src/HOL/BNF/Tools/bnf_fp_util.ML
author blanchet
Thu May 16 13:34:13 2013 +0200 (2013-05-16)
changeset 52031 9a9238342963
parent 51918 3c152334f794
child 52207 21026c312cc3
permissions -rw-r--r--
tuning -- renamed '_from_' to '_of_' in Sledgehammer
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(*  Title:      HOL/BNF/Tools/bnf_fp_util.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012, 2013
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Shared library for the datatype and codatatype constructions.
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*)
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signature BNF_FP_UTIL =
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sig
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  type fp_result =
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    {Ts: typ list,
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     bnfs: BNF_Def.bnf list,
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     ctors: term list,
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     dtors: term list,
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     un_folds: term list,
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     co_recs: term list,
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     co_induct: thm,
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     strong_co_induct: thm,
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     dtor_ctors: thm list,
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     ctor_dtors: thm list,
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     ctor_injects: thm list,
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     map_thms: thm list,
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     set_thmss: thm list list,
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     rel_thms: thm list,
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     un_fold_thms: thm list,
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     co_rec_thms: thm list}
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  val morph_fp_result: morphism -> fp_result -> fp_result
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  val eq_fp_result: fp_result * fp_result -> bool
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  val time: Timer.real_timer -> string -> Timer.real_timer
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  val IITN: string
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  val LevN: string
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  val algN: string
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  val behN: string
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  val bisN: string
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  val carTN: string
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  val caseN: string
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  val coN: string
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  val coinductN: string
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  val corecN: string
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  val ctorN: string
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  val ctor_dtorN: string
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  val ctor_dtor_corecN: string
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  val ctor_dtor_unfoldN: string
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  val ctor_exhaustN: string
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  val ctor_induct2N: string
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  val ctor_inductN: string
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  val ctor_injectN: string
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  val ctor_foldN: string
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  val ctor_fold_uniqueN: string
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  val ctor_mapN: string
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  val ctor_map_uniqueN: string
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  val ctor_recN: string
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  val ctor_rec_uniqueN: string
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  val ctor_relN: string
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  val ctor_set_inclN: string
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  val ctor_set_set_inclN: string
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  val disc_unfoldN: string
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  val disc_unfold_iffN: string
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  val disc_corecN: string
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  val disc_corec_iffN: string
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  val dtorN: string
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  val dtor_coinductN: string
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  val dtor_corecN: string
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  val dtor_corec_uniqueN: string
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  val dtor_ctorN: string
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  val dtor_exhaustN: string
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  val dtor_injectN: string
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  val dtor_mapN: string
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  val dtor_map_coinductN: string
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  val dtor_map_strong_coinductN: string
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  val dtor_map_uniqueN: string
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  val dtor_relN: string
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  val dtor_set_inclN: string
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  val dtor_set_set_inclN: string
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  val dtor_strong_coinductN: string
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  val dtor_unfoldN: string
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  val dtor_unfold_uniqueN: string
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  val exhaustN: string
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  val foldN: string
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  val hsetN: string
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  val hset_recN: string
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  val inductN: string
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  val injectN: string
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  val isNodeN: string
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  val lsbisN: string
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  val mapN: string
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  val map_uniqueN: string
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  val min_algN: string
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  val morN: string
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  val nchotomyN: string
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  val recN: string
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  val rel_coinductN: string
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  val rel_inductN: string
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  val rel_injectN: string
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  val rel_distinctN: string
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  val rvN: string
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  val sel_corecN: string
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  val set_inclN: string
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  val set_set_inclN: string
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  val sel_unfoldN: string
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  val setsN: string
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  val simpsN: string
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  val strTN: string
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  val str_initN: string
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  val strong_coinductN: string
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  val sum_bdN: string
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  val sum_bdTN: string
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  val unfoldN: string
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  val uniqueN: string
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  (* TODO: Don't index set facts. Isabelle packages traditionally generate uniform names. *)
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  val mk_ctor_setN: int -> string
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  val mk_dtor_setN: int -> string
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  val mk_dtor_set_inductN: int -> string
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  val mk_set_inductN: int -> string
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  val datatype_word: bool -> string
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  val base_name_of_typ: typ -> string
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  val mk_common_name: string list -> string
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  val variant_types: string list -> sort list -> Proof.context ->
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    (string * sort) list * Proof.context
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  val variant_tfrees: string list -> Proof.context -> typ list * Proof.context
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  val split_conj_thm: thm -> thm list
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  val split_conj_prems: int -> thm -> thm
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  val mk_sumTN: typ list -> typ
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  val mk_sumTN_balanced: typ list -> typ
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  val id_const: typ -> term
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  val Inl_const: typ -> typ -> term
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  val Inr_const: typ -> typ -> term
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  val mk_Inl: typ -> term -> term
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  val mk_Inr: typ -> term -> term
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  val mk_InN: typ list -> term -> int -> term
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  val mk_InN_balanced: typ -> int -> term -> int -> term
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  val mk_sum_case: term * term -> term
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  val mk_sum_caseN: term list -> term
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  val mk_sum_caseN_balanced: term list -> term
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  val dest_sumT: typ -> typ * typ
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  val dest_sumTN: int -> typ -> typ list
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  val dest_sumTN_balanced: int -> typ -> typ list
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  val dest_tupleT: int -> typ -> typ list
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  val mk_Field: term -> term
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  val mk_If: term -> term -> term -> term
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  val mk_union: term * term -> term
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  val mk_sumEN: int -> thm
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  val mk_sumEN_balanced: int -> thm
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  val mk_sumEN_tupled_balanced: int list -> thm
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  val mk_sum_casesN: int -> int -> thm
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  val mk_sum_casesN_balanced: int -> int -> thm
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  val fixpoint: ('a * 'a -> bool) -> ('a list -> 'a list) -> 'a list -> 'a list
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  val fp_bnf: (binding list -> (string * sort) list -> typ list * typ list list ->
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      BNF_Def.bnf list -> local_theory -> 'a) ->
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    binding list -> (string * sort) list -> ((string * sort) * typ) list -> local_theory ->
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    BNF_Def.bnf list * 'a
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end;
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structure BNF_FP_Util : BNF_FP_UTIL =
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struct
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open BNF_Comp
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open BNF_Def
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open BNF_Util
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type fp_result =
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  {Ts: typ list,
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   bnfs: BNF_Def.bnf list,
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   ctors: term list,
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   dtors: term list,
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   un_folds: term list,
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   co_recs: term list,
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   co_induct: thm,
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   strong_co_induct: thm,
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   dtor_ctors: thm list,
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   ctor_dtors: thm list,
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   ctor_injects: thm list,
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   map_thms: thm list,
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   set_thmss: thm list list,
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   rel_thms: thm list,
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   un_fold_thms: thm list,
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   co_rec_thms: thm list};
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fun morph_fp_result phi {Ts, bnfs, ctors, dtors, un_folds, co_recs, co_induct, strong_co_induct,
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    dtor_ctors, ctor_dtors, ctor_injects, map_thms, set_thmss, rel_thms, un_fold_thms,
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    co_rec_thms} =
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  {Ts = map (Morphism.typ phi) Ts,
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   bnfs = map (morph_bnf phi) bnfs,
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   ctors = map (Morphism.term phi) ctors,
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   dtors = map (Morphism.term phi) dtors,
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   un_folds = map (Morphism.term phi) un_folds,
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   co_recs = map (Morphism.term phi) co_recs,
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   co_induct = Morphism.thm phi co_induct,
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   strong_co_induct = Morphism.thm phi strong_co_induct,
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   dtor_ctors = map (Morphism.thm phi) dtor_ctors,
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   ctor_dtors = map (Morphism.thm phi) ctor_dtors,
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   ctor_injects = map (Morphism.thm phi) ctor_injects,
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   map_thms = map (Morphism.thm phi) map_thms,
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   set_thmss = map (map (Morphism.thm phi)) set_thmss,
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   rel_thms = map (Morphism.thm phi) rel_thms,
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   un_fold_thms = map (Morphism.thm phi) un_fold_thms,
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   co_rec_thms = map (Morphism.thm phi) co_rec_thms};
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fun eq_fp_result ({bnfs = bnfs1, ...} : fp_result, {bnfs = bnfs2, ...} : fp_result) =
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  eq_list eq_bnf (bnfs1, bnfs2);
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val timing = true;
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fun time timer msg = (if timing
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  then warning (msg ^ ": " ^ ATP_Util.string_of_time (Timer.checkRealTimer timer))
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  else (); Timer.startRealTimer ());
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val preN = "pre_"
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val rawN = "raw_"
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val coN = "co"
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val unN = "un"
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val algN = "alg"
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val IITN = "IITN"
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val foldN = "fold"
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val unfoldN = unN ^ foldN
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val uniqueN = "_unique"
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val simpsN = "simps"
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val ctorN = "ctor"
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val dtorN = "dtor"
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val ctor_foldN = ctorN ^ "_" ^ foldN
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val dtor_unfoldN = dtorN ^ "_" ^ unfoldN
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val ctor_fold_uniqueN = ctor_foldN ^ uniqueN
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val dtor_unfold_uniqueN = dtor_unfoldN ^ uniqueN
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val ctor_dtor_unfoldN = ctorN ^ "_" ^ dtor_unfoldN
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val ctor_mapN = ctorN ^ "_" ^ mapN
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val dtor_mapN = dtorN ^ "_" ^ mapN
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val map_uniqueN = mapN ^ uniqueN
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val ctor_map_uniqueN = ctorN ^ "_" ^ map_uniqueN
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val dtor_map_uniqueN = dtorN ^ "_" ^ map_uniqueN
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val min_algN = "min_alg"
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val morN = "mor"
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val bisN = "bis"
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val lsbisN = "lsbis"
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val sum_bdTN = "sbdT"
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val sum_bdN = "sbd"
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val carTN = "carT"
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val strTN = "strT"
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val isNodeN = "isNode"
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val LevN = "Lev"
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val rvN = "recover"
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val behN = "beh"
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val setsN = "sets"
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val mk_ctor_setN = prefix (ctorN ^ "_") o mk_setN
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val mk_dtor_setN = prefix (dtorN ^ "_") o mk_setN
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fun mk_set_inductN i = mk_setN i ^ "_induct"
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val mk_dtor_set_inductN = prefix (dtorN ^ "_") o mk_set_inductN
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val str_initN = "str_init"
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val recN = "rec"
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val corecN = coN ^ recN
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val ctor_recN = ctorN ^ "_" ^ recN
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val ctor_rec_uniqueN = ctor_recN ^ uniqueN
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val dtor_corecN = dtorN ^ "_" ^ corecN
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val dtor_corec_uniqueN = dtor_corecN ^ uniqueN
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val ctor_dtor_corecN = ctorN ^ "_" ^ dtor_corecN
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val ctor_dtorN = ctorN ^ "_" ^ dtorN
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val dtor_ctorN = dtorN ^ "_" ^ ctorN
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val nchotomyN = "nchotomy"
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val injectN = "inject"
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val exhaustN = "exhaust"
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val ctor_injectN = ctorN ^ "_" ^ injectN
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val ctor_exhaustN = ctorN ^ "_" ^ exhaustN
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val dtor_injectN = dtorN ^ "_" ^ injectN
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val dtor_exhaustN = dtorN ^ "_" ^ exhaustN
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val ctor_relN = ctorN ^ "_" ^ relN
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val dtor_relN = dtorN ^ "_" ^ relN
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val inductN = "induct"
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val coinductN = coN ^ inductN
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val ctor_inductN = ctorN ^ "_" ^ inductN
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val ctor_induct2N = ctor_inductN ^ "2"
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val dtor_map_coinductN = dtor_mapN ^ "_" ^ coinductN
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val dtor_coinductN = dtorN ^ "_" ^ coinductN
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val strong_coinductN = "strong_" ^ coinductN
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val dtor_map_strong_coinductN = dtor_mapN ^ "_" ^ strong_coinductN
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val dtor_strong_coinductN = dtorN ^ "_" ^ strong_coinductN
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val hsetN = "Hset"
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val hset_recN = hsetN ^ "_rec"
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val set_inclN = "set_incl"
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val ctor_set_inclN = ctorN ^ "_" ^ set_inclN
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val dtor_set_inclN = dtorN ^ "_" ^ set_inclN
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val set_set_inclN = "set_set_incl"
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val ctor_set_set_inclN = ctorN ^ "_" ^ set_set_inclN
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val dtor_set_set_inclN = dtorN ^ "_" ^ set_set_inclN
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val caseN = "case"
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val discN = "disc"
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val disc_unfoldN = discN ^ "_" ^ unfoldN
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val disc_corecN = discN ^ "_" ^ corecN
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val iffN = "_iff"
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val disc_unfold_iffN = discN ^ "_" ^ unfoldN ^ iffN
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val disc_corec_iffN = discN ^ "_" ^ corecN ^ iffN
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val distinctN = "distinct"
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val rel_distinctN = relN ^ "_" ^ distinctN
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val injectN = "inject"
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val rel_injectN = relN ^ "_" ^ injectN
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val rel_coinductN = relN ^ "_" ^ coinductN
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val rel_inductN = relN ^ "_" ^ inductN
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val selN = "sel"
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val sel_unfoldN = selN ^ "_" ^ unfoldN
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val sel_corecN = selN ^ "_" ^ corecN
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fun datatype_word lfp = (if lfp then "" else "co") ^ "datatype";
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   323
fun add_components_of_typ (Type (s, Ts)) =
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   324
    fold add_components_of_typ Ts #> cons (Long_Name.base_name s)
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   325
  | add_components_of_typ _ = I;
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   326
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   327
fun base_name_of_typ T = space_implode "_" (add_components_of_typ T []);
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   328
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   329
val mk_common_name = space_implode "_";
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   330
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   331
fun dest_sumT (Type (@{type_name sum}, [T, T'])) = (T, T');
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   332
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   333
fun dest_sumTN 1 T = [T]
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   334
  | dest_sumTN n (Type (@{type_name sum}, [T, T'])) = T :: dest_sumTN (n - 1) T';
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   335
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   336
val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT;
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   337
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   338
(* TODO: move something like this to "HOLogic"? *)
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   339
fun dest_tupleT 0 @{typ unit} = []
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   340
  | dest_tupleT 1 T = [T]
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   341
  | dest_tupleT n (Type (@{type_name prod}, [T, T'])) = T :: dest_tupleT (n - 1) T';
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   342
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   343
val mk_sumTN = Library.foldr1 mk_sumT;
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   344
val mk_sumTN_balanced = Balanced_Tree.make mk_sumT;
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   345
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   346
fun id_const T = Const (@{const_name id}, T --> T);
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   347
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   348
fun Inl_const LT RT = Const (@{const_name Inl}, LT --> mk_sumT (LT, RT));
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   349
fun mk_Inl RT t = Inl_const (fastype_of t) RT $ t;
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   350
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   351
fun Inr_const LT RT = Const (@{const_name Inr}, RT --> mk_sumT (LT, RT));
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   352
fun mk_Inr LT t = Inr_const LT (fastype_of t) $ t;
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   353
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   354
fun mk_InN [_] t 1 = t
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   355
  | mk_InN (_ :: Ts) t 1 = mk_Inl (mk_sumTN Ts) t
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   356
  | mk_InN (LT :: Ts) t m = mk_Inr LT (mk_InN Ts t (m - 1))
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   357
  | mk_InN Ts t _ = raise (TYPE ("mk_InN", Ts, [t]));
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   358
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   359
fun mk_InN_balanced sum_T n t k =
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   360
  let
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   361
    fun repair_types T (Const (s as @{const_name Inl}, _) $ t) = repair_inj_types T s fst t
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   362
      | repair_types T (Const (s as @{const_name Inr}, _) $ t) = repair_inj_types T s snd t
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   363
      | repair_types _ t = t
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   364
    and repair_inj_types T s get t =
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   365
      let val T' = get (dest_sumT T) in
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   366
        Const (s, T' --> T) $ repair_types T' t
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   367
      end;
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   368
  in
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   369
    Balanced_Tree.access {left = mk_Inl dummyT, right = mk_Inr dummyT, init = t} n k
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   370
    |> repair_types sum_T
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   371
  end;
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   372
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   373
fun mk_sum_case (f, g) =
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   374
  let
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   375
    val fT = fastype_of f;
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   376
    val gT = fastype_of g;
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   377
  in
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   378
    Const (@{const_name sum_case},
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   379
      fT --> gT --> mk_sumT (domain_type fT, domain_type gT) --> range_type fT) $ f $ g
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   380
  end;
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   381
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   382
val mk_sum_caseN = Library.foldr1 mk_sum_case;
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   383
val mk_sum_caseN_balanced = Balanced_Tree.make mk_sum_case;
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   384
blanchet@49275
   385
fun mk_If p t f =
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   386
  let val T = fastype_of t;
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   387
  in Const (@{const_name If}, HOLogic.boolT --> T --> T --> T) $ p $ t $ f end;
blanchet@49275
   388
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   389
fun mk_Field r =
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   390
  let val T = fst (dest_relT (fastype_of r));
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   391
  in Const (@{const_name Field}, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end;
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   392
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   393
val mk_union = HOLogic.mk_binop @{const_name sup};
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   394
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   395
(*dangerous; use with monotonic, converging functions only!*)
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   396
fun fixpoint eq f X = if subset eq (f X, X) then X else fixpoint eq f (f X);
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   397
blanchet@51858
   398
fun variant_types ss Ss ctxt =
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   399
  let
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   400
    val (tfrees, _) =
blanchet@51858
   401
      fold_map2 (fn s => fn S => Name.variant s #> apfst (rpair S)) ss Ss (Variable.names_of ctxt);
blanchet@51858
   402
    val ctxt' = fold (Variable.declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
blanchet@51858
   403
  in (tfrees, ctxt') end;
blanchet@51858
   404
blanchet@51858
   405
fun variant_tfrees ss =
blanchet@51858
   406
  apfst (map TFree) o variant_types (map (prefix "'") ss) (replicate (length ss) HOLogic.typeS);
blanchet@51858
   407
blanchet@48975
   408
(* stolen from "~~/src/HOL/Tools/Datatype/datatype_aux.ML" *)
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   409
fun split_conj_thm th =
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   410
  ((th RS conjunct1) :: split_conj_thm (th RS conjunct2)) handle THM _ => [th];
blanchet@48975
   411
blanchet@48975
   412
fun split_conj_prems limit th =
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   413
  let
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   414
    fun split n i th =
blanchet@48975
   415
      if i = n then th else split n (i + 1) (conjI RSN (i, th)) handle THM _ => th;
blanchet@48975
   416
  in split limit 1 th end;
blanchet@48975
   417
blanchet@49255
   418
fun mk_sumEN 1 = @{thm one_pointE}
traytel@49240
   419
  | mk_sumEN 2 = @{thm sumE}
traytel@49240
   420
  | mk_sumEN n =
traytel@49240
   421
    (fold (fn i => fn thm => @{thm obj_sum_step} RSN (i, thm)) (2 upto n - 1) @{thm obj_sumE}) OF
traytel@49240
   422
      replicate n (impI RS allI);
blanchet@49125
   423
blanchet@49335
   424
fun mk_obj_sumEN_balanced n =
blanchet@49335
   425
  Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f})))
blanchet@49335
   426
    (replicate n asm_rl);
blanchet@49335
   427
blanchet@49335
   428
fun mk_sumEN_balanced' n all_impIs = mk_obj_sumEN_balanced n OF all_impIs RS @{thm obj_one_pointE};
blanchet@49335
   429
blanchet@49335
   430
fun mk_sumEN_balanced 1 = @{thm one_pointE} (*optimization*)
blanchet@49264
   431
  | mk_sumEN_balanced 2 = @{thm sumE} (*optimization*)
blanchet@49335
   432
  | mk_sumEN_balanced n = mk_sumEN_balanced' n (replicate n (impI RS allI));
blanchet@49335
   433
blanchet@49335
   434
fun mk_tupled_allIN 0 = @{thm unit_all_impI}
blanchet@49335
   435
  | mk_tupled_allIN 1 = @{thm impI[THEN allI]}
blanchet@49335
   436
  | mk_tupled_allIN 2 = @{thm prod_all_impI} (*optimization*)
blanchet@49335
   437
  | mk_tupled_allIN n = mk_tupled_allIN (n - 1) RS @{thm prod_all_impI_step};
blanchet@49335
   438
blanchet@49335
   439
fun mk_sumEN_tupled_balanced ms =
blanchet@49335
   440
  let val n = length ms in
blanchet@49335
   441
    if forall (curry (op =) 1) ms then mk_sumEN_balanced n
blanchet@49335
   442
    else mk_sumEN_balanced' n (map mk_tupled_allIN ms)
blanchet@49335
   443
  end;
blanchet@49264
   444
blanchet@49264
   445
fun mk_sum_casesN 1 1 = refl
blanchet@49130
   446
  | mk_sum_casesN _ 1 = @{thm sum.cases(1)}
blanchet@49130
   447
  | mk_sum_casesN 2 2 = @{thm sum.cases(2)}
blanchet@49264
   448
  | mk_sum_casesN n k = trans OF [@{thm sum_case_step(2)}, mk_sum_casesN (n - 1) (k - 1)];
blanchet@49264
   449
blanchet@49264
   450
fun mk_sum_step base step thm =
blanchet@49264
   451
  if Thm.eq_thm_prop (thm, refl) then base else trans OF [step, thm];
blanchet@49264
   452
blanchet@49264
   453
fun mk_sum_casesN_balanced 1 1 = refl
blanchet@49264
   454
  | mk_sum_casesN_balanced n k =
blanchet@49264
   455
    Balanced_Tree.access {left = mk_sum_step @{thm sum.cases(1)} @{thm sum_case_step(1)},
blanchet@49264
   456
      right = mk_sum_step @{thm sum.cases(2)} @{thm sum_case_step(2)}, init = refl} n k;
blanchet@49130
   457
blanchet@51868
   458
fun fp_bnf construct_fp bs resBs eqs lthy =
blanchet@51868
   459
  let
blanchet@51868
   460
    val timer = time (Timer.startRealTimer ());
blanchet@51868
   461
    val (lhss, rhss) = split_list eqs;
blanchet@48975
   462
blanchet@51868
   463
    (* FIXME: because of "@ lhss", the output could contain type variables that are not in the
blanchet@51868
   464
       input; also, "fp_sort" should put the "resBs" first and in the order in which they appear *)
blanchet@51868
   465
    fun fp_sort Ass =
blanchet@51868
   466
      subtract (op =) lhss (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs) @ lhss;
blanchet@51868
   467
blanchet@51868
   468
    fun raw_qualify b = Binding.qualify true (Binding.name_of (Binding.prefix_name rawN b));
blanchet@51868
   469
blanchet@51868
   470
    val ((bnfs, (deadss, livess)), (unfold_set, lthy)) = apfst (apsnd split_list o split_list)
blanchet@51868
   471
      (fold_map2 (fn b => bnf_of_typ Smart_Inline (raw_qualify b) fp_sort) bs rhss
blanchet@51868
   472
        (empty_unfolds, lthy));
blanchet@51868
   473
blanchet@49498
   474
    val name = mk_common_name (map Binding.name_of bs);
traytel@49425
   475
    fun qualify i =
traytel@49425
   476
      let val namei = name ^ nonzero_string_of_int i;
traytel@49425
   477
      in Binding.qualify true namei end;
blanchet@48975
   478
blanchet@49132
   479
    val Ass = map (map dest_TFree) livess;
blanchet@51866
   480
    val resDs = fold (subtract (op =)) Ass resBs;
traytel@49185
   481
    val Ds = fold (fold Term.add_tfreesT) deadss [];
blanchet@49132
   482
traytel@49156
   483
    val _ = (case Library.inter (op =) Ds lhss of [] => ()
blanchet@49591
   484
      | A :: _ => error ("Inadmissible type recursion (cannot take fixed point of dead type \
blanchet@49132
   485
        \variable " ^ quote (Syntax.string_of_typ lthy (TFree A)) ^ ")"));
blanchet@48975
   486
blanchet@48975
   487
    val timer = time (timer "Construction of BNFs");
blanchet@48975
   488
blanchet@49502
   489
    val ((kill_poss, _), (bnfs', (unfold_set', lthy'))) =
blanchet@51868
   490
      normalize_bnfs qualify Ass Ds fp_sort bnfs unfold_set lthy;
blanchet@48975
   491
blanchet@49132
   492
    val Dss = map3 (append oo map o nth) livess kill_poss deadss;
blanchet@48975
   493
blanchet@51865
   494
    val ((pre_bnfs, deadss), lthy'') =
blanchet@49502
   495
      fold_map3 (seal_bnf unfold_set') (map (Binding.prefix_name preN) bs) Dss bnfs' lthy'
traytel@49185
   496
      |>> split_list;
blanchet@48975
   497
blanchet@48975
   498
    val timer = time (timer "Normalization & sealing of BNFs");
blanchet@48975
   499
blanchet@51867
   500
    val res = construct_fp bs resBs (map TFree resDs, deadss) pre_bnfs lthy'';
blanchet@48975
   501
blanchet@48975
   502
    val timer = time (timer "FP construction in total");
blanchet@48975
   503
  in
blanchet@51865
   504
    timer; (pre_bnfs, res)
blanchet@48975
   505
  end;
blanchet@48975
   506
blanchet@48975
   507
end;