diff --git a/src/HOL/Tools/Nitpick/nitpick_hol.ML b/src/HOL/Tools/Nitpick/nitpick_hol.ML --- a/src/HOL/Tools/Nitpick/nitpick_hol.ML +++ b/src/HOL/Tools/Nitpick/nitpick_hol.ML @@ -1,2428 +1,2429 @@ (* Title: HOL/Tools/Nitpick/nitpick_hol.ML Author: Jasmin Blanchette, TU Muenchen Copyright 2008, 2009, 2010 Auxiliary HOL-related functions used by Nitpick. *) signature NITPICK_HOL = sig type const_table = term list Symtab.table type special_fun = ((string * typ) * int list * term list) * (string * typ) type unrolled = (string * typ) * (string * typ) type wf_cache = ((string * typ) * (bool * bool)) list type hol_context = {thy: theory, ctxt: Proof.context, max_bisim_depth: int, boxes: (typ option * bool option) list, wfs: ((string * typ) option * bool option) list, user_axioms: bool option, debug: bool, whacks: term list, binary_ints: bool option, destroy_constrs: bool, specialize: bool, star_linear_preds: bool, total_consts: bool option, needs: term list option, tac_timeout: Time.time, evals: term list, case_names: (string * int) list, def_tables: const_table * const_table, nondef_table: const_table, nondefs: term list, simp_table: const_table Unsynchronized.ref, psimp_table: const_table, choice_spec_table: const_table, intro_table: const_table, ground_thm_table: term list Inttab.table, ersatz_table: (string * string) list, skolems: (string * string list) list Unsynchronized.ref, special_funs: special_fun list Unsynchronized.ref, unrolled_preds: unrolled list Unsynchronized.ref, wf_cache: wf_cache Unsynchronized.ref, constr_cache: (typ * (string * typ) list) list Unsynchronized.ref} datatype fixpoint_kind = Lfp | Gfp | NoFp datatype boxability = InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2 val name_sep : string val numeral_prefix : string val base_prefix : string val step_prefix : string val unrolled_prefix : string val ubfp_prefix : string val lbfp_prefix : string val quot_normal_prefix : string val skolem_prefix : string val special_prefix : string val uncurry_prefix : string val eval_prefix : string val iter_var_prefix : string val strip_first_name_sep : string -> string * string val original_name : string -> string val abs_var : indexname * typ -> term -> term val s_conj : term * term -> term val s_disj : term * term -> term val strip_any_connective : term -> term list * term val conjuncts_of : term -> term list val disjuncts_of : term -> term list val unarize_unbox_etc_type : typ -> typ val uniterize_unarize_unbox_etc_type : typ -> typ val string_for_type : Proof.context -> typ -> string val pretty_for_type : Proof.context -> typ -> Pretty.T val prefix_name : string -> string -> string val shortest_name : string -> string val short_name : string -> string val shorten_names_in_term : term -> term val strict_type_match : theory -> typ * typ -> bool val type_match : theory -> typ * typ -> bool val const_match : theory -> (string * typ) * (string * typ) -> bool val term_match : theory -> term * term -> bool val frac_from_term_pair : typ -> term -> term -> term val is_fun_type : typ -> bool val is_set_type : typ -> bool val is_fun_or_set_type : typ -> bool val is_set_like_type : typ -> bool val is_pair_type : typ -> bool val is_lfp_iterator_type : typ -> bool val is_gfp_iterator_type : typ -> bool val is_fp_iterator_type : typ -> bool val is_iterator_type : typ -> bool val is_boolean_type : typ -> bool val is_integer_type : typ -> bool val is_bit_type : typ -> bool val is_word_type : typ -> bool val is_integer_like_type : typ -> bool val is_number_type : Proof.context -> typ -> bool val is_higher_order_type : typ -> bool val elem_type : typ -> typ val pseudo_domain_type : typ -> typ val pseudo_range_type : typ -> typ val const_for_iterator_type : typ -> string * typ val strip_n_binders : int -> typ -> typ list * typ val nth_range_type : int -> typ -> typ val num_factors_in_type : typ -> int val curried_binder_types : typ -> typ list val mk_flat_tuple : typ -> term list -> term val dest_n_tuple : int -> term -> term list val is_codatatype : Proof.context -> typ -> bool val is_quot_type : Proof.context -> typ -> bool val is_pure_typedef : Proof.context -> typ -> bool val is_univ_typedef : Proof.context -> typ -> bool val is_data_type : Proof.context -> typ -> bool val is_record_get : theory -> string * typ -> bool val is_record_update : theory -> string * typ -> bool val is_abs_fun : Proof.context -> string * typ -> bool val is_rep_fun : Proof.context -> string * typ -> bool val is_quot_abs_fun : Proof.context -> string * typ -> bool val is_quot_rep_fun : Proof.context -> string * typ -> bool val mate_of_rep_fun : Proof.context -> string * typ -> string * typ val is_nonfree_constr : Proof.context -> string * typ -> bool val is_free_constr : Proof.context -> string * typ -> bool val is_constr : Proof.context -> string * typ -> bool val is_sel : string -> bool val is_sel_like_and_no_discr : string -> bool val box_type : hol_context -> boxability -> typ -> typ val binarize_nat_and_int_in_type : typ -> typ val binarize_nat_and_int_in_term : term -> term val discr_for_constr : string * typ -> string * typ val num_sels_for_constr_type : typ -> int val nth_sel_name_for_constr_name : string -> int -> string val nth_sel_for_constr : string * typ -> int -> string * typ val binarized_and_boxed_nth_sel_for_constr : hol_context -> bool -> string * typ -> int -> string * typ val sel_no_from_name : string -> int val close_form : term -> term val distinctness_formula : typ -> term list -> term val register_frac_type : string -> (string * string) list -> morphism -> Context.generic -> Context.generic val register_frac_type_global : string -> (string * string) list -> theory -> theory val unregister_frac_type : string -> morphism -> Context.generic -> Context.generic val unregister_frac_type_global : string -> theory -> theory val register_ersatz : (string * string) list -> morphism -> Context.generic -> Context.generic val register_ersatz_global : (string * string) list -> theory -> theory val register_codatatype : typ -> string -> (string * typ) list -> morphism -> Context.generic -> Context.generic val register_codatatype_global : typ -> string -> (string * typ) list -> theory -> theory val unregister_codatatype : typ -> morphism -> Context.generic -> Context.generic val unregister_codatatype_global : typ -> theory -> theory val binarized_and_boxed_data_type_constrs : hol_context -> bool -> typ -> (string * typ) list val constr_name_for_sel_like : string -> string val binarized_and_boxed_constr_for_sel : hol_context -> bool -> string * typ -> string * typ val card_of_type : (typ * int) list -> typ -> int val bounded_card_of_type : int -> int -> (typ * int) list -> typ -> int val bounded_exact_card_of_type : hol_context -> typ list -> int -> int -> (typ * int) list -> typ -> int val typical_card_of_type : typ -> int val is_finite_type : hol_context -> typ -> bool val is_special_eligible_arg : bool -> typ list -> term -> bool val s_let : typ list -> string -> int -> typ -> typ -> (term -> term) -> term -> term val s_betapply : typ list -> term * term -> term val s_betapplys : typ list -> term * term list -> term val discriminate_value : hol_context -> string * typ -> term -> term val select_nth_constr_arg : Proof.context -> string * typ -> term -> int -> typ -> term val construct_value : Proof.context -> string * typ -> term list -> term val coerce_term : hol_context -> typ list -> typ -> typ -> term -> term val special_bounds : term list -> (indexname * typ) list val is_funky_typedef : Proof.context -> typ -> bool val all_defs_of : theory -> (term * term) list -> term list val all_nondefs_of : Proof.context -> (term * term) list -> term list val arity_of_built_in_const : string * typ -> int option val is_built_in_const : string * typ -> bool val term_under_def : term -> term val case_const_names : Proof.context -> (string * int) list val unfold_defs_in_term : hol_context -> term -> term val const_def_tables : Proof.context -> (term * term) list -> term list -> const_table * const_table val const_nondef_table : term list -> const_table val const_simp_table : Proof.context -> (term * term) list -> const_table val const_psimp_table : Proof.context -> (term * term) list -> const_table val const_choice_spec_table : Proof.context -> (term * term) list -> const_table val inductive_intro_table : Proof.context -> (term * term) list -> const_table * const_table -> const_table val ground_theorem_table : theory -> term list Inttab.table val ersatz_table : Proof.context -> (string * string) list val add_simps : const_table Unsynchronized.ref -> string -> term list -> unit val inverse_axioms_for_rep_fun : Proof.context -> string * typ -> term list val optimized_typedef_axioms : Proof.context -> string * typ list -> term list val optimized_quot_type_axioms : Proof.context -> string * typ list -> term list val def_of_const : theory -> const_table * const_table -> string * typ -> term option val fixpoint_kind_of_rhs : term -> fixpoint_kind val fixpoint_kind_of_const : theory -> const_table * const_table -> string * typ -> fixpoint_kind val is_raw_inductive_pred : hol_context -> string * typ -> bool val is_constr_pattern : Proof.context -> term -> bool val is_constr_pattern_lhs : Proof.context -> term -> bool val is_constr_pattern_formula : Proof.context -> term -> bool val nondef_props_for_const : theory -> bool -> const_table -> string * typ -> term list val is_choice_spec_fun : hol_context -> string * typ -> bool val is_choice_spec_axiom : Proof.context -> const_table -> term -> bool val is_raw_equational_fun : hol_context -> string * typ -> bool val is_equational_fun : hol_context -> string * typ -> bool val codatatype_bisim_axioms : hol_context -> typ -> term list val is_well_founded_inductive_pred : hol_context -> string * typ -> bool val unrolled_inductive_pred_const : hol_context -> bool -> string * typ -> term val equational_fun_axioms : hol_context -> string * typ -> term list val is_equational_fun_surely_complete : hol_context -> string * typ -> bool val merged_type_var_table_for_terms : theory -> term list -> (sort * string) list val merge_type_vars_in_term : theory -> bool -> (sort * string) list -> term -> term val ground_types_in_type : hol_context -> bool -> typ -> typ list val ground_types_in_terms : hol_context -> bool -> term list -> typ list end; structure Nitpick_HOL : NITPICK_HOL = struct open Nitpick_Util type const_table = term list Symtab.table type special_fun = ((string * typ) * int list * term list) * (string * typ) type unrolled = (string * typ) * (string * typ) type wf_cache = ((string * typ) * (bool * bool)) list type hol_context = {thy: theory, ctxt: Proof.context, max_bisim_depth: int, boxes: (typ option * bool option) list, wfs: ((string * typ) option * bool option) list, user_axioms: bool option, debug: bool, whacks: term list, binary_ints: bool option, destroy_constrs: bool, specialize: bool, star_linear_preds: bool, total_consts: bool option, needs: term list option, tac_timeout: Time.time, evals: term list, case_names: (string * int) list, def_tables: const_table * const_table, nondef_table: const_table, nondefs: term list, simp_table: const_table Unsynchronized.ref, psimp_table: const_table, choice_spec_table: const_table, intro_table: const_table, ground_thm_table: term list Inttab.table, ersatz_table: (string * string) list, skolems: (string * string list) list Unsynchronized.ref, special_funs: special_fun list Unsynchronized.ref, unrolled_preds: unrolled list Unsynchronized.ref, wf_cache: wf_cache Unsynchronized.ref, constr_cache: (typ * (string * typ) list) list Unsynchronized.ref} datatype fixpoint_kind = Lfp | Gfp | NoFp datatype boxability = InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2 (* FIXME: Get rid of 'codatatypes' and related functionality *) structure Data = Generic_Data ( type T = {frac_types: (string * (string * string) list) list, ersatz_table: (string * string) list, codatatypes: (string * (string * (string * typ) list)) list} val empty = {frac_types = [], ersatz_table = [], codatatypes = []} val extend = I fun merge ({frac_types = fs1, ersatz_table = et1, codatatypes = cs1}, {frac_types = fs2, ersatz_table = et2, codatatypes = cs2}) : T = {frac_types = AList.merge (op =) (K true) (fs1, fs2), ersatz_table = AList.merge (op =) (K true) (et1, et2), codatatypes = AList.merge (op =) (K true) (cs1, cs2)} ) val name_sep = "$" val numeral_prefix = nitpick_prefix ^ "num" ^ name_sep val sel_prefix = nitpick_prefix ^ "sel" val discr_prefix = nitpick_prefix ^ "is" ^ name_sep val lfp_iterator_prefix = nitpick_prefix ^ "lfpit" ^ name_sep val gfp_iterator_prefix = nitpick_prefix ^ "gfpit" ^ name_sep val unrolled_prefix = nitpick_prefix ^ "unroll" ^ name_sep val base_prefix = nitpick_prefix ^ "base" ^ name_sep val step_prefix = nitpick_prefix ^ "step" ^ name_sep val ubfp_prefix = nitpick_prefix ^ "ubfp" ^ name_sep val lbfp_prefix = nitpick_prefix ^ "lbfp" ^ name_sep val quot_normal_prefix = nitpick_prefix ^ "qn" ^ name_sep val skolem_prefix = nitpick_prefix ^ "sk" val special_prefix = nitpick_prefix ^ "sp" val uncurry_prefix = nitpick_prefix ^ "unc" val eval_prefix = nitpick_prefix ^ "eval" val iter_var_prefix = "i" (** Constant/type information and term/type manipulation **) fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep fun quot_normal_name_for_type ctxt T = quot_normal_prefix ^ YXML.content_of (Syntax.string_of_typ ctxt T) val strip_first_name_sep = Substring.full #> Substring.position name_sep ##> Substring.triml 1 #> apply2 Substring.string fun original_name s = if String.isPrefix nitpick_prefix s then case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2 else s fun s_conj (t1, \<^const>\True\) = t1 | s_conj (\<^const>\True\, t2) = t2 | s_conj (t1, t2) = if t1 = \<^const>\False\ orelse t2 = \<^const>\False\ then \<^const>\False\ else HOLogic.mk_conj (t1, t2) fun s_disj (t1, \<^const>\False\) = t1 | s_disj (\<^const>\False\, t2) = t2 | s_disj (t1, t2) = if t1 = \<^const>\True\ orelse t2 = \<^const>\True\ then \<^const>\True\ else HOLogic.mk_disj (t1, t2) fun strip_connective conn_t (t as (t0 $ t1 $ t2)) = if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t] | strip_connective _ t = [t] fun strip_any_connective (t as (t0 $ _ $ _)) = if t0 = \<^const>\HOL.conj\ orelse t0 = \<^const>\HOL.disj\ then (strip_connective t0 t, t0) else ([t], \<^const>\Not\) | strip_any_connective t = ([t], \<^const>\Not\) val conjuncts_of = strip_connective \<^const>\HOL.conj\ val disjuncts_of = strip_connective \<^const>\HOL.disj\ (* When you add constants to these lists, make sure to handle them in "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as well. *) val built_in_consts = [(\<^const_name>\Pure.all\, 1), (\<^const_name>\Pure.eq\, 2), (\<^const_name>\Pure.imp\, 2), (\<^const_name>\Pure.conjunction\, 2), (\<^const_name>\Trueprop\, 1), (\<^const_name>\Not\, 1), (\<^const_name>\False\, 0), (\<^const_name>\True\, 0), (\<^const_name>\All\, 1), (\<^const_name>\Ex\, 1), (\<^const_name>\HOL.eq\, 1), (\<^const_name>\HOL.conj\, 2), (\<^const_name>\HOL.disj\, 2), (\<^const_name>\HOL.implies\, 2), (\<^const_name>\If\, 3), (\<^const_name>\Let\, 2), (\<^const_name>\Pair\, 2), (\<^const_name>\fst\, 1), (\<^const_name>\snd\, 1), (\<^const_name>\Set.member\, 2), (\<^const_name>\Collect\, 1), (\<^const_name>\Id\, 0), (\<^const_name>\converse\, 1), (\<^const_name>\trancl\, 1), (\<^const_name>\relcomp\, 2), (\<^const_name>\finite\, 1), (\<^const_name>\unknown\, 0), (\<^const_name>\is_unknown\, 1), (\<^const_name>\safe_The\, 1), (\<^const_name>\Frac\, 0), (\<^const_name>\norm_frac\, 0), (\<^const_name>\Suc\, 0), (\<^const_name>\nat\, 0), (\<^const_name>\nat_gcd\, 0), (\<^const_name>\nat_lcm\, 0)] val built_in_typed_consts = [((\<^const_name>\zero_class.zero\, nat_T), 0), ((\<^const_name>\one_class.one\, nat_T), 0), ((\<^const_name>\plus_class.plus\, nat_T --> nat_T --> nat_T), 0), ((\<^const_name>\minus_class.minus\, nat_T --> nat_T --> nat_T), 0), ((\<^const_name>\times_class.times\, nat_T --> nat_T --> nat_T), 0), ((\<^const_name>\Rings.divide\, nat_T --> nat_T --> nat_T), 0), ((\<^const_name>\ord_class.less\, nat_T --> nat_T --> bool_T), 2), ((\<^const_name>\ord_class.less_eq\, nat_T --> nat_T --> bool_T), 2), ((\<^const_name>\of_nat\, nat_T --> int_T), 0), ((\<^const_name>\zero_class.zero\, int_T), 0), ((\<^const_name>\one_class.one\, int_T), 0), ((\<^const_name>\plus_class.plus\, int_T --> int_T --> int_T), 0), ((\<^const_name>\minus_class.minus\, int_T --> int_T --> int_T), 0), ((\<^const_name>\times_class.times\, int_T --> int_T --> int_T), 0), ((\<^const_name>\Rings.divide\, int_T --> int_T --> int_T), 0), ((\<^const_name>\uminus_class.uminus\, int_T --> int_T), 0), ((\<^const_name>\ord_class.less\, int_T --> int_T --> bool_T), 2), ((\<^const_name>\ord_class.less_eq\, int_T --> int_T --> bool_T), 2)] fun unarize_type \<^typ>\unsigned_bit word\ = nat_T | unarize_type \<^typ>\signed_bit word\ = int_T | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts) | unarize_type T = T fun unarize_unbox_etc_type (Type (\<^type_name>\fun_box\, Ts)) = unarize_unbox_etc_type (Type (\<^type_name>\fun\, Ts)) | unarize_unbox_etc_type (Type (\<^type_name>\pair_box\, Ts)) = Type (\<^type_name>\prod\, map unarize_unbox_etc_type Ts) | unarize_unbox_etc_type \<^typ>\unsigned_bit word\ = nat_T | unarize_unbox_etc_type \<^typ>\signed_bit word\ = int_T | unarize_unbox_etc_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_unbox_etc_type Ts) | unarize_unbox_etc_type T = T fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts) | uniterize_type \<^typ>\bisim_iterator\ = nat_T | uniterize_type T = T val uniterize_unarize_unbox_etc_type = uniterize_type o unarize_unbox_etc_type fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_unbox_etc_type fun pretty_for_type ctxt = Syntax.pretty_typ ctxt o unarize_unbox_etc_type val prefix_name = Long_Name.qualify o Long_Name.base_name val shortest_name = Long_Name.base_name val prefix_abs_vars = Term.map_abs_vars o prefix_name fun short_name s = case space_explode name_sep s of [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix | ss => map shortest_name ss |> space_implode "_" fun shorten_names_in_type (Type (s, Ts)) = Type (short_name s, map shorten_names_in_type Ts) | shorten_names_in_type T = T val shorten_names_in_term = map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t) #> map_types shorten_names_in_type fun strict_type_match thy (T1, T2) = (Sign.typ_match thy (T2, T1) Vartab.empty; true) handle Type.TYPE_MATCH => false fun type_match thy = strict_type_match thy o apply2 unarize_unbox_etc_type fun const_match thy ((s1, T1), (s2, T2)) = s1 = s2 andalso type_match thy (T1, T2) fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2) | term_match thy (Free (s1, T1), Free (s2, T2)) = const_match thy ((shortest_name s1, T1), (shortest_name s2, T2)) | term_match _ (t1, t2) = t1 aconv t2 fun frac_from_term_pair T t1 t2 = case snd (HOLogic.dest_number t1) of 0 => HOLogic.mk_number T 0 | n1 => case snd (HOLogic.dest_number t2) of 1 => HOLogic.mk_number T n1 | n2 => Const (\<^const_name>\divide\, T --> T --> T) $ HOLogic.mk_number T n1 $ HOLogic.mk_number T n2 fun is_fun_type (Type (\<^type_name>\fun\, _)) = true | is_fun_type _ = false fun is_set_type (Type (\<^type_name>\set\, _)) = true | is_set_type _ = false val is_fun_or_set_type = is_fun_type orf is_set_type fun is_set_like_type (Type (\<^type_name>\fun\, [_, T'])) = (body_type T' = bool_T) | is_set_like_type (Type (\<^type_name>\set\, _)) = true | is_set_like_type _ = false fun is_pair_type (Type (\<^type_name>\prod\, _)) = true | is_pair_type _ = false fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s | is_lfp_iterator_type _ = false fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s | is_gfp_iterator_type _ = false val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type fun is_iterator_type T = (T = \<^typ>\bisim_iterator\ orelse is_fp_iterator_type T) fun is_boolean_type T = (T = prop_T orelse T = bool_T) fun is_integer_type T = (T = nat_T orelse T = int_T) fun is_bit_type T = (T = \<^typ>\unsigned_bit\ orelse T = \<^typ>\signed_bit\) fun is_word_type (Type (\<^type_name>\word\, _)) = true | is_word_type _ = false val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type fun is_frac_type ctxt (Type (s, [])) = s |> AList.defined (op =) (#frac_types (Data.get (Context.Proof ctxt))) | is_frac_type _ _ = false fun is_number_type ctxt = is_integer_like_type orf is_frac_type ctxt fun is_higher_order_type (Type (\<^type_name>\fun\, _)) = true | is_higher_order_type (Type (\<^type_name>\set\, _)) = true | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts | is_higher_order_type _ = false fun elem_type (Type (\<^type_name>\set\, [T'])) = T' | elem_type T = raise TYPE ("Nitpick_HOL.elem_type", [T], []) fun pseudo_domain_type (Type (\<^type_name>\fun\, [T1, _])) = T1 | pseudo_domain_type T = elem_type T fun pseudo_range_type (Type (\<^type_name>\fun\, [_, T2])) = T2 | pseudo_range_type (Type (\<^type_name>\set\, _)) = bool_T | pseudo_range_type T = raise TYPE ("Nitpick_HOL.pseudo_range_type", [T], []) fun iterator_type_for_const gfp (s, T) = Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s, binder_types T) fun const_for_iterator_type (Type (s, Ts)) = (strip_first_name_sep s |> snd, Ts ---> bool_T) | const_for_iterator_type T = raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], []) fun strip_n_binders 0 T = ([], T) | strip_n_binders n (Type (\<^type_name>\fun\, [T1, T2])) = strip_n_binders (n - 1) T2 |>> cons T1 | strip_n_binders n (Type (\<^type_name>\fun_box\, Ts)) = strip_n_binders n (Type (\<^type_name>\fun\, Ts)) | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], []) val nth_range_type = snd oo strip_n_binders fun num_factors_in_type (Type (\<^type_name>\prod\, [T1, T2])) = fold (Integer.add o num_factors_in_type) [T1, T2] 0 | num_factors_in_type _ = 1 val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types fun maybe_curried_binder_types T = (if is_pair_type (body_type T) then binder_types else curried_binder_types) T fun mk_flat_tuple _ [t] = t | mk_flat_tuple (Type (\<^type_name>\prod\, [T1, T2])) (t :: ts) = HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts) | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts) fun dest_n_tuple 1 t = [t] | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op :: fun typedef_info ctxt s = if is_frac_type ctxt (Type (s, [])) then SOME {abs_type = Type (s, []), rep_type = \<^typ>\int * int\, Abs_name = \<^const_name>\Abs_Frac\, Rep_name = \<^const_name>\Rep_Frac\, prop_of_Rep = \<^prop>\Rep_Frac x \ Collect Frac\ |> Logic.varify_global, Abs_inverse = NONE, Rep_inverse = NONE} else case Typedef.get_info ctxt s of (* When several entries are returned, it shouldn't matter much which one we take (according to Florian Haftmann). *) (* The "Logic.varifyT_global" calls are a temporary hack because these types's type variables sometimes clash with locally fixed type variables. Remove these calls once "Typedef" is fully localized. *) ({abs_type, rep_type, Abs_name, Rep_name, ...}, {Rep, Abs_inverse, Rep_inverse, ...}) :: _ => SOME {abs_type = Logic.varifyT_global abs_type, rep_type = Logic.varifyT_global rep_type, Abs_name = Abs_name, Rep_name = Rep_name, prop_of_Rep = Thm.prop_of Rep, Abs_inverse = SOME Abs_inverse, Rep_inverse = SOME Rep_inverse} | _ => NONE val is_raw_typedef = is_some oo typedef_info val is_raw_free_datatype = is_some oo Ctr_Sugar.ctr_sugar_of val is_interpreted_type = member (op =) [\<^type_name>\prod\, \<^type_name>\set\, \<^type_name>\bool\, \<^type_name>\nat\, \<^type_name>\int\, \<^type_name>\natural\, \<^type_name>\integer\] fun repair_constr_type (Type (_, Ts)) T = snd (dest_Const (Ctr_Sugar.mk_ctr Ts (Const (Name.uu, T)))) fun register_frac_type_generic frac_s ersaetze generic = let val {frac_types, ersatz_table, codatatypes} = Data.get generic val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types in Data.put {frac_types = frac_types, ersatz_table = ersatz_table, codatatypes = codatatypes} generic end (* TODO: Consider morphism. *) fun register_frac_type frac_s ersaetze (_ : morphism) = register_frac_type_generic frac_s ersaetze val register_frac_type_global = Context.theory_map oo register_frac_type_generic fun unregister_frac_type_generic frac_s = register_frac_type_generic frac_s [] (* TODO: Consider morphism. *) fun unregister_frac_type frac_s (_ : morphism) = unregister_frac_type_generic frac_s val unregister_frac_type_global = Context.theory_map o unregister_frac_type_generic fun register_ersatz_generic ersatz generic = let val {frac_types, ersatz_table, codatatypes} = Data.get generic val ersatz_table = AList.merge (op =) (K true) (ersatz_table, ersatz) in Data.put {frac_types = frac_types, ersatz_table = ersatz_table, codatatypes = codatatypes} generic end (* TODO: Consider morphism. *) fun register_ersatz ersatz (_ : morphism) = register_ersatz_generic ersatz val register_ersatz_global = Context.theory_map o register_ersatz_generic fun register_codatatype_generic coT case_name constr_xs generic = let val {frac_types, ersatz_table, codatatypes} = Data.get generic val constr_xs = map (apsnd (repair_constr_type coT)) constr_xs val (co_s, coTs) = dest_Type coT val _ = if forall is_TFree coTs andalso not (has_duplicates (op =) coTs) andalso co_s <> \<^type_name>\fun\ andalso not (is_interpreted_type co_s) then () else raise TYPE ("Nitpick_HOL.register_codatatype_generic", [coT], []) val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs)) codatatypes in Data.put {frac_types = frac_types, ersatz_table = ersatz_table, codatatypes = codatatypes} generic end (* TODO: Consider morphism. *) fun register_codatatype coT case_name constr_xs (_ : morphism) = register_codatatype_generic coT case_name constr_xs val register_codatatype_global = Context.theory_map ooo register_codatatype_generic fun unregister_codatatype_generic coT = register_codatatype_generic coT "" [] (* TODO: Consider morphism. *) fun unregister_codatatype coT (_ : morphism) = unregister_codatatype_generic coT val unregister_codatatype_global = Context.theory_map o unregister_codatatype_generic fun is_raw_codatatype ctxt s = Option.map #fp (BNF_FP_Def_Sugar.fp_sugar_of ctxt s) = SOME BNF_Util.Greatest_FP fun is_registered_codatatype ctxt s = not (null (these (Option.map snd (AList.lookup (op =) (#codatatypes (Data.get (Context.Proof ctxt))) s)))) fun is_codatatype ctxt (Type (s, _)) = is_raw_codatatype ctxt s orelse is_registered_codatatype ctxt s | is_codatatype _ _ = false fun is_registered_type ctxt (T as Type (s, _)) = is_frac_type ctxt T orelse is_registered_codatatype ctxt s | is_registered_type _ _ = false fun is_raw_quot_type ctxt (Type (s, _)) = is_some (Quotient_Info.lookup_quotients ctxt s) | is_raw_quot_type _ _ = false fun is_quot_type ctxt T = is_raw_quot_type ctxt T andalso not (is_registered_type ctxt T) andalso T <> \<^typ>\int\ fun is_pure_typedef ctxt (T as Type (s, _)) = is_frac_type ctxt T orelse (is_raw_typedef ctxt s andalso not (is_raw_free_datatype ctxt s orelse is_raw_quot_type ctxt T orelse is_codatatype ctxt T orelse is_integer_like_type T)) | is_pure_typedef _ _ = false fun is_univ_typedef ctxt (Type (s, _)) = (case typedef_info ctxt s of SOME {prop_of_Rep, ...} => let val t_opt = try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop) prop_of_Rep in case t_opt of SOME (Const (\<^const_name>\top\, _)) => true (* "Multiset.multiset" FIXME unchecked *) | SOME (Const (\<^const_name>\Collect\, _) $ Abs (_, _, Const (\<^const_name>\finite\, _) $ _)) => true (* "FinFun.finfun" FIXME unchecked *) | SOME (Const (\<^const_name>\Collect\, _) $ Abs (_, _, Const (\<^const_name>\Ex\, _) $ Abs (_, _, Const (\<^const_name>\finite\, _) $ _))) => true | _ => false end | NONE => false) | is_univ_typedef _ _ = false fun is_data_type ctxt (T as Type (s, _)) = (is_raw_typedef ctxt s orelse is_registered_type ctxt T orelse T = \<^typ>\ind\ orelse is_raw_quot_type ctxt T) andalso not (is_interpreted_type s) | is_data_type _ _ = false fun all_record_fields thy T = let val (recs, more) = Record.get_extT_fields thy T in recs @ more :: all_record_fields thy (snd more) end handle TYPE _ => [] val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields fun no_of_record_field thy s T1 = find_index (curry (op =) s o fst) (Record.get_extT_fields thy T1 ||> single |> op @) fun is_record_get thy (s, Type (\<^type_name>\fun\, [T1, _])) = exists (curry (op =) s o fst) (all_record_fields thy T1) | is_record_get _ _ = false fun is_record_update thy (s, T) = String.isSuffix Record.updateN s andalso exists (curry (op =) (unsuffix Record.updateN s) o fst) (all_record_fields thy (body_type T)) handle TYPE _ => false fun is_abs_fun ctxt (s, Type (\<^type_name>\fun\, [_, Type (s', _)])) = (case typedef_info ctxt s' of SOME {Abs_name, ...} => s = Abs_name | NONE => false) | is_abs_fun _ _ = false fun is_rep_fun ctxt (s, Type (\<^type_name>\fun\, [Type (s', _), _])) = (case typedef_info ctxt s' of SOME {Rep_name, ...} => s = Rep_name | NONE => false) | is_rep_fun _ _ = false fun is_quot_abs_fun ctxt (x as (_, Type (\<^type_name>\fun\, [_, abs_T as Type (s', _)]))) = try (Quotient_Term.absrep_const_chk ctxt Quotient_Term.AbsF) s' = SOME (Const x) andalso not (is_registered_type ctxt abs_T) | is_quot_abs_fun _ _ = false fun is_quot_rep_fun ctxt (s, Type (\<^type_name>\fun\, [abs_T as Type (abs_s, _), _])) = (case try (Quotient_Term.absrep_const_chk ctxt Quotient_Term.RepF) abs_s of SOME (Const (s', _)) => s = s' andalso not (is_registered_type ctxt abs_T) | _ => false) | is_quot_rep_fun _ _ = false fun mate_of_rep_fun ctxt (x as (_, Type (\<^type_name>\fun\, [T1 as Type (s', _), T2]))) = (case typedef_info ctxt s' of SOME {Abs_name, ...} => (Abs_name, Type (\<^type_name>\fun\, [T2, T1])) | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])) | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]) fun rep_type_for_quot_type ctxt (T as Type (s, _)) = let val thy = Proof_Context.theory_of ctxt val {qtyp, rtyp, ...} = the (Quotient_Info.lookup_quotients ctxt s) in instantiate_type thy qtyp T rtyp end | rep_type_for_quot_type _ T = raise TYPE ("Nitpick_HOL.rep_type_for_quot_type", [T], []) fun equiv_relation_for_quot_type thy (Type (s, Ts)) = let val {qtyp, equiv_rel, equiv_thm, ...} = the (Quotient_Info.lookup_quotients thy s) val partial = case Thm.prop_of equiv_thm of \<^const>\Trueprop\ $ (Const (\<^const_name>\equivp\, _) $ _) => false | \<^const>\Trueprop\ $ (Const (\<^const_name>\part_equivp\, _) $ _) => true | _ => raise NOT_SUPPORTED "Ill-formed quotient type equivalence \ \relation theorem" val Ts' = qtyp |> dest_Type |> snd in (subst_atomic_types (Ts' ~~ Ts) equiv_rel, partial) end | equiv_relation_for_quot_type _ T = raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], []) fun is_raw_free_datatype_constr ctxt (s, T) = case body_type T of dtT as Type (dt_s, _) => let val ctrs = case Ctr_Sugar.ctr_sugar_of ctxt dt_s of SOME {ctrs, ...} => map dest_Const ctrs | _ => [] in exists (fn (s', T') => s = s' andalso repair_constr_type dtT T' = T) ctrs end | _ => false fun is_registered_coconstr ctxt (s, T) = case body_type T of coT as Type (co_s, _) => let val ctrs = co_s |> AList.lookup (op =) (#codatatypes (Data.get (Context.Proof ctxt))) |> Option.map snd |> these in exists (fn (s', T') => s = s' andalso repair_constr_type coT T' = T) ctrs end | _ => false fun is_nonfree_constr ctxt (s, T) = member (op =) [\<^const_name>\FunBox\, \<^const_name>\PairBox\, \<^const_name>\Quot\, \<^const_name>\Zero_Rep\, \<^const_name>\Suc_Rep\] s orelse let val (x as (_, T)) = (s, unarize_unbox_etc_type T) in is_raw_free_datatype_constr ctxt x orelse (is_abs_fun ctxt x andalso is_pure_typedef ctxt (range_type T)) orelse is_registered_coconstr ctxt x end fun is_free_constr ctxt (s, T) = is_nonfree_constr ctxt (s, T) andalso let val (x as (_, T)) = (s, unarize_unbox_etc_type T) in not (is_abs_fun ctxt x) orelse is_univ_typedef ctxt (range_type T) end fun is_stale_constr ctxt (x as (s, T)) = is_registered_type ctxt (body_type T) andalso is_nonfree_constr ctxt x andalso not (s = \<^const_name>\Abs_Frac\ orelse is_registered_coconstr ctxt x) fun is_constr ctxt (x as (_, T)) = is_nonfree_constr ctxt x andalso not (is_interpreted_type (fst (dest_Type (unarize_type (body_type T))))) andalso not (is_stale_constr ctxt x) val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix val is_sel_like_and_no_discr = String.isPrefix sel_prefix orf (member (op =) [\<^const_name>\fst\, \<^const_name>\snd\]) fun in_fun_lhs_for InConstr = InSel | in_fun_lhs_for _ = InFunLHS fun in_fun_rhs_for InConstr = InConstr | in_fun_rhs_for InSel = InSel | in_fun_rhs_for InFunRHS1 = InFunRHS2 | in_fun_rhs_for _ = InFunRHS1 fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T = case T of Type (\<^type_name>\fun\, _) => (boxy = InPair orelse boxy = InFunLHS) andalso not (is_boolean_type (body_type T)) | Type (\<^type_name>\prod\, Ts) => boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse ((boxy = InExpr orelse boxy = InFunLHS) andalso exists (is_boxing_worth_it hol_ctxt InPair) (map (box_type hol_ctxt InPair) Ts)) | _ => false and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z = case triple_lookup (type_match thy) boxes (Type z) of SOME (SOME box_me) => box_me | _ => is_boxing_worth_it hol_ctxt boxy (Type z) and box_type hol_ctxt boxy T = case T of Type (z as (\<^type_name>\fun\, [T1, T2])) => if boxy <> InConstr andalso boxy <> InSel andalso should_box_type hol_ctxt boxy z then Type (\<^type_name>\fun_box\, [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2]) else box_type hol_ctxt (in_fun_lhs_for boxy) T1 --> box_type hol_ctxt (in_fun_rhs_for boxy) T2 | Type (z as (\<^type_name>\prod\, Ts)) => if boxy <> InConstr andalso boxy <> InSel andalso should_box_type hol_ctxt boxy z then Type (\<^type_name>\pair_box\, map (box_type hol_ctxt InSel) Ts) else Type (\<^type_name>\prod\, map (box_type hol_ctxt (if boxy = InConstr orelse boxy = InSel then boxy else InPair)) Ts) | _ => T fun binarize_nat_and_int_in_type \<^typ>\nat\ = \<^typ>\unsigned_bit word\ | binarize_nat_and_int_in_type \<^typ>\int\ = \<^typ>\signed_bit word\ | binarize_nat_and_int_in_type (Type (s, Ts)) = Type (s, map binarize_nat_and_int_in_type Ts) | binarize_nat_and_int_in_type T = T val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T) fun num_sels_for_constr_type T = length (maybe_curried_binder_types T) fun nth_sel_name_for_constr_name s n = if s = \<^const_name>\Pair\ then if n = 0 then \<^const_name>\fst\ else \<^const_name>\snd\ else sel_prefix_for n ^ s fun nth_sel_for_constr x ~1 = discr_for_constr x | nth_sel_for_constr (s, T) n = (nth_sel_name_for_constr_name s n, body_type T --> nth (maybe_curried_binder_types T) n) fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize = apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel) oo nth_sel_for_constr fun sel_no_from_name s = if String.isPrefix discr_prefix s then ~1 else if String.isPrefix sel_prefix s then s |> unprefix sel_prefix |> Int.fromString |> the else if s = \<^const_name>\snd\ then 1 else 0 val close_form = let fun close_up zs zs' = fold (fn (z as ((s, _), T)) => fn t' => Logic.all_const T $ Abs (s, T, abstract_over (Var z, t'))) (take (length zs' - length zs) zs') fun aux zs (\<^const>\Pure.imp\ $ t1 $ t2) = let val zs' = Term.add_vars t1 zs in close_up zs zs' (Logic.mk_implies (t1, aux zs' t2)) end | aux zs t = close_up zs (Term.add_vars t zs) t in aux [] end fun distinctness_formula T = all_distinct_unordered_pairs_of #> map (fn (t1, t2) => \<^const>\Not\ $ (HOLogic.eq_const T $ t1 $ t2)) #> List.foldr (s_conj o swap) \<^const>\True\ fun zero_const T = Const (\<^const_name>\zero_class.zero\, T) fun suc_const T = Const (\<^const_name>\Suc\, T --> T) fun uncached_data_type_constrs ({ctxt, ...} : hol_context) (T as Type (s, _)) = if is_interpreted_type s then [] else (case AList.lookup (op =) (#codatatypes (Data.get (Context.Proof ctxt))) s of SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type T)) xs' | _ => if is_frac_type ctxt T then case typedef_info ctxt s of SOME {abs_type, rep_type, Abs_name, ...} => [(Abs_name, varify_and_instantiate_type ctxt abs_type T rep_type --> T)] | NONE => [] (* impossible *) else case Ctr_Sugar.ctr_sugar_of ctxt s of SOME {ctrs, ...} => map (apsnd (repair_constr_type T) o dest_Const) ctrs | NONE => if is_raw_quot_type ctxt T then [(\<^const_name>\Quot\, rep_type_for_quot_type ctxt T --> T)] else case typedef_info ctxt s of SOME {abs_type, rep_type, Abs_name, ...} => [(Abs_name, varify_and_instantiate_type ctxt abs_type T rep_type --> T)] | NONE => if T = \<^typ>\ind\ then [dest_Const \<^const>\Zero_Rep\, dest_Const \<^const>\Suc_Rep\] else []) | uncached_data_type_constrs _ _ = [] fun data_type_constrs (hol_ctxt as {constr_cache, ...}) T = case AList.lookup (op =) (!constr_cache) T of SOME xs => xs | NONE => let val xs = uncached_data_type_constrs hol_ctxt T in (Unsynchronized.change constr_cache (cons (T, xs)); xs) end fun binarized_and_boxed_data_type_constrs hol_ctxt binarize = map (apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InConstr)) o data_type_constrs hol_ctxt fun constr_name_for_sel_like \<^const_name>\fst\ = \<^const_name>\Pair\ | constr_name_for_sel_like \<^const_name>\snd\ = \<^const_name>\Pair\ | constr_name_for_sel_like s' = original_name s' fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') = let val s = constr_name_for_sel_like s' in AList.lookup (op =) (binarized_and_boxed_data_type_constrs hol_ctxt binarize (domain_type T')) s |> the |> pair s end fun card_of_type assigns (Type (\<^type_name>\fun\, [T1, T2])) = reasonable_power (card_of_type assigns T2) (card_of_type assigns T1) | card_of_type assigns (Type (\<^type_name>\prod\, [T1, T2])) = card_of_type assigns T1 * card_of_type assigns T2 | card_of_type assigns (Type (\<^type_name>\set\, [T'])) = reasonable_power 2 (card_of_type assigns T') | card_of_type _ (Type (\<^type_name>\itself\, _)) = 1 | card_of_type _ \<^typ>\prop\ = 2 | card_of_type _ \<^typ>\bool\ = 2 | card_of_type assigns T = case AList.lookup (op =) assigns T of SOME k => k | NONE => if T = \<^typ>\bisim_iterator\ then 0 else raise TYPE ("Nitpick_HOL.card_of_type", [T], []) fun bounded_card_of_type max default_card assigns (Type (\<^type_name>\fun\, [T1, T2])) = let val k1 = bounded_card_of_type max default_card assigns T1 val k2 = bounded_card_of_type max default_card assigns T2 in if k1 = max orelse k2 = max then max else Int.min (max, reasonable_power k2 k1) handle TOO_LARGE _ => max end | bounded_card_of_type max default_card assigns (Type (\<^type_name>\prod\, [T1, T2])) = let val k1 = bounded_card_of_type max default_card assigns T1 val k2 = bounded_card_of_type max default_card assigns T2 in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end | bounded_card_of_type max default_card assigns (Type (\<^type_name>\set\, [T'])) = bounded_card_of_type max default_card assigns (T' --> bool_T) | bounded_card_of_type max default_card assigns T = Int.min (max, if default_card = ~1 then card_of_type assigns T else card_of_type assigns T handle TYPE ("Nitpick_HOL.card_of_type", _, _) => default_card) (* Similar to "ATP_Util.tiny_card_of_type". *) fun bounded_exact_card_of_type hol_ctxt finitizable_dataTs max default_card assigns T = let fun aux avoid T = (if member (op =) avoid T then 0 else if member (op =) finitizable_dataTs T then raise SAME () else case T of Type (\<^type_name>\fun\, [T1, T2]) => (case (aux avoid T1, aux avoid T2) of (_, 1) => 1 | (0, _) => 0 | (_, 0) => 0 | (k1, k2) => if k1 >= max orelse k2 >= max then max else Int.min (max, reasonable_power k2 k1)) | Type (\<^type_name>\prod\, [T1, T2]) => (case (aux avoid T1, aux avoid T2) of (0, _) => 0 | (_, 0) => 0 | (k1, k2) => if k1 >= max orelse k2 >= max then max else Int.min (max, k1 * k2)) | Type (\<^type_name>\set\, [T']) => aux avoid (T' --> bool_T) | Type (\<^type_name>\itself\, _) => 1 | \<^typ>\prop\ => 2 | \<^typ>\bool\ => 2 | Type _ => (case data_type_constrs hol_ctxt T of [] => if is_integer_type T orelse is_bit_type T then 0 else raise SAME () | constrs => let val constr_cards = map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd) constrs in if exists (curry (op =) 0) constr_cards then 0 else Int.min (max, Integer.sum constr_cards) end) | _ => raise SAME ()) handle SAME () => AList.lookup (op =) assigns T |> the_default default_card in Int.min (max, aux [] T) end val typical_atomic_card = 4 val typical_card_of_type = bounded_card_of_type 16777217 typical_atomic_card [] fun is_finite_type hol_ctxt T = bounded_exact_card_of_type hol_ctxt [] 1 2 [] T > 0 fun is_special_eligible_arg strict Ts t = case map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t) of [] => true | bad_Ts => let val bad_Ts_cost = if strict then fold (curry (op *) o typical_card_of_type) bad_Ts 1 else fold (Integer.max o typical_card_of_type) bad_Ts 0 val T_cost = typical_card_of_type (fastype_of1 (Ts, t)) in (bad_Ts_cost, T_cost) |> (if strict then op < else op <=) end fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body)) fun let_var s = (nitpick_prefix ^ s, 999) val let_inline_threshold = 20 fun s_let Ts s n abs_T body_T f t = if (n - 1) * (size_of_term t - 1) <= let_inline_threshold orelse is_special_eligible_arg false Ts t then f t else let val z = (let_var s, abs_T) in Const (\<^const_name>\Let\, abs_T --> (abs_T --> body_T) --> body_T) $ t $ abs_var z (incr_boundvars 1 (f (Var z))) end fun loose_bvar1_count (Bound i, k) = if i = k then 1 else 0 | loose_bvar1_count (t1 $ t2, k) = loose_bvar1_count (t1, k) + loose_bvar1_count (t2, k) | loose_bvar1_count (Abs (_, _, t), k) = loose_bvar1_count (t, k + 1) | loose_bvar1_count _ = 0 fun s_betapply _ (t1 as Const (\<^const_name>\Pure.eq\, _) $ t1', t2) = if t1' aconv t2 then \<^prop>\True\ else t1 $ t2 | s_betapply _ (t1 as Const (\<^const_name>\HOL.eq\, _) $ t1', t2) = if t1' aconv t2 then \<^term>\True\ else t1 $ t2 | s_betapply _ (Const (\<^const_name>\If\, _) $ \<^const>\True\ $ t1', _) = t1' | s_betapply _ (Const (\<^const_name>\If\, _) $ \<^const>\False\ $ _, t2) = t2 | s_betapply Ts (Const (\<^const_name>\Let\, Type (_, [bound_T, Type (_, [_, body_T])])) $ t12 $ Abs (s, T, t13'), t2) = let val body_T' = range_type body_T in Const (\<^const_name>\Let\, bound_T --> (bound_T --> body_T') --> body_T') $ t12 $ Abs (s, T, s_betapply (T :: Ts) (t13', incr_boundvars 1 t2)) end | s_betapply Ts (t1 as Abs (s1, T1, t1'), t2) = (s_let Ts s1 (loose_bvar1_count (t1', 0)) T1 (fastype_of1 (T1 :: Ts, t1')) (curry betapply t1) t2 (* FIXME: fix all "s_betapply []" calls *) handle TERM _ => betapply (t1, t2) | General.Subscript => betapply (t1, t2)) | s_betapply _ (t1, t2) = t1 $ t2 fun s_betapplys Ts = Library.foldl (s_betapply Ts) fun s_beta_norm Ts t = let fun aux _ (Var _) = raise Same.SAME | aux Ts (Abs (s, T, t')) = Abs (s, T, aux (T :: Ts) t') | aux Ts ((t1 as Abs _) $ t2) = Same.commit (aux Ts) (s_betapply Ts (t1, t2)) | aux Ts (t1 $ t2) = ((case aux Ts t1 of t1 as Abs _ => Same.commit (aux Ts) (s_betapply Ts (t1, t2)) | t1 => t1 $ Same.commit (aux Ts) t2) handle Same.SAME => t1 $ aux Ts t2) | aux _ _ = raise Same.SAME in aux Ts t handle Same.SAME => t end fun discr_term_for_constr hol_ctxt (x as (s, T)) = let val dataT = body_type T in if s = \<^const_name>\Suc\ then Abs (Name.uu, dataT, \<^const>\Not\ $ HOLogic.mk_eq (zero_const dataT, Bound 0)) else if length (data_type_constrs hol_ctxt dataT) >= 2 then Const (discr_for_constr x) else Abs (Name.uu, dataT, \<^const>\True\) end fun discriminate_value (hol_ctxt as {ctxt, ...}) x t = case head_of t of Const x' => if x = x' then \<^const>\True\ else if is_nonfree_constr ctxt x' then \<^const>\False\ else s_betapply [] (discr_term_for_constr hol_ctxt x, t) | _ => s_betapply [] (discr_term_for_constr hol_ctxt x, t) fun nth_arg_sel_term_for_constr (x as (s, T)) n = let val (arg_Ts, dataT) = strip_type T in if dataT = nat_T then \<^term>\%n::nat. n - 1\ else if is_pair_type dataT then Const (nth_sel_for_constr x n) else let fun aux m (Type (\<^type_name>\prod\, [T1, T2])) = let val (m, t1) = aux m T1 val (m, t2) = aux m T2 in (m, HOLogic.mk_prod (t1, t2)) end | aux m T = (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T) $ Bound 0) val m = fold (Integer.add o num_factors_in_type) (List.take (arg_Ts, n)) 0 in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end end fun select_nth_constr_arg ctxt x t n res_T = (case strip_comb t of (Const x', args) => if x = x' then if is_free_constr ctxt x then nth args n else raise SAME () else if is_nonfree_constr ctxt x' then Const (\<^const_name>\unknown\, res_T) else raise SAME () | _ => raise SAME()) handle SAME () => s_betapply [] (nth_arg_sel_term_for_constr x n, t) fun construct_value _ x [] = Const x | construct_value ctxt (x as (s, _)) args = let val args = map Envir.eta_contract args in case hd args of Const (s', _) $ t => if is_sel_like_and_no_discr s' andalso constr_name_for_sel_like s' = s andalso forall (fn (n, t') => select_nth_constr_arg ctxt x t n dummyT = t') (index_seq 0 (length args) ~~ args) then t else list_comb (Const x, args) | _ => list_comb (Const x, args) end fun constr_expand (hol_ctxt as {ctxt, ...}) T t = (case head_of t of Const x => if is_nonfree_constr ctxt x then t else raise SAME () | _ => raise SAME ()) handle SAME () => let val x' as (_, T') = if is_pair_type T then let val (T1, T2) = HOLogic.dest_prodT T in (\<^const_name>\Pair\, T1 --> T2 --> T) end else data_type_constrs hol_ctxt T |> hd val arg_Ts = binder_types T' in list_comb (Const x', map2 (select_nth_constr_arg ctxt x' t) (index_seq 0 (length arg_Ts)) arg_Ts) end fun coerce_bound_no f j t = case t of t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2 | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t') | Bound j' => if j' = j then f t else t | _ => t fun coerce_bound_0_in_term hol_ctxt new_T old_T = old_T <> new_T ? coerce_bound_no (coerce_term hol_ctxt [new_T] old_T new_T) 0 and coerce_term (hol_ctxt as {ctxt, ...}) Ts new_T old_T t = if old_T = new_T then t else case (new_T, old_T) of (Type (new_s, new_Ts as [new_T1, new_T2]), Type (\<^type_name>\fun\, [old_T1, old_T2])) => (case eta_expand Ts t 1 of Abs (s, _, t') => Abs (s, new_T1, t' |> coerce_bound_0_in_term hol_ctxt new_T1 old_T1 |> coerce_term hol_ctxt (new_T1 :: Ts) new_T2 old_T2) |> Envir.eta_contract |> new_s <> \<^type_name>\fun\ ? construct_value ctxt (\<^const_name>\FunBox\, Type (\<^type_name>\fun\, new_Ts) --> new_T) o single | t' => raise TERM ("Nitpick_HOL.coerce_term", [t'])) | (Type (new_s, new_Ts as [new_T1, new_T2]), Type (old_s, old_Ts as [old_T1, old_T2])) => if old_s = \<^type_name>\fun_box\ orelse old_s = \<^type_name>\pair_box\ orelse old_s = \<^type_name>\prod\ then case constr_expand hol_ctxt old_T t of Const (old_s, _) $ t1 => if new_s = \<^type_name>\fun\ then coerce_term hol_ctxt Ts new_T (Type (\<^type_name>\fun\, old_Ts)) t1 else construct_value ctxt (old_s, Type (\<^type_name>\fun\, new_Ts) --> new_T) [coerce_term hol_ctxt Ts (Type (\<^type_name>\fun\, new_Ts)) (Type (\<^type_name>\fun\, old_Ts)) t1] | Const _ $ t1 $ t2 => construct_value ctxt (if new_s = \<^type_name>\prod\ then \<^const_name>\Pair\ else \<^const_name>\PairBox\, new_Ts ---> new_T) (@{map 3} (coerce_term hol_ctxt Ts) [new_T1, new_T2] [old_T1, old_T2] [t1, t2]) | t' => raise TERM ("Nitpick_HOL.coerce_term", [t']) else raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t]) | _ => raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t]) fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2 | is_ground_term (Const _) = true | is_ground_term _ = false fun special_bounds ts = fold Term.add_vars ts [] |> sort (Term_Ord.fast_indexname_ord o apply2 fst) fun is_funky_typedef_name ctxt s = member (op =) [\<^type_name>\unit\, \<^type_name>\prod\, \<^type_name>\set\, \<^type_name>\Sum_Type.sum\, \<^type_name>\int\] s orelse is_frac_type ctxt (Type (s, [])) fun is_funky_typedef ctxt (Type (s, _)) = is_funky_typedef_name ctxt s | is_funky_typedef _ _ = false fun all_defs_of thy subst = let val def_names = thy |> Theory.defs_of |> Defs.all_specifications_of |> maps snd |> map_filter #def |> Ord_List.make fast_string_ord in Thm.all_axioms_of thy |> map (apsnd (subst_atomic subst o Thm.prop_of)) |> sort (fast_string_ord o apply2 fst) |> Ord_List.inter (fast_string_ord o apsnd fst) def_names |> map snd end (* Ideally we would check against "Complex_Main", not "Hilbert_Choice", but any theory will do as long as it contains all the "axioms" and "axiomatization" commands. *) fun is_built_in_theory thy_id = Context.subthy_id (thy_id, Context.theory_id \<^theory>\Hilbert_Choice\) fun all_nondefs_of ctxt subst = ctxt |> Spec_Rules.get |> filter (Spec_Rules.is_unknown o #rough_classification) |> maps #rules |> filter_out (is_built_in_theory o Thm.theory_id) |> map (subst_atomic subst o Thm.prop_of) fun arity_of_built_in_const (s, T) = if s = \<^const_name>\If\ then if nth_range_type 3 T = \<^typ>\bool\ then NONE else SOME 3 else case AList.lookup (op =) built_in_consts s of SOME n => SOME n | NONE => case AList.lookup (op =) built_in_typed_consts (s, unarize_type T) of SOME n => SOME n | NONE => case s of \<^const_name>\zero_class.zero\ => if is_iterator_type T then SOME 0 else NONE | \<^const_name>\Suc\ => if is_iterator_type (domain_type T) then SOME 0 else NONE | _ => NONE val is_built_in_const = is_some o arity_of_built_in_const (* This function is designed to work for both real definition axioms and simplification rules (equational specifications). *) fun term_under_def t = case t of \<^const>\Pure.imp\ $ _ $ t2 => term_under_def t2 | Const (\<^const_name>\Pure.eq\, _) $ t1 $ _ => term_under_def t1 | \<^const>\Trueprop\ $ t1 => term_under_def t1 | Const (\<^const_name>\HOL.eq\, _) $ t1 $ _ => term_under_def t1 | Abs (_, _, t') => term_under_def t' | t1 $ _ => term_under_def t1 | _ => t (* Here we crucially rely on "specialize_type" performing a preorder traversal of the term, without which the wrong occurrence of a constant could be matched in the face of overloading. *) fun def_props_for_const thy table (x as (s, _)) = if is_built_in_const x then [] else these (Symtab.lookup table s) |> map_filter (try (specialize_type thy x)) |> filter (curry (op =) (Const x) o term_under_def) fun normalized_rhs_of t = let fun aux (v as Var _) (SOME t) = SOME (lambda v t) | aux (c as Const (\<^const_name>\Pure.type\, _)) (SOME t) = SOME (lambda c t) | aux _ _ = NONE val (lhs, rhs) = case t of Const (\<^const_name>\Pure.eq\, _) $ t1 $ t2 => (t1, t2) | \<^const>\Trueprop\ $ (Const (\<^const_name>\HOL.eq\, _) $ t1 $ t2) => (t1, t2) | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t]) val args = strip_comb lhs |> snd in fold_rev aux args (SOME rhs) end fun get_def_of_const thy table (x as (s, _)) = x |> def_props_for_const thy table |> List.last |> normalized_rhs_of |> Option.map (prefix_abs_vars s) handle List.Empty => NONE | TERM _ => NONE fun def_of_const_ext thy (unfold_table, fallback_table) (x as (s, _)) = if is_built_in_const x orelse original_name s <> s then NONE else case get_def_of_const thy unfold_table x of SOME def => SOME (true, def) | NONE => get_def_of_const thy fallback_table x |> Option.map (pair false) val def_of_const = Option.map snd ooo def_of_const_ext fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t | fixpoint_kind_of_rhs (Const (\<^const_name>\lfp\, _) $ Abs _) = Lfp | fixpoint_kind_of_rhs (Const (\<^const_name>\gfp\, _) $ Abs _) = Gfp | fixpoint_kind_of_rhs _ = NoFp fun is_mutually_inductive_pred_def thy table t = let fun is_good_arg (Bound _) = true | is_good_arg (Const (s, _)) = s = \<^const_name>\True\ orelse s = \<^const_name>\False\ orelse s = \<^const_name>\undefined\ | is_good_arg _ = false in case t |> strip_abs_body |> strip_comb of (Const x, ts as (_ :: _)) => (case def_of_const thy table x of SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts | NONE => false) | _ => false end fun unfold_mutually_inductive_preds thy table = map_aterms (fn t as Const x => (case def_of_const thy table x of SOME t' => let val t' = Envir.eta_contract t' in if is_mutually_inductive_pred_def thy table t' then t' else t end | NONE => t) | t => t) fun case_const_names ctxt = map_filter (fn {casex = Const (s, T), ...} => (case rev (binder_types T) of [] => NONE | T :: Ts => if is_data_type ctxt T then SOME (s, length Ts) else NONE)) (Ctr_Sugar.ctr_sugars_of ctxt) @ map (apsnd length o snd) (#codatatypes (Data.get (Context.Proof ctxt))) fun fixpoint_kind_of_const thy table x = if is_built_in_const x then NoFp else fixpoint_kind_of_rhs (the (def_of_const thy table x)) handle Option.Option => NoFp fun is_raw_inductive_pred ({thy, def_tables, intro_table, ...} : hol_context) x = fixpoint_kind_of_const thy def_tables x <> NoFp andalso not (null (def_props_for_const thy intro_table x)) fun is_inductive_pred hol_ctxt (x as (s, _)) = String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s orelse is_raw_inductive_pred hol_ctxt x fun lhs_of_equation t = case t of Const (\<^const_name>\Pure.all\, _) $ Abs (_, _, t1) => lhs_of_equation t1 | Const (\<^const_name>\Pure.eq\, _) $ t1 $ _ => SOME t1 | \<^const>\Pure.imp\ $ _ $ t2 => lhs_of_equation t2 | \<^const>\Trueprop\ $ t1 => lhs_of_equation t1 | Const (\<^const_name>\All\, _) $ Abs (_, _, t1) => lhs_of_equation t1 | Const (\<^const_name>\HOL.eq\, _) $ t1 $ _ => SOME t1 | \<^const>\HOL.implies\ $ _ $ t2 => lhs_of_equation t2 | _ => NONE fun is_constr_pattern _ (Bound _) = true | is_constr_pattern _ (Var _) = true | is_constr_pattern ctxt t = case strip_comb t of (Const x, args) => is_nonfree_constr ctxt x andalso forall (is_constr_pattern ctxt) args | _ => false fun is_constr_pattern_lhs ctxt t = forall (is_constr_pattern ctxt) (snd (strip_comb t)) fun is_constr_pattern_formula ctxt t = case lhs_of_equation t of SOME t' => is_constr_pattern_lhs ctxt t' | NONE => false (* Similar to "specialize_type" but returns all matches rather than only the first (preorder) match. *) fun multi_specialize_type thy slack (s, T) t = let fun aux (Const (s', T')) ys = if s = s' then ys |> (if AList.defined (op =) ys T' then I else cons (T', Envir.subst_term_types (Sign.typ_match thy (T', T) Vartab.empty) t) handle Type.TYPE_MATCH => I | TERM _ => if slack then I else raise NOT_SUPPORTED ("too much polymorphism in axiom \"" ^ Syntax.string_of_term_global thy t ^ "\" involving " ^ quote s)) else ys | aux _ ys = ys in map snd (fold_aterms aux t []) end fun nondef_props_for_const thy slack table (x as (s, _)) = these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x) fun unvarify_term (t1 $ t2) = unvarify_term t1 $ unvarify_term t2 | unvarify_term (Var ((s, 0), T)) = Free (s, T) | unvarify_term (Abs (s, T, t')) = Abs (s, T, unvarify_term t') | unvarify_term t = t fun axiom_for_choice_spec ctxt = unvarify_term #> Object_Logic.atomize_term ctxt #> Choice_Specification.close_form #> HOLogic.mk_Trueprop fun is_choice_spec_fun ({thy, ctxt, def_tables, nondef_table, choice_spec_table, ...} : hol_context) x = case nondef_props_for_const thy true choice_spec_table x of [] => false | ts => case def_of_const thy def_tables x of SOME (Const (\<^const_name>\Eps\, _) $ _) => true | SOME _ => false | NONE => let val ts' = nondef_props_for_const thy true nondef_table x in length ts' = length ts andalso forall (fn t => exists (curry (op aconv) (axiom_for_choice_spec ctxt t)) ts') ts end fun is_choice_spec_axiom thy choice_spec_table t = Symtab.exists (exists (curry (op aconv) t o axiom_for_choice_spec thy) o snd) choice_spec_table fun is_raw_equational_fun ({thy, simp_table, psimp_table, ...} : hol_context) x = exists (fn table => not (null (def_props_for_const thy table x))) [!simp_table, psimp_table] fun is_equational_fun hol_ctxt = is_raw_equational_fun hol_ctxt orf is_inductive_pred hol_ctxt (** Constant unfolding **) fun constr_case_body ctxt Ts (func_t, (x as (_, T))) = let val arg_Ts = binder_types T in s_betapplys Ts (func_t, map2 (select_nth_constr_arg ctxt x (Bound 0)) (index_seq 0 (length arg_Ts)) arg_Ts) end fun add_constr_case res_T (body_t, guard_t) res_t = if res_T = bool_T then s_conj (HOLogic.mk_imp (guard_t, body_t), res_t) else Const (\<^const_name>\If\, bool_T --> res_T --> res_T --> res_T) $ guard_t $ body_t $ res_t fun optimized_case_def (hol_ctxt as {ctxt, ...}) Ts dataT res_T func_ts = let val xs = data_type_constrs hol_ctxt dataT val cases = func_ts ~~ xs |> map (fn (func_t, x) => (constr_case_body ctxt (dataT :: Ts) (incr_boundvars 1 func_t, x), discriminate_value hol_ctxt x (Bound 0))) |> AList.group (op aconv) |> map (apsnd (List.foldl s_disj \<^const>\False\)) |> sort (int_ord o apply2 (size_of_term o snd)) |> rev in if res_T = bool_T then if forall (member (op =) [\<^const>\False\, \<^const>\True\] o fst) cases then case cases of [(body_t, _)] => body_t | [_, (\<^const>\True\, head_t2)] => head_t2 | [_, (\<^const>\False\, head_t2)] => \<^const>\Not\ $ head_t2 | _ => raise BAD ("Nitpick_HOL.optimized_case_def", "impossible cases") else \<^const>\True\ |> fold_rev (add_constr_case res_T) cases else fst (hd cases) |> fold_rev (add_constr_case res_T) (tl cases) end |> absdummy dataT fun optimized_record_get (hol_ctxt as {thy, ctxt, ...}) s rec_T res_T t = let val constr_x = hd (data_type_constrs hol_ctxt rec_T) in case no_of_record_field thy s rec_T of ~1 => (case rec_T of Type (_, Ts as _ :: _) => let val rec_T' = List.last Ts val j = num_record_fields thy rec_T - 1 in select_nth_constr_arg ctxt constr_x t j res_T |> optimized_record_get hol_ctxt s rec_T' res_T end | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T], [])) | j => select_nth_constr_arg ctxt constr_x t j res_T end fun optimized_record_update (hol_ctxt as {thy, ctxt, ...}) s rec_T fun_t rec_t = let val constr_x as (_, constr_T) = hd (data_type_constrs hol_ctxt rec_T) val Ts = binder_types constr_T val n = length Ts val special_j = no_of_record_field thy s rec_T val ts = map2 (fn j => fn T => let val t = select_nth_constr_arg ctxt constr_x rec_t j T in if j = special_j then s_betapply [] (fun_t, t) else if j = n - 1 andalso special_j = ~1 then optimized_record_update hol_ctxt s (rec_T |> dest_Type |> snd |> List.last) fun_t t else t end) (index_seq 0 n) Ts in list_comb (Const constr_x, ts) end (* Prevents divergence in case of cyclic or infinite definition dependencies. *) val unfold_max_depth = 255 (* Inline definitions or define as an equational constant? Booleans tend to benefit more from inlining, due to the polarity analysis. (However, if "total_consts" is set, the polarity analysis is likely not to be so crucial.) *) val def_inline_threshold_for_booleans = 60 val def_inline_threshold_for_non_booleans = 20 fun unfold_defs_in_term (hol_ctxt as {thy, ctxt, whacks, total_consts, case_names, def_tables, ground_thm_table, ersatz_table, ...}) = let fun do_numeral depth Ts mult T some_t0 t1 t2 = (if is_number_type ctxt T then let val j = mult * HOLogic.dest_numeral t2 in if j = 1 then raise SAME () else let val s = numeral_prefix ^ signed_string_of_int j in if is_integer_like_type T then Const (s, T) else do_term depth Ts (Const (\<^const_name>\of_int\, int_T --> T) $ Const (s, int_T)) end end handle TERM _ => raise SAME () else raise SAME ()) handle SAME () => (case some_t0 of NONE => s_betapply [] (do_term depth Ts t1, do_term depth Ts t2) | SOME t0 => s_betapply [] (do_term depth Ts t0, s_betapply [] (do_term depth Ts t1, do_term depth Ts t2))) and do_term depth Ts t = case t of (t0 as Const (\<^const_name>\uminus\, _) $ ((t1 as Const (\<^const_name>\numeral\, Type (\<^type_name>\fun\, [_, ran_T]))) $ t2)) => do_numeral depth Ts ~1 ran_T (SOME t0) t1 t2 | (t1 as Const (\<^const_name>\numeral\, Type (\<^type_name>\fun\, [_, ran_T]))) $ t2 => do_numeral depth Ts 1 ran_T NONE t1 t2 | Const (\<^const_name>\refl_on\, T) $ Const (\<^const_name>\top\, _) $ t2 => do_const depth Ts t (\<^const_name>\refl'\, range_type T) [t2] | (t0 as Const (\<^const_name>\Sigma\, Type (_, [T1, Type (_, [T2, T3])]))) $ t1 $ (t2 as Abs (_, _, t2')) => if loose_bvar1 (t2', 0) then s_betapplys Ts (do_term depth Ts t0, map (do_term depth Ts) [t1, t2]) else do_term depth Ts (Const (\<^const_name>\prod\, T1 --> range_type T2 --> T3) $ t1 $ incr_boundvars ~1 t2') | Const (x as (\<^const_name>\distinct\, Type (\<^type_name>\fun\, [Type (\<^type_name>\list\, [T']), _]))) $ (t1 as _ $ _) => (t1 |> HOLogic.dest_list |> distinctness_formula T' handle TERM _ => do_const depth Ts t x [t1]) | Const (x as (\<^const_name>\If\, _)) $ t1 $ t2 $ t3 => if is_ground_term t1 andalso exists (Pattern.matches thy o rpair t1) (Inttab.lookup_list ground_thm_table (hash_term t1)) then do_term depth Ts t2 else do_const depth Ts t x [t1, t2, t3] | Const (\<^const_name>\Let\, _) $ t1 $ t2 => s_betapply Ts (apply2 (do_term depth Ts) (t2, t1)) | Const x => do_const depth Ts t x [] | t1 $ t2 => (case strip_comb t of (Const x, ts) => do_const depth Ts t x ts | _ => s_betapply [] (do_term depth Ts t1, do_term depth Ts t2)) | Bound _ => t | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body) | _ => if member (term_match thy) whacks t then Const (\<^const_name>\unknown\, fastype_of1 (Ts, t)) else t and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T = (Abs (Name.uu, body_type T, select_nth_constr_arg ctxt x (Bound 0) n res_T), []) | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T = (select_nth_constr_arg ctxt x (do_term depth Ts t) n res_T, ts) and quot_rep_of depth Ts abs_T rep_T ts = select_nth_constr_arg_with_args depth Ts (\<^const_name>\Quot\, rep_T --> abs_T) ts 0 rep_T and do_const depth Ts t (x as (s, T)) ts = if member (term_match thy) whacks (Const x) then Const (\<^const_name>\unknown\, fastype_of1 (Ts, t)) else case AList.lookup (op =) ersatz_table s of SOME s' => do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts | NONE => let fun def_inline_threshold () = if is_boolean_type (body_type T) andalso total_consts <> SOME true then def_inline_threshold_for_booleans else def_inline_threshold_for_non_booleans val (const, ts) = if is_built_in_const x then (Const x, ts) else case AList.lookup (op =) case_names s of SOME n => if length ts < n then (do_term depth Ts (eta_expand Ts t (n - length ts)), []) else let val (dataT, res_T) = nth_range_type n T |> pairf domain_type range_type in (optimized_case_def hol_ctxt Ts dataT res_T (map (do_term depth Ts) (take n ts)), drop n ts) end | _ => if is_constr ctxt x then (Const x, ts) else if is_stale_constr ctxt x then raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \ \(\"" ^ s ^ "\")") else if is_quot_abs_fun ctxt x then case T of Type (\<^type_name>\fun\, [rep_T, abs_T as Type (abs_s, _)]) => if is_interpreted_type abs_s then raise NOT_SUPPORTED ("abstraction function on " ^ quote abs_s) else (Abs (Name.uu, rep_T, Const (\<^const_name>\Quot\, rep_T --> abs_T) $ (Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T) $ Bound 0)), ts) else if is_quot_rep_fun ctxt x then case T of Type (\<^type_name>\fun\, [abs_T as Type (abs_s, _), rep_T]) => if is_interpreted_type abs_s then raise NOT_SUPPORTED ("representation function on " ^ quote abs_s) else quot_rep_of depth Ts abs_T rep_T ts else if is_record_get thy x then case length ts of 0 => (do_term depth Ts (eta_expand Ts t 1), []) | _ => (optimized_record_get hol_ctxt s (domain_type T) (range_type T) (do_term depth Ts (hd ts)), tl ts) else if is_record_update thy x then case length ts of 2 => (optimized_record_update hol_ctxt (unsuffix Record.updateN s) (nth_range_type 2 T) (do_term depth Ts (hd ts)) (do_term depth Ts (nth ts 1)), []) | n => (do_term depth Ts (eta_expand Ts t (2 - n)), []) else if is_abs_fun ctxt x andalso is_quot_type ctxt (range_type T) then let val abs_T = range_type T val rep_T = elem_type (domain_type T) val eps_fun = Const (\<^const_name>\Eps\, (rep_T --> bool_T) --> rep_T) val normal_fun = Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T) val abs_fun = Const (\<^const_name>\Quot\, rep_T --> abs_T) val pred = Abs (Name.uu, rep_T, Const (\<^const_name>\Set.member\, rep_T --> domain_type T --> bool_T) $ Bound 0 $ Bound 1) in (Abs (Name.uu, HOLogic.mk_setT rep_T, abs_fun $ (normal_fun $ (eps_fun $ pred))) |> do_term (depth + 1) Ts, ts) end else if is_rep_fun ctxt x then let val x' = mate_of_rep_fun ctxt x in if is_constr ctxt x' then select_nth_constr_arg_with_args depth Ts x' ts 0 (range_type T) else if is_quot_type ctxt (domain_type T) then let val abs_T = domain_type T val rep_T = elem_type (range_type T) val (rep_fun, _) = quot_rep_of depth Ts abs_T rep_T [] val (equiv_rel, _) = equiv_relation_for_quot_type ctxt abs_T in (Abs (Name.uu, abs_T, HOLogic.Collect_const rep_T $ (equiv_rel $ (rep_fun $ Bound 0))), ts) end else (Const x, ts) end else if is_equational_fun hol_ctxt x orelse is_choice_spec_fun hol_ctxt x then (Const x, ts) else case def_of_const_ext thy def_tables x of SOME (unfold, def) => if depth > unfold_max_depth then raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term", "too many nested definitions (" ^ string_of_int depth ^ ") while expanding " ^ quote s) else if s = \<^const_name>\wfrec'\ then (do_term (depth + 1) Ts (s_betapplys Ts (def, ts)), []) else if not unfold andalso size_of_term def > def_inline_threshold () then (Const x, ts) else (do_term (depth + 1) Ts def, ts) | NONE => (Const x, ts) in s_betapplys Ts (const, map (do_term depth Ts) ts) |> s_beta_norm Ts end in do_term 0 [] end (** Axiom extraction/generation **) fun extensional_equal j T t1 t2 = if is_fun_type T then let val dom_T = pseudo_domain_type T val ran_T = pseudo_range_type T val var_t = Var (("x", j), dom_T) in extensional_equal (j + 1) ran_T (betapply (t1, var_t)) (betapply (t2, var_t)) end else Const (\<^const_name>\HOL.eq\, T --> T --> bool_T) $ t1 $ t2 (* FIXME: needed? *) fun equationalize_term ctxt tag t = let val j = maxidx_of_term t + 1 val (prems, concl) = Logic.strip_horn t in Logic.list_implies (prems, case concl of \<^const>\Trueprop\ $ (Const (\<^const_name>\HOL.eq\, Type (_, [T, _])) $ t1 $ t2) => \<^const>\Trueprop\ $ extensional_equal j T t1 t2 | \<^const>\Trueprop\ $ t' => \<^const>\Trueprop\ $ HOLogic.mk_eq (t', \<^const>\True\) | Const (\<^const_name>\Pure.eq\, Type (_, [T, _])) $ t1 $ t2 => \<^const>\Trueprop\ $ extensional_equal j T t1 t2 | _ => (warning ("Ignoring " ^ quote tag ^ " for non-equation " ^ quote (Syntax.string_of_term ctxt t)); raise SAME ())) |> SOME end handle SAME () => NONE fun pair_for_prop t = case term_under_def t of Const (s, _) => (s, t) | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t']) fun def_table_for ts subst = ts |> map (pair_for_prop o subst_atomic subst) |> AList.group (op =) |> Symtab.make fun const_def_tables ctxt subst ts = (def_table_for (map Thm.prop_of (rev (Named_Theorems.get ctxt \<^named_theorems>\nitpick_unfold\))) subst, fold (fn (s, t) => Symtab.map_default (s, []) (cons t)) (map pair_for_prop ts) Symtab.empty) fun paired_with_consts t = map (rpair t) (Term.add_const_names t []) fun const_nondef_table ts = fold (append o paired_with_consts) ts [] |> AList.group (op =) |> Symtab.make fun const_simp_table ctxt = def_table_for (map_filter (equationalize_term ctxt "nitpick_simp" o Thm.prop_of) (rev (Named_Theorems.get ctxt \<^named_theorems>\nitpick_simp\))) fun const_psimp_table ctxt = def_table_for (map_filter (equationalize_term ctxt "nitpick_psimp" o Thm.prop_of) (rev (Named_Theorems.get ctxt \<^named_theorems>\nitpick_psimp\))) fun const_choice_spec_table ctxt subst = map (subst_atomic subst o Thm.prop_of) (rev (Named_Theorems.get ctxt \<^named_theorems>\nitpick_choice_spec\)) |> const_nondef_table fun inductive_intro_table ctxt subst def_tables = let val thy = Proof_Context.theory_of ctxt in def_table_for (maps (map (unfold_mutually_inductive_preds thy def_tables o Thm.prop_of) o #rules) (filter (Spec_Rules.is_relational o #rough_classification) (Spec_Rules.get ctxt))) subst end fun ground_theorem_table thy = fold ((fn \<^const>\Trueprop\ $ t1 => is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1) | _ => I) o Thm.prop_of o snd) (Global_Theory.all_thms_of thy true) Inttab.empty fun ersatz_table ctxt = #ersatz_table (Data.get (Context.Proof ctxt)) |> fold (append o snd) (#frac_types (Data.get (Context.Proof ctxt))) fun add_simps simp_table s eqs = Unsynchronized.change simp_table (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s))) fun inverse_axioms_for_rep_fun ctxt (x as (_, T)) = let val thy = Proof_Context.theory_of ctxt val abs_T = domain_type T in typedef_info ctxt (fst (dest_Type abs_T)) |> the |> pairf #Abs_inverse #Rep_inverse |> apply2 (specialize_type thy x o Thm.prop_of o the) ||> single |> op :: end fun optimized_typedef_axioms ctxt (abs_z as (abs_s, _)) = let val thy = Proof_Context.theory_of ctxt val abs_T = Type abs_z in if is_univ_typedef ctxt abs_T then [] else case typedef_info ctxt abs_s of SOME {abs_type, rep_type, Rep_name, prop_of_Rep, ...} => let val rep_T = varify_and_instantiate_type ctxt abs_type abs_T rep_type val rep_t = Const (Rep_name, abs_T --> rep_T) val set_t = prop_of_Rep |> HOLogic.dest_Trueprop |> specialize_type thy (dest_Const rep_t) |> HOLogic.dest_mem |> snd in [HOLogic.all_const abs_T $ Abs (Name.uu, abs_T, HOLogic.mk_mem (rep_t $ Bound 0, set_t)) |> HOLogic.mk_Trueprop] end | NONE => [] end fun optimized_quot_type_axioms ctxt abs_z = let val abs_T = Type abs_z val rep_T = rep_type_for_quot_type ctxt abs_T val (equiv_rel, partial) = equiv_relation_for_quot_type ctxt abs_T val a_var = Var (("a", 0), abs_T) val x_var = Var (("x", 0), rep_T) val y_var = Var (("y", 0), rep_T) val x = (\<^const_name>\Quot\, rep_T --> abs_T) val sel_a_t = select_nth_constr_arg ctxt x a_var 0 rep_T val normal_fun = Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T) val normal_x = normal_fun $ x_var val normal_y = normal_fun $ y_var val is_unknown_t = Const (\<^const_name>\is_unknown\, rep_T --> bool_T) in [Logic.mk_equals (normal_fun $ sel_a_t, sel_a_t), Logic.list_implies ([\<^const>\Not\ $ (is_unknown_t $ normal_x), \<^const>\Not\ $ (is_unknown_t $ normal_y), equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop, Logic.mk_equals (normal_x, normal_y)), Logic.list_implies ([HOLogic.mk_Trueprop (\<^const>\Not\ $ (is_unknown_t $ normal_x)), HOLogic.mk_Trueprop (\<^const>\Not\ $ HOLogic.mk_eq (normal_x, x_var))], HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))] |> partial ? cons (HOLogic.mk_Trueprop (equiv_rel $ sel_a_t $ sel_a_t)) end fun codatatype_bisim_axioms (hol_ctxt as {ctxt, ...}) T = let val xs = data_type_constrs hol_ctxt T val pred_T = T --> bool_T val iter_T = \<^typ>\bisim_iterator\ val bisim_max = \<^const>\bisim_iterator_max\ val n_var = Var (("n", 0), iter_T) val n_var_minus_1 = Const (\<^const_name>\safe_The\, (iter_T --> bool_T) --> iter_T) $ Abs ("m", iter_T, HOLogic.eq_const iter_T $ (suc_const iter_T $ Bound 0) $ n_var) val x_var = Var (("x", 0), T) val y_var = Var (("y", 0), T) fun bisim_const T = Const (\<^const_name>\bisim\, [iter_T, T, T] ---> bool_T) fun nth_sub_bisim x n nth_T = (if is_codatatype ctxt nth_T then bisim_const nth_T $ n_var_minus_1 else HOLogic.eq_const nth_T) $ select_nth_constr_arg ctxt x x_var n nth_T $ select_nth_constr_arg ctxt x y_var n nth_T fun case_func (x as (_, T)) = let val arg_Ts = binder_types T val core_t = discriminate_value hol_ctxt x y_var :: map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts |> foldr1 s_conj in fold_rev absdummy arg_Ts core_t end in [HOLogic.mk_imp (HOLogic.mk_disj (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T, s_betapply [] (optimized_case_def hol_ctxt [] T bool_T (map case_func xs), x_var)), bisim_const T $ n_var $ x_var $ y_var), - HOLogic.eq_const pred_T $ (bisim_const T $ bisim_max $ x_var) - $ Abs (Name.uu, T, HOLogic.mk_eq (x_var, Bound 0))] + HOLogic.mk_imp + (bisim_const T $ bisim_max $ x_var $ y_var, + HOLogic.mk_eq (x_var, y_var))] |> map HOLogic.mk_Trueprop end exception NO_TRIPLE of unit fun triple_for_intro_rule ctxt x t = let val prems = Logic.strip_imp_prems t |> map (Object_Logic.atomize_term ctxt) val concl = Logic.strip_imp_concl t |> Object_Logic.atomize_term ctxt val (main, side) = List.partition (exists_Const (curry (op =) x)) prems val is_good_head = curry (op =) (Const x) o head_of in if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE () end val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb fun wf_constraint_for rel side concl main = let val core = HOLogic.mk_mem (HOLogic.mk_prod (apply2 tuple_for_args (main, concl)), Var rel) val t = List.foldl HOLogic.mk_imp core side val vars = filter_out (curry (op =) rel) (Term.add_vars t []) in Library.foldl (fn (t', ((x, j), T)) => HOLogic.all_const T $ Abs (x, T, abstract_over (Var ((x, j), T), t'))) (t, vars) end fun wf_constraint_for_triple rel (side, main, concl) = map (wf_constraint_for rel side concl) main |> foldr1 s_conj fun terminates_by ctxt timeout goal tac = can (SINGLE (Classical.safe_tac ctxt) #> the #> SINGLE (DETERM_TIMEOUT timeout (tac ctxt (auto_tac ctxt))) #> the #> Goal.finish ctxt) goal val max_cached_wfs = 50 val cached_timeout = Synchronized.var "Nitpick_HOL.cached_timeout" Time.zeroTime val cached_wf_props = Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list) val termination_tacs = [Lexicographic_Order.lex_order_tac true, ScnpReconstruct.sizechange_tac] fun uncached_is_well_founded_inductive_pred ({thy, ctxt, debug, tac_timeout, intro_table, ...} : hol_context) (x as (_, T)) = case def_props_for_const thy intro_table x of [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive", [Const x]) | intro_ts => (case map (triple_for_intro_rule ctxt x) intro_ts |> filter_out (null o #2) of [] => true | triples => let val binders_T = HOLogic.mk_tupleT (binder_types T) val rel_T = HOLogic.mk_setT (HOLogic.mk_prodT (binders_T, binders_T)) val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1 val rel = (("R", j), rel_T) val prop = Const (\<^const_name>\wf\, rel_T --> bool_T) $ Var rel :: map (wf_constraint_for_triple rel) triples |> foldr1 s_conj |> HOLogic.mk_Trueprop val _ = if debug then writeln ("Wellfoundedness goal: " ^ Syntax.string_of_term ctxt prop) else () in if tac_timeout = Synchronized.value cached_timeout andalso length (Synchronized.value cached_wf_props) < max_cached_wfs then () else (Synchronized.change cached_wf_props (K []); Synchronized.change cached_timeout (K tac_timeout)); case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of SOME wf => wf | NONE => let val goal = prop |> Thm.cterm_of ctxt |> Goal.init val wf = exists (terminates_by ctxt tac_timeout goal) termination_tacs in Synchronized.change cached_wf_props (cons (prop, wf)); wf end end) handle List.Empty => false | NO_TRIPLE () => false (* The type constraint below is a workaround for a Poly/ML crash. *) fun is_well_founded_inductive_pred (hol_ctxt as {thy, wfs, def_tables, wf_cache, ...} : hol_context) (x as (s, _)) = case triple_lookup (const_match thy) wfs x of SOME (SOME b) => b | _ => s = \<^const_name>\Nats\ orelse s = \<^const_name>\fold_graph'\ orelse case AList.lookup (op =) (!wf_cache) x of SOME (_, wf) => wf | NONE => let val gfp = (fixpoint_kind_of_const thy def_tables x = Gfp) val wf = uncached_is_well_founded_inductive_pred hol_ctxt x in Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf end fun ap_curry [_] _ t = t | ap_curry arg_Ts tuple_T t = let val n = length arg_Ts in fold_rev (Term.abs o pair "c") arg_Ts (incr_boundvars n t $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0))) end fun num_occs_of_bound_in_term j (t1 $ t2) = op + (apply2 (num_occs_of_bound_in_term j) (t1, t2)) | num_occs_of_bound_in_term j (Abs (_, _, t')) = num_occs_of_bound_in_term (j + 1) t' | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0 | num_occs_of_bound_in_term _ _ = 0 val is_linear_inductive_pred_def = let fun do_disjunct j (Const (\<^const_name>\Ex\, _) $ Abs (_, _, t2)) = do_disjunct (j + 1) t2 | do_disjunct j t = case num_occs_of_bound_in_term j t of 0 => true | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t) | _ => false fun do_lfp_def (Const (\<^const_name>\lfp\, _) $ t2) = let val (xs, body) = strip_abs t2 in case length xs of 1 => false | n => forall (do_disjunct (n - 1)) (disjuncts_of body) end | do_lfp_def _ = false in do_lfp_def o strip_abs_body end fun n_ptuple_paths 0 = [] | n_ptuple_paths 1 = [] | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1)) val ap_n_split = HOLogic.mk_ptupleabs o n_ptuple_paths val linear_pred_base_and_step_rhss = let fun aux (Const (\<^const_name>\lfp\, _) $ t2) = let val (xs, body) = strip_abs t2 val arg_Ts = map snd (tl xs) val tuple_T = HOLogic.mk_tupleT arg_Ts val j = length arg_Ts fun repair_rec j (Const (\<^const_name>\Ex\, T1) $ Abs (s2, T2, t2')) = Const (\<^const_name>\Ex\, T1) $ Abs (s2, T2, repair_rec (j + 1) t2') | repair_rec j (\<^const>\HOL.conj\ $ t1 $ t2) = \<^const>\HOL.conj\ $ repair_rec j t1 $ repair_rec j t2 | repair_rec j t = let val (head, args) = strip_comb t in if head = Bound j then HOLogic.eq_const tuple_T $ Bound j $ mk_flat_tuple tuple_T args else t end val (nonrecs, recs) = List.partition (curry (op =) 0 o num_occs_of_bound_in_term j) (disjuncts_of body) val base_body = nonrecs |> List.foldl s_disj \<^const>\False\ val step_body = recs |> map (repair_rec j) |> List.foldl s_disj \<^const>\False\ in (fold_rev Term.abs (tl xs) (incr_bv (~1, j, base_body)) |> ap_n_split (length arg_Ts) tuple_T bool_T, Abs ("y", tuple_T, fold_rev Term.abs (tl xs) step_body |> ap_n_split (length arg_Ts) tuple_T bool_T)) end | aux t = raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t]) in aux end fun predicatify T t = let val set_T = HOLogic.mk_setT T in Abs (Name.uu, T, Const (\<^const_name>\Set.member\, T --> set_T --> bool_T) $ Bound 0 $ incr_boundvars 1 t) end fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (s, T) def = let val j = maxidx_of_term def + 1 val (outer, fp_app) = strip_abs def val outer_bounds = map Bound (length outer - 1 downto 0) val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer val fp_app = subst_bounds (rev outer_vars, fp_app) val (outer_Ts, rest_T) = strip_n_binders (length outer) T val tuple_arg_Ts = strip_type rest_T |> fst val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts val prod_T = HOLogic.mk_prodT (tuple_T, tuple_T) val set_T = HOLogic.mk_setT tuple_T val rel_T = HOLogic.mk_setT prod_T val pred_T = tuple_T --> bool_T val curried_T = tuple_T --> pred_T val uncurried_T = prod_T --> bool_T val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> pred_T) val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs) |> HOLogic.mk_Trueprop val _ = add_simps simp_table base_s [base_eq] val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T) val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs) |> HOLogic.mk_Trueprop val _ = add_simps simp_table step_s [step_eq] val image_const = Const (\<^const_name>\Image\, rel_T --> set_T --> set_T) val rtrancl_const = Const (\<^const_name>\rtrancl\, rel_T --> rel_T) val base_set = HOLogic.Collect_const tuple_T $ list_comb (Const base_x, outer_bounds) val step_set = HOLogic.Collect_const prod_T $ (Const (\<^const_name>\case_prod\, curried_T --> uncurried_T) $ list_comb (Const step_x, outer_bounds)) val image_set = image_const $ (rtrancl_const $ step_set) $ base_set |> predicatify tuple_T in fold_rev Term.abs outer (image_set |> ap_curry tuple_arg_Ts tuple_T) |> unfold_defs_in_term hol_ctxt end fun is_good_starred_linear_pred_type (Type (\<^type_name>\fun\, Ts)) = forall (not o (is_fun_or_set_type orf is_pair_type)) Ts | is_good_starred_linear_pred_type _ = false fun unrolled_inductive_pred_const (hol_ctxt as {thy, star_linear_preds, def_tables, simp_table, ...}) gfp (x as (s, T)) = let val iter_T = iterator_type_for_const gfp x val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T) val unrolled_const = Const x' $ zero_const iter_T val def = the (def_of_const thy def_tables x) in if is_equational_fun hol_ctxt x' then unrolled_const (* already done *) else if not gfp andalso star_linear_preds andalso is_linear_inductive_pred_def def andalso is_good_starred_linear_pred_type T then starred_linear_pred_const hol_ctxt x def else let val j = maxidx_of_term def + 1 val (outer, fp_app) = strip_abs def val outer_bounds = map Bound (length outer - 1 downto 0) val cur = Var ((iter_var_prefix, j + 1), iter_T) val next = suc_const iter_T $ cur val rhs = case fp_app of Const _ $ t => s_betapply [] (t, list_comb (Const x', next :: outer_bounds)) | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_const", [fp_app]) val (inner, naked_rhs) = strip_abs rhs val all = outer @ inner val bounds = map Bound (length all - 1 downto 0) val vars = map (fn (s, T) => Var ((s, j), T)) all val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs) |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars) val _ = add_simps simp_table s' [eq] in unrolled_const end end fun raw_inductive_pred_axiom ({thy, def_tables, ...} : hol_context) x = let val def = the (def_of_const thy def_tables x) val (outer, fp_app) = strip_abs def val outer_bounds = map Bound (length outer - 1 downto 0) val rhs = case fp_app of Const _ $ t => s_betapply [] (t, list_comb (Const x, outer_bounds)) | _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom", [fp_app]) val (inner, naked_rhs) = strip_abs rhs val all = outer @ inner val bounds = map Bound (length all - 1 downto 0) val j = maxidx_of_term def + 1 val vars = map (fn (s, T) => Var ((s, j), T)) all in HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs) |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars) end fun inductive_pred_axiom hol_ctxt (x as (s, T)) = if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then let val x' = (strip_first_name_sep s |> snd, T) in raw_inductive_pred_axiom hol_ctxt x' |> subst_atomic [(Const x', Const x)] end else raw_inductive_pred_axiom hol_ctxt x fun equational_fun_axioms (hol_ctxt as {thy, ctxt, def_tables, simp_table, psimp_table, ...}) x = case def_props_for_const thy (!simp_table) x of [] => (case def_props_for_const thy psimp_table x of [] => (if is_inductive_pred hol_ctxt x then [inductive_pred_axiom hol_ctxt x] else case def_of_const thy def_tables x of SOME def => \<^const>\Trueprop\ $ HOLogic.mk_eq (Const x, def) |> equationalize_term ctxt "" |> the |> single | NONE => []) | psimps => psimps) | simps => simps fun is_equational_fun_surely_complete hol_ctxt x = case equational_fun_axioms hol_ctxt x of [\<^const>\Trueprop\ $ (Const (\<^const_name>\HOL.eq\, _) $ t1 $ _)] => strip_comb t1 |> snd |> forall is_Var | _ => false (** Type preprocessing **) fun merged_type_var_table_for_terms thy ts = let fun add (s, S) table = table |> (case AList.lookup (Sign.subsort thy o swap) table S of SOME _ => I | NONE => filter_out (fn (S', _) => Sign.subsort thy (S, S')) #> cons (S, s)) val tfrees = [] |> fold Term.add_tfrees ts |> sort (string_ord o apply2 fst) in [] |> fold add tfrees |> rev end fun merge_type_vars_in_term thy merge_type_vars table = merge_type_vars ? map_types (map_atyps (fn TFree (_, S) => TFree (table |> find_first (fn (S', _) => Sign.subsort thy (S', S)) |> the |> swap) | T => T)) fun add_ground_types hol_ctxt binarize = let fun aux T accum = case T of Type (\<^type_name>\fun\, Ts) => fold aux Ts accum | Type (\<^type_name>\prod\, Ts) => fold aux Ts accum | Type (\<^type_name>\set\, Ts) => fold aux Ts accum | Type (\<^type_name>\itself\, [T1]) => aux T1 accum | Type (_, Ts) => if member (op =) (\<^typ>\prop\ :: \<^typ>\bool\ :: accum) T then accum else T :: accum |> fold aux (case binarized_and_boxed_data_type_constrs hol_ctxt binarize T of [] => Ts | xs => map snd xs) | _ => insert (op =) T accum in aux end fun ground_types_in_type hol_ctxt binarize T = add_ground_types hol_ctxt binarize T [] fun ground_types_in_terms hol_ctxt binarize ts = fold (fold_types (add_ground_types hol_ctxt binarize)) ts [] end;