
|
2968 |
Const (s0 as @{const_name all}, T0) $ Abs (s1, T1, t1) =>
|
blanchet@33192
|
2969 |
do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
|
blanchet@33192
|
2970 |
| Const (s0 as @{const_name "=="}, T0) $ t1 $ t2 =>
|
blanchet@33192
|
2971 |
do_equals new_Ts old_Ts s0 T0 t1 t2
|
blanchet@33192
|
2972 |
| @{const "==>"} $ t1 $ t2 =>
|
blanchet@33192
|
2973 |
@{const "==>"} $ do_term new_Ts old_Ts (flip_polarity polar) t1
|
blanchet@33192
|
2974 |
$ do_term new_Ts old_Ts polar t2
|
blanchet@33192
|
2975 |
| @{const Pure.conjunction} $ t1 $ t2 =>
|
blanchet@33192
|
2976 |
@{const Pure.conjunction} $ do_term new_Ts old_Ts polar t1
|
blanchet@33192
|
2977 |
$ do_term new_Ts old_Ts polar t2
|
blanchet@33192
|
2978 |
| @{const Trueprop} $ t1 =>
|
blanchet@33192
|
2979 |
@{const Trueprop} $ do_term new_Ts old_Ts polar t1
|
blanchet@33192
|
2980 |
| @{const Not} $ t1 =>
|
blanchet@33192
|
2981 |
@{const Not} $ do_term new_Ts old_Ts (flip_polarity polar) t1
|
blanchet@33192
|
2982 |
| Const (s0 as @{const_name All}, T0) $ Abs (s1, T1, t1) =>
|
blanchet@33192
|
2983 |
do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
|
blanchet@33192
|
2984 |
| Const (s0 as @{const_name Ex}, T0) $ Abs (s1, T1, t1) =>
|
blanchet@33192
|
2985 |
do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
|
blanchet@33192
|
2986 |
| Const (s0 as @{const_name "op ="}, T0) $ t1 $ t2 =>
|
blanchet@33192
|
2987 |
do_equals new_Ts old_Ts s0 T0 t1 t2
|
blanchet@33192
|
2988 |
| @{const "op &"} $ t1 $ t2 =>
|
blanchet@33192
|
2989 |
@{const "op &"} $ do_term new_Ts old_Ts polar t1
|
blanchet@33192
|
2990 |
$ do_term new_Ts old_Ts polar t2
|
blanchet@33192
|
2991 |
| @{const "op |"} $ t1 $ t2 =>
|
blanchet@33192
|
2992 |
@{const "op |"} $ do_term new_Ts old_Ts polar t1
|
blanchet@33192
|
2993 |
$ do_term new_Ts old_Ts polar t2
|
blanchet@33192
|
2994 |
| @{const "op -->"} $ t1 $ t2 =>
|
blanchet@33192
|
2995 |
@{const "op -->"} $ do_term new_Ts old_Ts (flip_polarity polar) t1
|
blanchet@33192
|
2996 |
$ do_term new_Ts old_Ts polar t2
|
blanchet@33192
|
2997 |
| Const (s as @{const_name The}, T) => do_description_operator s T
|
blanchet@33192
|
2998 |
| Const (s as @{const_name Eps}, T) => do_description_operator s T
|
blanchet@34923
|
2999 |
| Const (@{const_name quot_normal}, Type ("fun", [_, T2])) =>
|
blanchet@34969
|
3000 |
let val T' = box_type ext_ctxt InSel T2 in
|
blanchet@34923
|
3001 |
Const (@{const_name quot_normal}, T' --> T')
|
blanchet@34923
|
3002 |
end
|
blanchet@33192
|
3003 |
| Const (s as @{const_name Tha}, T) => do_description_operator s T
|
blanchet@33192
|
3004 |
| Const (x as (s, T)) =>
|
blanchet@34923
|
3005 |
Const (s, if s = @{const_name converse} orelse
|
blanchet@34923
|
3006 |
s = @{const_name trancl} then
|
blanchet@33192
|
3007 |
box_relational_operator_type T
|
blanchet@34923
|
3008 |
else if is_built_in_const fast_descrs x orelse
|
blanchet@34923
|
3009 |
s = @{const_name Sigma} then
|
blanchet@33192
|
3010 |
T
|
blanchet@33192
|
3011 |
else if is_constr_like thy x then
|
blanchet@33192
|
3012 |
box_type ext_ctxt InConstr T
|
blanchet@34969
|
3013 |
else if is_sel s
|
blanchet@34969
|
3014 |
orelse is_rep_fun thy x then
|
blanchet@33192
|
3015 |
box_type ext_ctxt InSel T
|
blanchet@33192
|
3016 |
else
|
blanchet@33192
|
3017 |
box_type ext_ctxt InExpr T)
|
blanchet@33192
|
3018 |
| t1 $ Abs (s, T, t2') =>
|
blanchet@33192
|
3019 |
let
|
blanchet@33192
|
3020 |
val t1 = do_term new_Ts old_Ts Neut t1
|
blanchet@33192
|
3021 |
val T1 = fastype_of1 (new_Ts, t1)
|
blanchet@33192
|
3022 |
val (s1, Ts1) = dest_Type T1
|
blanchet@33192
|
3023 |
val T' = hd (snd (dest_Type (hd Ts1)))
|
blanchet@33192
|
3024 |
val t2 = Abs (s, T', do_term (T' :: new_Ts) (T :: old_Ts) Neut t2')
|
blanchet@33192
|
3025 |
val T2 = fastype_of1 (new_Ts, t2)
|
blanchet@33192
|
3026 |
val t2 = coerce_term new_Ts (hd Ts1) T2 t2
|
blanchet@33192
|
3027 |
in
|
blanchet@33192
|
3028 |
betapply (if s1 = "fun" then
|
blanchet@33192
|
3029 |
t1
|
blanchet@33192
|
3030 |
else
|
blanchet@33192
|
3031 |
select_nth_constr_arg thy
|
blanchet@33192
|
3032 |
(@{const_name FunBox}, Type ("fun", Ts1) --> T1) t1 0
|
blanchet@33192
|
3033 |
(Type ("fun", Ts1)), t2)
|
blanchet@33192
|
3034 |
end
|
blanchet@33192
|
3035 |
| t1 $ t2 =>
|
blanchet@33192
|
3036 |
let
|
blanchet@33192
|
3037 |
val t1 = do_term new_Ts old_Ts Neut t1
|
blanchet@33192
|
3038 |
val T1 = fastype_of1 (new_Ts, t1)
|
blanchet@33192
|
3039 |
val (s1, Ts1) = dest_Type T1
|
blanchet@33192
|
3040 |
val t2 = do_term new_Ts old_Ts Neut t2
|
blanchet@33192
|
3041 |
val T2 = fastype_of1 (new_Ts, t2)
|
blanchet@33192
|
3042 |
val t2 = coerce_term new_Ts (hd Ts1) T2 t2
|
blanchet@33192
|
3043 |
in
|
blanchet@33192
|
3044 |
betapply (if s1 = "fun" then
|
blanchet@33192
|
3045 |
t1
|
blanchet@33192
|
3046 |
else
|
blanchet@33192
|
3047 |
select_nth_constr_arg thy
|
blanchet@33192
|
3048 |
(@{const_name FunBox}, Type ("fun", Ts1) --> T1) t1 0
|
blanchet@33192
|
3049 |
(Type ("fun", Ts1)), t2)
|
blanchet@33192
|
3050 |
end
|
blanchet@33192
|
3051 |
| Free (s, T) => Free (s, box_type ext_ctxt InExpr T)
|
blanchet@33192
|
3052 |
| Var (z as (x, T)) =>
|
blanchet@33192
|
3053 |
Var (x, if def then box_var_in_def new_Ts old_Ts orig_t z
|
blanchet@33192
|
3054 |
else box_type ext_ctxt InExpr T)
|
blanchet@33192
|
3055 |
| Bound _ => t
|
blanchet@33192
|
3056 |
| Abs (s, T, t') =>
|
blanchet@33192
|
3057 |
Abs (s, T, do_term (T :: new_Ts) (T :: old_Ts) Neut t')
|
blanchet@33192
|
3058 |
in do_term [] [] Pos orig_t end
|
blanchet@33192
|
3059 |
|
blanchet@33192
|
3060 |
(* int -> term -> term *)
|
blanchet@33192
|
3061 |
fun eval_axiom_for_term j t =
|
blanchet@33192
|
3062 |
Logic.mk_equals (Const (eval_prefix ^ string_of_int j, fastype_of t), t)
|
blanchet@33192
|
3063 |
|
blanchet@33192
|
3064 |
(* extended_context -> styp -> bool *)
|
blanchet@33192
|
3065 |
fun is_equational_fun_surely_complete ext_ctxt x =
|
blanchet@33192
|
3066 |
case raw_equational_fun_axioms ext_ctxt x of
|
blanchet@33192
|
3067 |
[@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)] =>
|
blanchet@33192
|
3068 |
strip_comb t1 |> snd |> forall is_Var
|
blanchet@33192
|
3069 |
| _ => false
|
blanchet@33192
|
3070 |
|
blanchet@33192
|
3071 |
type special = int list * term list * styp
|
blanchet@33192
|
3072 |
|
blanchet@33192
|
3073 |
(* styp -> special -> special -> term *)
|
blanchet@33192
|
3074 |
fun special_congruence_axiom (s, T) (js1, ts1, x1) (js2, ts2, x2) =
|
blanchet@33192
|
3075 |
let
|
blanchet@33192
|
3076 |
val (bounds1, bounds2) = pairself (map Var o special_bounds) (ts1, ts2)
|
blanchet@33192
|
3077 |
val Ts = binder_types T
|
blanchet@33882
|
3078 |
val max_j = fold (fold Integer.max) [js1, js2] ~1
|
blanchet@33192
|
3079 |
val (eqs, (args1, args2)) =
|
blanchet@33192
|
3080 |
fold (fn j => case pairself (fn ps => AList.lookup (op =) ps j)
|
blanchet@33192
|
3081 |
(js1 ~~ ts1, js2 ~~ ts2) of
|
blanchet@33192
|
3082 |
(SOME t1, SOME t2) => apfst (cons (t1, t2))
|
blanchet@33192
|
3083 |
| (SOME t1, NONE) => apsnd (apsnd (cons t1))
|
blanchet@33192
|
3084 |
| (NONE, SOME t2) => apsnd (apfst (cons t2))
|
blanchet@33192
|
3085 |
| (NONE, NONE) =>
|
blanchet@33192
|
3086 |
let val v = Var ((cong_var_prefix ^ nat_subscript j, 0),
|
blanchet@33192
|
3087 |
nth Ts j) in
|
blanchet@33192
|
3088 |
apsnd (pairself (cons v))
|
blanchet@33192
|
3089 |
end) (max_j downto 0) ([], ([], []))
|
blanchet@33192
|
3090 |
in
|
blanchet@33192
|
3091 |
Logic.list_implies (eqs |> filter_out (op =) |> distinct (op =)
|
blanchet@33192
|
3092 |
|> map Logic.mk_equals,
|
blanchet@33192
|
3093 |
Logic.mk_equals (list_comb (Const x1, bounds1 @ args1),
|
blanchet@33192
|
3094 |
list_comb (Const x2, bounds2 @ args2)))
|
blanchet@34923
|
3095 |
|> Refute.close_form (* TODO: needed? *)
|
blanchet@33192
|
3096 |
end
|
blanchet@33192
|
3097 |
|
blanchet@33192
|
3098 |
(* extended_context -> styp list -> term list *)
|
blanchet@33192
|
3099 |
fun special_congruence_axioms (ext_ctxt as {special_funs, ...}) xs =
|
blanchet@33192
|
3100 |
let
|
blanchet@33192
|
3101 |
val groups =
|
blanchet@33192
|
3102 |
!special_funs
|
blanchet@33192
|
3103 |
|> map (fn ((x, js, ts), x') => (x, (js, ts, x')))
|
blanchet@33192
|
3104 |
|> AList.group (op =)
|
blanchet@33192
|
3105 |
|> filter_out (is_equational_fun_surely_complete ext_ctxt o fst)
|
blanchet@34118
|
3106 |
|> map (fn (x, zs) => (x, zs |> member (op =) xs x ? cons ([], [], x)))
|
blanchet@33192
|
3107 |
(* special -> int *)
|
blanchet@33192
|
3108 |
fun generality (js, _, _) = ~(length js)
|
blanchet@33192
|
3109 |
(* special -> special -> bool *)
|
blanchet@33192
|
3110 |
fun is_more_specific (j1, t1, x1) (j2, t2, x2) =
|
blanchet@33192
|
3111 |
x1 <> x2 andalso OrdList.subset (prod_ord int_ord TermOrd.term_ord)
|
blanchet@33192
|
3112 |
(j2 ~~ t2, j1 ~~ t1)
|
blanchet@33192
|
3113 |
(* styp -> special list -> special list -> special list -> term list
|
blanchet@33192
|
3114 |
-> term list *)
|
blanchet@33192
|
3115 |
fun do_pass_1 _ [] [_] [_] = I
|
blanchet@33192
|
3116 |
| do_pass_1 x skipped _ [] = do_pass_2 x skipped
|
blanchet@33192
|
3117 |
| do_pass_1 x skipped all (z :: zs) =
|
blanchet@33192
|
3118 |
case filter (is_more_specific z) all
|
blanchet@33192
|
3119 |
|> sort (int_ord o pairself generality) of
|
blanchet@33192
|
3120 |
[] => do_pass_1 x (z :: skipped) all zs
|
blanchet@33192
|
3121 |
| (z' :: _) => cons (special_congruence_axiom x z z')
|
blanchet@33192
|
3122 |
#> do_pass_1 x skipped all zs
|
blanchet@33192
|
3123 |
(* styp -> special list -> term list -> term list *)
|
blanchet@33192
|
3124 |
and do_pass_2 _ [] = I
|
blanchet@33192
|
3125 |
| do_pass_2 x (z :: zs) =
|
blanchet@33192
|
3126 |
fold (cons o special_congruence_axiom x z) zs #> do_pass_2 x zs
|
blanchet@33192
|
3127 |
in fold (fn (x, zs) => do_pass_1 x [] zs zs) groups [] end
|
blanchet@33192
|
3128 |
|
blanchet@33192
|
3129 |
(* term -> bool *)
|
blanchet@33192
|
3130 |
val is_trivial_equation = the_default false o try (op aconv o Logic.dest_equals)
|
blanchet@33192
|
3131 |
|
blanchet@33192
|
3132 |
(* 'a Symtab.table -> 'a list *)
|
blanchet@33192
|
3133 |
fun all_table_entries table = Symtab.fold (append o snd) table []
|
blanchet@33192
|
3134 |
(* const_table -> string -> const_table *)
|
blanchet@33192
|
3135 |
fun extra_table table s = Symtab.make [(s, all_table_entries table)]
|
blanchet@33192
|
3136 |
|
blanchet@33192
|
3137 |
(* extended_context -> term -> (term list * term list) * (bool * bool) *)
|
blanchet@33192
|
3138 |
fun axioms_for_term
|
blanchet@33192
|
3139 |
(ext_ctxt as {thy, max_bisim_depth, user_axioms, fast_descrs, evals,
|
blanchet@33192
|
3140 |
def_table, nondef_table, user_nondefs, ...}) t =
|
blanchet@33192
|
3141 |
let
|
blanchet@33192
|
3142 |
type accumulator = styp list * (term list * term list)
|
blanchet@33192
|
3143 |
(* (term list * term list -> term list)
|
blanchet@33192
|
3144 |
-> ((term list -> term list) -> term list * term list
|
blanchet@33192
|
3145 |
-> term list * term list)
|
blanchet@33192
|
3146 |
-> int -> term -> accumulator -> accumulator *)
|
blanchet@33192
|
3147 |
fun add_axiom get app depth t (accum as (xs, axs)) =
|
blanchet@33192
|
3148 |
let
|
blanchet@33192
|
3149 |
val t = t |> unfold_defs_in_term ext_ctxt
|
blanchet@33192
|
3150 |
|> skolemize_term_and_more ext_ctxt ~1
|
blanchet@33192
|
3151 |
in
|
blanchet@33192
|
3152 |
if is_trivial_equation t then
|
blanchet@33192
|
3153 |
accum
|
blanchet@33192
|
3154 |
else
|
blanchet@33192
|
3155 |
let val t' = t |> specialize_consts_in_term ext_ctxt depth in
|
blanchet@33192
|
3156 |
if exists (member (op aconv) (get axs)) [t, t'] then accum
|
blanchet@33192
|
3157 |
else add_axioms_for_term (depth + 1) t' (xs, app (cons t') axs)
|
blanchet@33192
|
3158 |
end
|
blanchet@33192
|
3159 |
end
|
blanchet@33192
|
3160 |
(* int -> term -> accumulator -> accumulator *)
|
blanchet@33864
|
3161 |
and add_def_axiom depth = add_axiom fst apfst depth
|
blanchet@33192
|
3162 |
and add_nondef_axiom depth = add_axiom snd apsnd depth
|
blanchet@33864
|
3163 |
and add_maybe_def_axiom depth t =
|
blanchet@33864
|
3164 |
(if head_of t <> @{const "==>"} then add_def_axiom
|
blanchet@33864
|
3165 |
else add_nondef_axiom) depth t
|
blanchet@33864
|
3166 |
and add_eq_axiom depth t =
|
blanchet@33864
|
3167 |
(if is_constr_pattern_formula thy t then add_def_axiom
|
blanchet@33864
|
3168 |
else add_nondef_axiom) depth t
|
blanchet@33192
|
3169 |
(* int -> term -> accumulator -> accumulator *)
|
blanchet@33192
|
3170 |
and add_axioms_for_term depth t (accum as (xs, axs)) =
|
blanchet@33192
|
3171 |
case t of
|
blanchet@33192
|
3172 |
t1 $ t2 => accum |> fold (add_axioms_for_term depth) [t1, t2]
|
blanchet@33192
|
3173 |
| Const (x as (s, T)) =>
|
blanchet@34118
|
3174 |
(if member (op =) xs x orelse is_built_in_const fast_descrs x then
|
blanchet@33192
|
3175 |
accum
|
blanchet@33192
|
3176 |
else
|
blanchet@33192
|
3177 |
let val accum as (xs, _) = (x :: xs, axs) in
|
blanchet@33192
|
3178 |
if depth > axioms_max_depth then
|
blanchet@34121
|
3179 |
raise TOO_LARGE ("Nitpick_HOL.axioms_for_term.\
|
blanchet@34121
|
3180 |
\add_axioms_for_term",
|
blanchet@34121
|
3181 |
"too many nested axioms (" ^
|
blanchet@34121
|
3182 |
string_of_int depth ^ ")")
|
blanchet@33192
|
3183 |
else if Refute.is_const_of_class thy x then
|
blanchet@33192
|
3184 |
let
|
blanchet@33192
|
3185 |
val class = Logic.class_of_const s
|
blanchet@33192
|
3186 |
val of_class = Logic.mk_of_class (TVar (("'a", 0), [class]),
|
blanchet@33192
|
3187 |
class)
|
blanchet@33192
|
3188 |
val ax1 = try (Refute.specialize_type thy x) of_class
|
blanchet@33192
|
3189 |
val ax2 = Option.map (Refute.specialize_type thy x o snd)
|
blanchet@33192
|
3190 |
(Refute.get_classdef thy class)
|
blanchet@33864
|
3191 |
in
|
blanchet@33864
|
3192 |
fold (add_maybe_def_axiom depth) (map_filter I [ax1, ax2])
|
blanchet@33864
|
3193 |
accum
|
blanchet@33864
|
3194 |
end
|
blanchet@33192
|
3195 |
else if is_constr thy x then
|
blanchet@33192
|
3196 |
accum
|
blanchet@33192
|
3197 |
else if is_equational_fun ext_ctxt x then
|
blanchet@33864
|
3198 |
fold (add_eq_axiom depth) (equational_fun_axioms ext_ctxt x)
|
blanchet@33192
|
3199 |
accum
|
blanchet@33192
|
3200 |
else if is_abs_fun thy x then
|
blanchet@34923
|
3201 |
if is_quot_type thy (range_type T) then
|
blanchet@34923
|
3202 |
raise NOT_SUPPORTED "\"Abs_\" function of quotient type"
|
blanchet@34923
|
3203 |
else
|
blanchet@34923
|
3204 |
accum |> fold (add_nondef_axiom depth)
|
blanchet@34923
|
3205 |
(nondef_props_for_const thy false nondef_table x)
|
blanchet@34923
|
3206 |
|> is_funky_typedef thy (range_type T)
|
blanchet@34923
|
3207 |
? fold (add_maybe_def_axiom depth)
|
blanchet@34923
|
3208 |
(nondef_props_for_const thy true
|
blanchet@33192
|
3209 |
(extra_table def_table s) x)
|
blanchet@33192
|
3210 |
else if is_rep_fun thy x then
|
blanchet@34923
|
3211 |
if is_quot_type thy (domain_type T) then
|
blanchet@34923
|
3212 |
raise NOT_SUPPORTED "\"Rep_\" function of quotient type"
|
blanchet@34923
|
3213 |
else
|
blanchet@34923
|
3214 |
accum |> fold (add_nondef_axiom depth)
|
blanchet@34923
|
3215 |
(nondef_props_for_const thy false nondef_table x)
|
blanchet@34923
|
3216 |
|> is_funky_typedef thy (range_type T)
|
blanchet@34923
|
3217 |
? fold (add_maybe_def_axiom depth)
|
blanchet@34923
|
3218 |
(nondef_props_for_const thy true
|
blanchet@33192
|
3219 |
(extra_table def_table s) x)
|
blanchet@34923
|
3220 |
|> add_axioms_for_term depth
|
blanchet@34923
|
3221 |
(Const (mate_of_rep_fun thy x))
|
blanchet@34923
|
3222 |
|> fold (add_def_axiom depth)
|
blanchet@34923
|
3223 |
(inverse_axioms_for_rep_fun thy x)
|
blanchet@33192
|
3224 |
else
|
blanchet@33192
|
3225 |
accum |> user_axioms <> SOME false
|
blanchet@33192
|
3226 |
? fold (add_nondef_axiom depth)
|
blanchet@33197
|
3227 |
(nondef_props_for_const thy false nondef_table x)
|
blanchet@33192
|
3228 |
end)
|
blanchet@33192
|
3229 |
|> add_axioms_for_type depth T
|
blanchet@33192
|
3230 |
| Free (_, T) => add_axioms_for_type depth T accum
|
blanchet@33192
|
3231 |
| Var (_, T) => add_axioms_for_type depth T accum
|
blanchet@33192
|
3232 |
| Bound _ => accum
|
blanchet@33192
|
3233 |
| Abs (_, T, t) => accum |> add_axioms_for_term depth t
|
blanchet@33192
|
3234 |
|> add_axioms_for_type depth T
|
blanchet@33192
|
3235 |
(* int -> typ -> accumulator -> accumulator *)
|
blanchet@33192
|
3236 |
and add_axioms_for_type depth T =
|
blanchet@33192
|
3237 |
case T of
|
blanchet@33192
|
3238 |
Type ("fun", Ts) => fold (add_axioms_for_type depth) Ts
|
blanchet@33192
|
3239 |
| Type ("*", Ts) => fold (add_axioms_for_type depth) Ts
|
blanchet@33192
|
3240 |
| @{typ prop} => I
|
blanchet@33192
|
3241 |
| @{typ bool} => I
|
blanchet@33192
|
3242 |
| @{typ unit} => I
|
blanchet@33192
|
3243 |
| TFree (_, S) => add_axioms_for_sort depth T S
|
blanchet@33192
|
3244 |
| TVar (_, S) => add_axioms_for_sort depth T S
|
blanchet@34923
|
3245 |
| Type (z as (s, Ts)) =>
|
blanchet@33192
|
3246 |
fold (add_axioms_for_type depth) Ts
|
blanchet@33192
|
3247 |
#> (if is_pure_typedef thy T then
|
blanchet@33864
|
3248 |
fold (add_maybe_def_axiom depth) (optimized_typedef_axioms thy z)
|
blanchet@34923
|
3249 |
else if is_quot_type thy T then
|
blanchet@34923
|
3250 |
fold (add_def_axiom depth) (optimized_quot_type_axioms thy z)
|
blanchet@33192
|
3251 |
else if max_bisim_depth >= 0 andalso is_codatatype thy T then
|
blanchet@33864
|
3252 |
fold (add_maybe_def_axiom depth)
|
blanchet@33864
|
3253 |
(codatatype_bisim_axioms ext_ctxt T)
|
blanchet@33192
|
3254 |
else
|
blanchet@33192
|
3255 |
I)
|
blanchet@33192
|
3256 |
(* int -> typ -> sort -> accumulator -> accumulator *)
|
blanchet@33192
|
3257 |
and add_axioms_for_sort depth T S =
|
blanchet@33192
|
3258 |
let
|
blanchet@33192
|
3259 |
val supers = Sign.complete_sort thy S
|
blanchet@33192
|
3260 |
val class_axioms =
|
blanchet@33192
|
3261 |
maps (fn class => map prop_of (AxClass.get_info thy class |> #axioms
|
blanchet@33192
|
3262 |
handle ERROR _ => [])) supers
|
blanchet@33192
|
3263 |
val monomorphic_class_axioms =
|
blanchet@33192
|
3264 |
map (fn t => case Term.add_tvars t [] of
|
blanchet@33192
|
3265 |
[] => t
|
blanchet@33192
|
3266 |
| [(x, S)] =>
|
blanchet@33192
|
3267 |
Refute.monomorphic_term (Vartab.make [(x, (S, T))]) t
|
blanchet@33224
|
3268 |
| _ => raise TERM ("Nitpick_HOL.axioms_for_term.\
|
blanchet@33192
|
3269 |
\add_axioms_for_sort", [t]))
|
blanchet@33192
|
3270 |
class_axioms
|
blanchet@33192
|
3271 |
in fold (add_nondef_axiom depth) monomorphic_class_axioms end
|
blanchet@33192
|
3272 |
val (mono_user_nondefs, poly_user_nondefs) =
|
blanchet@33192
|
3273 |
List.partition (null o Term.hidden_polymorphism) user_nondefs
|
blanchet@33192
|
3274 |
val eval_axioms = map2 eval_axiom_for_term (index_seq 0 (length evals))
|
blanchet@33192
|
3275 |
evals
|
blanchet@33192
|
3276 |
val (xs, (defs, nondefs)) =
|
blanchet@33192
|
3277 |
([], ([], [])) |> add_axioms_for_term 1 t
|
blanchet@33192
|
3278 |
|> fold_rev (add_def_axiom 1) eval_axioms
|
blanchet@33192
|
3279 |
|> user_axioms = SOME true
|
blanchet@33192
|
3280 |
? fold (add_nondef_axiom 1) mono_user_nondefs
|
blanchet@33192
|
3281 |
val defs = defs @ special_congruence_axioms ext_ctxt xs
|
blanchet@33192
|
3282 |
in
|
blanchet@33192
|
3283 |
((defs, nondefs), (user_axioms = SOME true orelse null mono_user_nondefs,
|
blanchet@33192
|
3284 |
null poly_user_nondefs))
|
blanchet@33192
|
3285 |
end
|
blanchet@33192
|
3286 |
|
blanchet@33192
|
3287 |
(* theory -> const_table -> styp -> int list *)
|
blanchet@33192
|
3288 |
fun const_format thy def_table (x as (s, T)) =
|
blanchet@33192
|
3289 |
if String.isPrefix unrolled_prefix s then
|
blanchet@33192
|
3290 |
const_format thy def_table (original_name s, range_type T)
|
blanchet@33192
|
3291 |
else if String.isPrefix skolem_prefix s then
|
blanchet@33192
|
3292 |
let
|
blanchet@33192
|
3293 |
val k = unprefix skolem_prefix s
|
blanchet@33192
|
3294 |
|> strip_first_name_sep |> fst |> space_explode "@"
|
blanchet@33192
|
3295 |
|> hd |> Int.fromString |> the
|
blanchet@33192
|
3296 |
in [k, num_binder_types T - k] end
|
blanchet@33192
|
3297 |
else if original_name s <> s then
|
blanchet@33192
|
3298 |
[num_binder_types T]
|
blanchet@33192
|
3299 |
else case def_of_const thy def_table x of
|
blanchet@33192
|
3300 |
SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
|
blanchet@33192
|
3301 |
let val k = length (strip_abs_vars t') in
|
blanchet@33192
|
3302 |
[k, num_binder_types T - k]
|
blanchet@33192
|
3303 |
end
|
blanchet@33192
|
3304 |
else
|
blanchet@33192
|
3305 |
[num_binder_types T]
|
blanchet@33192
|
3306 |
| NONE => [num_binder_types T]
|
blanchet@33192
|
3307 |
(* int list -> int list -> int list *)
|
blanchet@33192
|
3308 |
fun intersect_formats _ [] = []
|
blanchet@33192
|
3309 |
| intersect_formats [] _ = []
|
blanchet@33192
|
3310 |
| intersect_formats ks1 ks2 =
|
blanchet@33192
|
3311 |
let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
|
blanchet@33192
|
3312 |
intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
|
blanchet@33192
|
3313 |
(ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
|
blanchet@33192
|
3314 |
[Int.min (k1, k2)]
|
blanchet@33192
|
3315 |
end
|
blanchet@33192
|
3316 |
|
blanchet@33192
|
3317 |
(* theory -> const_table -> (term option * int list) list -> term -> int list *)
|
blanchet@33192
|
3318 |
fun lookup_format thy def_table formats t =
|
blanchet@33192
|
3319 |
case AList.lookup (fn (SOME x, SOME y) =>
|
blanchet@33192
|
3320 |
(term_match thy) (x, y) | _ => false)
|
blanchet@33192
|
3321 |
formats (SOME t) of
|
blanchet@33192
|
3322 |
SOME format => format
|
blanchet@33192
|
3323 |
| NONE => let val format = the (AList.lookup (op =) formats NONE) in
|
blanchet@33192
|
3324 |
case t of
|
blanchet@33192
|
3325 |
Const x => intersect_formats format
|
blanchet@33192
|
3326 |
(const_format thy def_table x)
|
blanchet@33192
|
3327 |
| _ => format
|
blanchet@33192
|
3328 |
end
|
blanchet@33192
|
3329 |
|
blanchet@33192
|
3330 |
(* int list -> int list -> typ -> typ *)
|
blanchet@33192
|
3331 |
fun format_type default_format format T =
|
blanchet@33192
|
3332 |
let
|
blanchet@34121
|
3333 |
val T = unbit_and_unbox_type T
|
blanchet@33192
|
3334 |
val format = format |> filter (curry (op <) 0)
|
blanchet@33192
|
3335 |
in
|
blanchet@34118
|
3336 |
if forall (curry (op =) 1) format then
|
blanchet@33192
|
3337 |
T
|
blanchet@33192
|
3338 |
else
|
blanchet@33192
|
3339 |
let
|
blanchet@33192
|
3340 |
val (binder_Ts, body_T) = strip_type T
|
blanchet@33192
|
3341 |
val batched =
|
blanchet@33192
|
3342 |
binder_Ts
|
blanchet@33192
|
3343 |
|> map (format_type default_format default_format)
|
blanchet@33192
|
3344 |
|> rev |> chunk_list_unevenly (rev format)
|
blanchet@33192
|
3345 |
|> map (HOLogic.mk_tupleT o rev)
|
blanchet@33192
|
3346 |
in List.foldl (op -->) body_T batched end
|
blanchet@33192
|
3347 |
end
|
blanchet@33192
|
3348 |
(* theory -> const_table -> (term option * int list) list -> term -> typ *)
|
blanchet@33192
|
3349 |
fun format_term_type thy def_table formats t =
|
blanchet@33192
|
3350 |
format_type (the (AList.lookup (op =) formats NONE))
|
blanchet@33192
|
3351 |
(lookup_format thy def_table formats t) (fastype_of t)
|
blanchet@33192
|
3352 |
|
blanchet@33192
|
3353 |
(* int list -> int -> int list -> int list *)
|
blanchet@33192
|
3354 |
fun repair_special_format js m format =
|
blanchet@33192
|
3355 |
m - 1 downto 0 |> chunk_list_unevenly (rev format)
|
blanchet@33192
|
3356 |
|> map (rev o filter_out (member (op =) js))
|
blanchet@33192
|
3357 |
|> filter_out null |> map length |> rev
|
blanchet@33192
|
3358 |
|
blanchet@33192
|
3359 |
(* extended_context -> string * string -> (term option * int list) list
|
blanchet@33192
|
3360 |
-> styp -> term * typ *)
|
blanchet@33192
|
3361 |
fun user_friendly_const ({thy, evals, def_table, skolems, special_funs, ...}
|
blanchet@33192
|
3362 |
: extended_context) (base_name, step_name) formats =
|
blanchet@33192
|
3363 |
let
|
blanchet@33192
|
3364 |
val default_format = the (AList.lookup (op =) formats NONE)
|
blanchet@33192
|
3365 |
(* styp -> term * typ *)
|
blanchet@33192
|
3366 |
fun do_const (x as (s, T)) =
|
blanchet@33192
|
3367 |
(if String.isPrefix special_prefix s then
|
blanchet@33192
|
3368 |
let
|
blanchet@33192
|
3369 |
(* term -> term *)
|
blanchet@33192
|
3370 |
val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
|
blanchet@33192
|
3371 |
val (x' as (_, T'), js, ts) =
|
blanchet@34121
|
3372 |
AList.find (op =) (!special_funs) (s, unbit_and_unbox_type T)
|
blanchet@34121
|
3373 |
|> the_single
|
blanchet@33192
|
3374 |
val max_j = List.last js
|
blanchet@33192
|
3375 |
val Ts = List.take (binder_types T', max_j + 1)
|
blanchet@33192
|
3376 |
val missing_js = filter_out (member (op =) js) (0 upto max_j)
|
blanchet@33192
|
3377 |
val missing_Ts = filter_indices missing_js Ts
|
blanchet@33192
|
3378 |
(* int -> indexname *)
|
blanchet@33192
|
3379 |
fun nth_missing_var n =
|
blanchet@33192
|
3380 |
((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
|
blanchet@33192
|
3381 |
val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
|
blanchet@33192
|
3382 |
val vars = special_bounds ts @ missing_vars
|
blanchet@33192
|
3383 |
val ts' = map2 (fn T => fn j =>
|
blanchet@33192
|
3384 |
case AList.lookup (op =) (js ~~ ts) j of
|
blanchet@33192
|
3385 |
SOME t => do_term t
|
blanchet@33192
|
3386 |
| NONE =>
|
blanchet@33192
|
3387 |
Var (nth missing_vars
|
blanchet@34118
|
3388 |
(find_index (curry (op =) j)
|
blanchet@34118
|
3389 |
missing_js)))
|
blanchet@33192
|
3390 |
Ts (0 upto max_j)
|
blanchet@33192
|
3391 |
val t = do_const x' |> fst
|
blanchet@33192
|
3392 |
val format =
|
blanchet@33192
|
3393 |
case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
|
blanchet@33192
|
3394 |
| _ => false) formats (SOME t) of
|
blanchet@33192
|
3395 |
SOME format =>
|
blanchet@33192
|
3396 |
repair_special_format js (num_binder_types T') format
|
blanchet@33192
|
3397 |
| NONE =>
|
blanchet@33192
|
3398 |
const_format thy def_table x'
|
blanchet@33192
|
3399 |
|> repair_special_format js (num_binder_types T')
|
blanchet@33192
|
3400 |
|> intersect_formats default_format
|
blanchet@33192
|
3401 |
in
|
blanchet@33192
|
3402 |
(list_comb (t, ts') |> fold_rev abs_var vars,
|
blanchet@33192
|
3403 |
format_type default_format format T)
|
blanchet@33192
|
3404 |
end
|
blanchet@33192
|
3405 |
else if String.isPrefix uncurry_prefix s then
|
blanchet@33192
|
3406 |
let
|
blanchet@33192
|
3407 |
val (ss, s') = unprefix uncurry_prefix s
|
blanchet@33192
|
3408 |
|> strip_first_name_sep |>> space_explode "@"
|
blanchet@33192
|
3409 |
in
|
blanchet@33192
|
3410 |
if String.isPrefix step_prefix s' then
|
blanchet@33192
|
3411 |
do_const (s', T)
|
blanchet@33192
|
3412 |
else
|
blanchet@33192
|
3413 |
let
|
blanchet@33192
|
3414 |
val k = the (Int.fromString (hd ss))
|
blanchet@33192
|
3415 |
val j = the (Int.fromString (List.last ss))
|
blanchet@33192
|
3416 |
val (before_Ts, (tuple_T, rest_T)) =
|
blanchet@33192
|
3417 |
strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
|
blanchet@33192
|
3418 |
val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
|
blanchet@33192
|
3419 |
in do_const (s', T') end
|
blanchet@33192
|
3420 |
end
|
blanchet@33192
|
3421 |
else if String.isPrefix unrolled_prefix s then
|
blanchet@33192
|
3422 |
let val t = Const (original_name s, range_type T) in
|
blanchet@33192
|
3423 |
(lambda (Free (iter_var_prefix, nat_T)) t,
|
blanchet@33192
|
3424 |
format_type default_format
|
blanchet@33192
|
3425 |
(lookup_format thy def_table formats t) T)
|
blanchet@33192
|
3426 |
end
|
blanchet@33192
|
3427 |
else if String.isPrefix base_prefix s then
|
blanchet@33192
|
3428 |
(Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
|
blanchet@33192
|
3429 |
format_type default_format default_format T)
|
blanchet@33192
|
3430 |
else if String.isPrefix step_prefix s then
|
blanchet@33192
|
3431 |
(Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
|
blanchet@33192
|
3432 |
format_type default_format default_format T)
|
blanchet@33192
|
3433 |
else if String.isPrefix skolem_prefix s then
|
blanchet@33192
|
3434 |
let
|
blanchet@33192
|
3435 |
val ss = the (AList.lookup (op =) (!skolems) s)
|
blanchet@33192
|
3436 |
val (Ts, Ts') = chop (length ss) (binder_types T)
|
blanchet@33192
|
3437 |
val frees = map Free (ss ~~ Ts)
|
blanchet@33192
|
3438 |
val s' = original_name s
|
blanchet@33192
|
3439 |
in
|
blanchet@33192
|
3440 |
(fold lambda frees (Const (s', Ts' ---> T)),
|
blanchet@33192
|
3441 |
format_type default_format
|
blanchet@33192
|
3442 |
(lookup_format thy def_table formats (Const x)) T)
|
blanchet@33192
|
3443 |
end
|
blanchet@33192
|
3444 |
else if String.isPrefix eval_prefix s then
|
blanchet@33192
|
3445 |
let
|
blanchet@33192
|
3446 |
val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
|
blanchet@33192
|
3447 |
in (t, format_term_type thy def_table formats t) end
|
blanchet@33192
|
3448 |
else if s = @{const_name undefined_fast_The} then
|
blanchet@33192
|
3449 |
(Const (nitpick_prefix ^ "The fallback", T),
|
blanchet@33192
|
3450 |
format_type default_format
|
blanchet@33192
|
3451 |
(lookup_format thy def_table formats
|
blanchet@33192
|
3452 |
(Const (@{const_name The}, (T --> bool_T) --> T))) T)
|
blanchet@33192
|
3453 |
else if s = @{const_name undefined_fast_Eps} then
|
blanchet@33192
|
3454 |
(Const (nitpick_prefix ^ "Eps fallback", T),
|
blanchet@33192
|
3455 |
format_type default_format
|
blanchet@33192
|
3456 |
(lookup_format thy def_table formats
|
blanchet@33192
|
3457 |
(Const (@{const_name Eps}, (T --> bool_T) --> T))) T)
|
blanchet@33192
|
3458 |
else
|
blanchet@33192
|
3459 |
let val t = Const (original_name s, T) in
|
blanchet@33192
|
3460 |
(t, format_term_type thy def_table formats t)
|
blanchet@33192
|
3461 |
end)
|
blanchet@34121
|
3462 |
|>> map_types unbit_and_unbox_type
|
blanchet@34118
|
3463 |
|>> shorten_names_in_term |>> shorten_abs_vars
|
blanchet@33192
|
3464 |
in do_const end
|
blanchet@33192
|
3465 |
|
blanchet@33192
|
3466 |
(* styp -> string *)
|
blanchet@33192
|
3467 |
fun assign_operator_for_const (s, T) =
|
blanchet@33192
|
3468 |
if String.isPrefix ubfp_prefix s then
|
blanchet@33192
|
3469 |
if is_fun_type T then "\<subseteq>" else "\<le>"
|
blanchet@33192
|
3470 |
else if String.isPrefix lbfp_prefix s then
|
blanchet@33192
|
3471 |
if is_fun_type T then "\<supseteq>" else "\<ge>"
|
blanchet@33192
|
3472 |
else if original_name s <> s then
|
blanchet@33192
|
3473 |
assign_operator_for_const (after_name_sep s, T)
|
blanchet@33192
|
3474 |
else
|
blanchet@33192
|
3475 |
"="
|
blanchet@33192
|
3476 |
|
blanchet@34121
|
3477 |
val binary_int_threshold = 4
|
blanchet@34121
|
3478 |
|
blanchet@34121
|
3479 |
(* term -> bool *)
|
blanchet@34121
|
3480 |
fun may_use_binary_ints (t1 $ t2) =
|
blanchet@34121
|
3481 |
may_use_binary_ints t1 andalso may_use_binary_ints t2
|
blanchet@34123
|
3482 |
| may_use_binary_ints (t as Const (s, _)) =
|
blanchet@34123
|
3483 |
t <> @{const Suc} andalso
|
blanchet@34121
|
3484 |
not (member (op =) [@{const_name Abs_Frac}, @{const_name Rep_Frac},
|
blanchet@34123
|
3485 |
@{const_name nat_gcd}, @{const_name nat_lcm},
|
blanchet@34123
|
3486 |
@{const_name Frac}, @{const_name norm_frac}] s)
|
blanchet@34121
|
3487 |
| may_use_binary_ints (Abs (_, _, t')) = may_use_binary_ints t'
|
blanchet@34121
|
3488 |
| may_use_binary_ints _ = true
|
blanchet@34121
|
3489 |
fun should_use_binary_ints (t1 $ t2) =
|
blanchet@34121
|
3490 |
should_use_binary_ints t1 orelse should_use_binary_ints t2
|
blanchet@34121
|
3491 |
| should_use_binary_ints (Const (s, _)) =
|
blanchet@34121
|
3492 |
member (op =) [@{const_name times_nat_inst.times_nat},
|
blanchet@34121
|
3493 |
@{const_name div_nat_inst.div_nat},
|
blanchet@34121
|
3494 |
@{const_name times_int_inst.times_int},
|
blanchet@34923
|
3495 |
@{const_name div_int_inst.div_int}] s orelse
|
blanchet@34923
|
3496 |
(String.isPrefix numeral_prefix s andalso
|
blanchet@34923
|
3497 |
let val n = the (Int.fromString (unprefix numeral_prefix s)) in
|
blanchet@34923
|
3498 |
n <= ~ binary_int_threshold orelse n >= binary_int_threshold
|
blanchet@34923
|
3499 |
end)
|
blanchet@34121
|
3500 |
| should_use_binary_ints (Abs (_, _, t')) = should_use_binary_ints t'
|
blanchet@34121
|
3501 |
| should_use_binary_ints _ = false
|
blanchet@34121
|
3502 |
|
blanchet@34121
|
3503 |
(* typ -> typ *)
|
blanchet@34121
|
3504 |
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
|
blanchet@34121
|
3505 |
| binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
|
blanchet@34121
|
3506 |
| binarize_nat_and_int_in_type (Type (s, Ts)) =
|
blanchet@34121
|
3507 |
Type (s, map binarize_nat_and_int_in_type Ts)
|
blanchet@34121
|
3508 |
| binarize_nat_and_int_in_type T = T
|
blanchet@34121
|
3509 |
(* term -> term *)
|
blanchet@34121
|
3510 |
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
|
blanchet@34121
|
3511 |
|
blanchet@33192
|
3512 |
(* extended_context -> term
|
blanchet@33192
|
3513 |
-> ((term list * term list) * (bool * bool)) * term *)
|
blanchet@34121
|
3514 |
fun preprocess_term (ext_ctxt as {thy, binary_ints, destroy_constrs, boxes,
|
blanchet@34121
|
3515 |
skolemize, uncurry, ...}) t =
|
blanchet@33192
|
3516 |
let
|
blanchet@33192
|
3517 |
val skolem_depth = if skolemize then 4 else ~1
|
blanchet@33192
|
3518 |
val (((def_ts, nondef_ts), (got_all_mono_user_axioms, no_poly_user_axioms)),
|
blanchet@33192
|
3519 |
core_t) = t |> unfold_defs_in_term ext_ctxt
|
blanchet@33192
|
3520 |
|> Refute.close_form
|
blanchet@33192
|
3521 |
|> skolemize_term_and_more ext_ctxt skolem_depth
|
blanchet@33192
|
3522 |
|> specialize_consts_in_term ext_ctxt 0
|
blanchet@33192
|
3523 |
|> `(axioms_for_term ext_ctxt)
|
blanchet@34121
|
3524 |
val binarize =
|
blanchet@34121
|
3525 |
case binary_ints of
|
blanchet@34121
|
3526 |
SOME false => false
|
blanchet@34121
|
3527 |
| _ =>
|
blanchet@34121
|
3528 |
forall may_use_binary_ints (core_t :: def_ts @ nondef_ts) andalso
|
blanchet@34923
|
3529 |
(binary_ints = SOME true orelse
|
blanchet@34923
|
3530 |
exists should_use_binary_ints (core_t :: def_ts @ nondef_ts))
|
blanchet@34121
|
3531 |
val box = exists (not_equal (SOME false) o snd) boxes
|
blanchet@33192
|
3532 |
val table =
|
blanchet@33192
|
3533 |
Termtab.empty |> uncurry
|
blanchet@33192
|
3534 |
? fold (add_to_uncurry_table thy) (core_t :: def_ts @ nondef_ts)
|
blanchet@33192
|
3535 |
(* bool -> bool -> term -> term *)
|
blanchet@33192
|
3536 |
fun do_rest def core =
|
blanchet@34121
|
3537 |
binarize ? binarize_nat_and_int_in_term
|
blanchet@34121
|
3538 |
#> uncurry ? uncurry_term table
|
blanchet@34121
|
3539 |
#> box ? box_fun_and_pair_in_term ext_ctxt def
|
blanchet@33192
|
3540 |
#> destroy_constrs ? (pull_out_universal_constrs thy def
|
blanchet@33192
|
3541 |
#> pull_out_existential_constrs thy
|
blanchet@33571
|
3542 |
#> destroy_pulled_out_constrs ext_ctxt def)
|
blanchet@33192
|
3543 |
#> curry_assms
|
blanchet@33192
|
3544 |
#> destroy_universal_equalities
|
blanchet@33192
|
3545 |
#> destroy_existential_equalities thy
|
blanchet@33192
|
3546 |
#> simplify_constrs_and_sels thy
|
blanchet@33192
|
3547 |
#> distribute_quantifiers
|
blanchet@33192
|
3548 |
#> push_quantifiers_inward thy
|
blanchet@33192
|
3549 |
#> not core ? Refute.close_form
|
blanchet@33192
|
3550 |
#> shorten_abs_vars
|
blanchet@33192
|
3551 |
in
|
blanchet@33192
|
3552 |
(((map (do_rest true false) def_ts, map (do_rest false false) nondef_ts),
|
blanchet@33192
|
3553 |
(got_all_mono_user_axioms, no_poly_user_axioms)),
|
blanchet@33192
|
3554 |
do_rest false true core_t)
|
blanchet@33192
|
3555 |
end
|
blanchet@33192
|
3556 |
|
blanchet@33192
|
3557 |
end;
|