src/Pure/Isar/isar_thy.ML

added 'insert' method (again);

(*  Title:      Pure/Isar/isar_thy.ML
    ID:         $Id$
    Author:     Markus Wenzel, TU Muenchen

Pure/Isar derived theory operations.
*)

signature ISAR_THY =
sig
  val add_title: Comment.text -> Comment.text -> Comment.text -> theory -> theory
  val add_chapter: Comment.text -> theory -> theory
  val add_section: Comment.text -> theory -> theory
  val add_subsection: Comment.text -> theory -> theory
  val add_subsubsection: Comment.text -> theory -> theory
  val add_text: Comment.text -> theory -> theory
  val add_sect: Comment.text -> ProofHistory.T -> ProofHistory.T
  val add_subsect: Comment.text -> ProofHistory.T -> ProofHistory.T
  val add_subsubsect: Comment.text -> ProofHistory.T -> ProofHistory.T
  val add_txt: Comment.text -> ProofHistory.T -> ProofHistory.T
  val add_classes: (bclass * xclass list) list * Comment.text -> theory -> theory
  val add_classes_i: (bclass * class list) list * Comment.text  -> theory -> theory
  val add_classrel: (xclass * xclass) * Comment.text -> theory -> theory
  val add_classrel_i: (class * class) * Comment.text -> theory -> theory
  val add_defsort: xsort * Comment.text -> theory -> theory
  val add_defsort_i: sort * Comment.text -> theory -> theory
  val add_nonterminals: (bstring * Comment.text) list -> theory -> theory
  val add_tyabbrs: ((bstring * string list * string * mixfix) * Comment.text) list
    -> theory -> theory
  val add_tyabbrs_i: ((bstring * string list * typ * mixfix) * Comment.text) list
    -> theory -> theory
  val add_arities: ((xstring * xsort list * xsort) * Comment.text) list -> theory -> theory
  val add_arities_i: ((string * sort list * sort) * Comment.text) list -> theory -> theory
  val add_typedecl: (bstring * string list * mixfix) * Comment.text -> theory -> theory
  val add_consts: ((bstring * string * mixfix) * Comment.text) list -> theory -> theory
  val add_consts_i: ((bstring * typ * mixfix) * Comment.text) list -> theory -> theory
  val add_modesyntax: string * bool -> ((bstring * string * mixfix) * Comment.text) list
    -> theory -> theory
  val add_modesyntax_i: string * bool -> ((bstring * typ * mixfix) * Comment.text) list
    -> theory -> theory
  val add_trrules: ((xstring * string) Syntax.trrule * Comment.text) list -> theory -> theory
  val add_trrules_i: (Syntax.ast Syntax.trrule * Comment.text) list -> theory -> theory
  val add_axioms: (((bstring * string) * Args.src list) * Comment.text) list -> theory -> theory
  val add_axioms_i: (((bstring * term) * theory attribute list) * Comment.text) list
    -> theory -> theory
  val add_defs: (((bstring * string) * Args.src list) * Comment.text) list -> theory -> theory
  val add_defs_i: (((bstring * term) * theory attribute list) * Comment.text) list
    -> theory -> theory
  val add_constdefs: (((bstring * string * mixfix) * Comment.text) * (string * Comment.text)) list
    -> theory -> theory
  val add_constdefs_i: (((bstring * typ * mixfix) * Comment.text) * (term * Comment.text)) list
    -> theory -> theory
  val apply_theorems: (xstring * Args.src list) list -> theory -> theory * thm list
  val apply_theorems_i: (thm * theory attribute list) list -> theory -> theory * thm list
  val have_theorems: ((bstring * Args.src list) * (xstring * Args.src list) list) * Comment.text
    -> theory -> theory
  val have_theorems_i: ((bstring * theory attribute list) * (thm * theory attribute list) list)
    * Comment.text -> theory -> theory
  val have_lemmas: ((bstring * Args.src list) * (xstring * Args.src list) list) * Comment.text
    -> theory -> theory
  val have_lemmas_i: ((bstring * theory attribute list) * (thm * theory attribute list) list)
    * Comment.text -> theory -> theory
  val have_facts: ((string * Args.src list) * (string * Args.src list) list) * Comment.text
    -> ProofHistory.T -> ProofHistory.T
  val have_facts_i: ((string * Proof.context attribute list) *
    (thm * Proof.context attribute list) list) * Comment.text -> ProofHistory.T -> ProofHistory.T
  val from_facts: (string * Args.src list) list * Comment.text -> ProofHistory.T -> ProofHistory.T
  val from_facts_i: (thm * Proof.context attribute list) list * Comment.text
    -> ProofHistory.T -> ProofHistory.T
  val with_facts: (string * Args.src list) list * Comment.text -> ProofHistory.T -> ProofHistory.T
  val with_facts_i: (thm * Proof.context attribute list) list * Comment.text
    -> ProofHistory.T -> ProofHistory.T
  val chain: Comment.text -> ProofHistory.T -> ProofHistory.T
  val export_chain: Comment.text -> ProofHistory.T -> ProofHistory.T
  val fix: ((string list * string option) * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val fix_i: ((string list * typ) * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val match_bind: ((string list * string) * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val match_bind_i: ((term list * term) * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val theorem: (bstring * Args.src list * (string * (string list * string list)))
    * Comment.text -> bool -> theory -> ProofHistory.T
  val theorem_i: (bstring * theory attribute list * (term * (term list * term list)))
    * Comment.text -> bool -> theory -> ProofHistory.T
  val lemma: (bstring * Args.src list * (string * (string list * string list)))
    * Comment.text -> bool -> theory -> ProofHistory.T
  val lemma_i: (bstring * theory attribute list * (term * (term list * term list)))
    * Comment.text -> bool -> theory -> ProofHistory.T
  val assume: ((string * Args.src list * (string * (string list * string list)) list)
    * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val assume_i: ((string * Proof.context attribute list * (term * (term list * term list)) list)
    * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val presume: ((string * Args.src list * (string * (string list * string list)) list)
    * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val presume_i: ((string * Proof.context attribute list * (term * (term list * term list)) list)
    * Comment.text) list -> ProofHistory.T -> ProofHistory.T
  val local_def: (string * Args.src list * ((string * string option) * (string * string list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val local_def_i: (string * Args.src list * ((string * typ) * (term * term list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val show: (string * Args.src list * (string * (string list * string list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val show_i: (string * Proof.context attribute list * (term * (term list * term list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val have: (string * Args.src list * (string * (string list * string list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val have_i: (string * Proof.context attribute list * (term * (term list * term list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val thus: (string * Args.src list * (string * (string list * string list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val thus_i: (string * Proof.context attribute list * (term * (term list * term list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val hence: (string * Args.src list * (string * (string list * string list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val hence_i: (string * Proof.context attribute list * (term * (term list * term list)))
    * Comment.text -> ProofHistory.T -> ProofHistory.T
  val begin_block: ProofHistory.T -> ProofHistory.T
  val next_block: ProofHistory.T -> ProofHistory.T
  val end_block: ProofHistory.T -> ProofHistory.T
  val tac: Method.text -> ProofHistory.T -> ProofHistory.T
  val then_tac: Method.text -> ProofHistory.T -> ProofHistory.T
  val proof: (Comment.interest * (Method.text * Comment.interest) option) * Comment.text
    -> ProofHistory.T -> ProofHistory.T
  val kill_proof: ProofHistory.T -> theory
  val qed: (Method.text * Comment.interest) option * Comment.text
    -> Toplevel.transition -> Toplevel.transition
  val terminal_proof: ((Method.text * Comment.interest) * (Method.text * Comment.interest) option)
    * Comment.text -> Toplevel.transition -> Toplevel.transition
  val immediate_proof: Comment.text -> Toplevel.transition -> Toplevel.transition
  val default_proof: Comment.text -> Toplevel.transition -> Toplevel.transition
  val skip_proof: Comment.text -> Toplevel.transition -> Toplevel.transition
  val get_thmss: (string * Args.src list) list -> Proof.state -> thm list
  val also: ((string * Args.src list) list * Comment.interest) option * Comment.text
    -> Toplevel.transition -> Toplevel.transition
  val also_i: (thm list * Comment.interest) option * Comment.text
    -> Toplevel.transition -> Toplevel.transition
  val finally: ((string * Args.src list) list * Comment.interest) option * Comment.text
    -> Toplevel.transition -> Toplevel.transition
  val finally_i: (thm list * Comment.interest) option * Comment.text
    -> Toplevel.transition -> Toplevel.transition
  val use_mltext: string -> theory option -> theory option
  val use_mltext_theory: string -> theory -> theory
  val use_setup: string -> theory -> theory
  val parse_ast_translation: string -> theory -> theory
  val parse_translation: string -> theory -> theory
  val print_translation: string -> theory -> theory
  val typed_print_translation: string -> theory -> theory
  val print_ast_translation: string -> theory -> theory
  val token_translation: string -> theory -> theory
  val add_oracle: (bstring * string) * Comment.text -> theory -> theory
  val begin_theory: string -> string list -> (string * bool) list -> theory
  val end_theory: theory -> theory
  val theory: string * string list * (string * bool) list
    -> Toplevel.transition -> Toplevel.transition
  val context: string -> Toplevel.transition -> Toplevel.transition
end;

structure IsarThy: ISAR_THY =
struct


(** derived theory and proof operations **)

(* formal comments *)

fun add_text comment thy = thy:theory;
fun add_title title author date thy = thy;
val add_chapter = add_text;
val add_section = add_text;
val add_subsection = add_text;
val add_subsubsection = add_text;

fun add_txt comment = ProofHistory.apply Proof.assert_forward;
val add_sect = add_txt;
val add_subsect = add_txt;
val add_subsubsect = add_txt;


(* signature and syntax *)

val add_classes = Theory.add_classes o Comment.ignore;
val add_classes_i = Theory.add_classes_i o Comment.ignore;
val add_classrel = Theory.add_classrel o single o Comment.ignore;
val add_classrel_i = Theory.add_classrel_i o single o Comment.ignore;
val add_defsort = Theory.add_defsort o Comment.ignore;
val add_defsort_i = Theory.add_defsort_i o Comment.ignore;
val add_nonterminals = Theory.add_nonterminals o map Comment.ignore;
val add_tyabbrs = Theory.add_tyabbrs o map Comment.ignore;
val add_tyabbrs_i = Theory.add_tyabbrs_i o map Comment.ignore;
val add_arities = Theory.add_arities o map Comment.ignore;
val add_arities_i = Theory.add_arities_i o map Comment.ignore;
val add_typedecl = PureThy.add_typedecls o single o Comment.ignore;
val add_consts = Theory.add_consts o map Comment.ignore;
val add_consts_i = Theory.add_consts_i o map Comment.ignore;
fun add_modesyntax mode = Theory.add_modesyntax mode o map Comment.ignore;
fun add_modesyntax_i mode = Theory.add_modesyntax_i mode o map Comment.ignore;
val add_trrules = Theory.add_trrules o map Comment.ignore;
val add_trrules_i = Theory.add_trrules_i o map Comment.ignore;



(* axioms and defs *)

fun add_axms f args thy =
  f (map (fn (x, srcs) => (x, map (Attrib.global_attribute thy) srcs)) args) thy;

val add_axioms = add_axms PureThy.add_axioms o map Comment.ignore;
val add_axioms_i = PureThy.add_axioms_i o map Comment.ignore;
val add_defs = add_axms PureThy.add_defs o map Comment.ignore;
val add_defs_i = PureThy.add_defs_i o map Comment.ignore;


(* constdefs *)

fun gen_add_constdefs consts defs args thy =
  thy
  |> consts (map (Comment.ignore o fst) args)
  |> defs (map (fn (((c, _, mx), _), (s, _)) =>
    (((Thm.def_name (Syntax.const_name c mx), s), []), Comment.none)) args);

fun add_constdefs args = gen_add_constdefs Theory.add_consts add_defs args;
fun add_constdefs_i args = gen_add_constdefs Theory.add_consts_i add_defs_i args;


(* theorems *)

fun gen_have_thmss get attrib f ((name, more_srcs), th_srcs) x =
  f name (map (attrib x) more_srcs)
    (map (fn (s, srcs) => (get x s, map (attrib x) srcs)) th_srcs) x;

fun global_have_thmss kind f (x as ((name, _), _)) thy =
  let val (thy', thms) = gen_have_thmss PureThy.get_thms Attrib.global_attribute f x thy in
    if kind <> "" then Context.setmp (Some thy') (Present.results kind name) thms else ();
    (thy', thms)
  end;

fun local_have_thmss x =
  gen_have_thmss (ProofContext.get_thms o Proof.context_of)
    (Attrib.local_attribute o Proof.theory_of) x;

fun gen_have_thmss_i f ((name, more_atts), th_atts) =
  f name more_atts (map (apfst single) th_atts);

fun have_lemss name atts = PureThy.have_thmss name (atts @ [Drule.tag_lemma]);


fun apply_theorems th_srcs = global_have_thmss "" PureThy.have_thmss (("", []), th_srcs);
fun apply_theorems_i th_srcs = gen_have_thmss_i PureThy.have_thmss (("", []), th_srcs);
val have_theorems = #1 oo (global_have_thmss "theorems" PureThy.have_thmss o Comment.ignore);
val have_theorems_i = #1 oo (gen_have_thmss_i PureThy.have_thmss o Comment.ignore);
val have_lemmas = #1 oo (global_have_thmss "lemmas" have_lemss o Comment.ignore);
val have_lemmas_i = #1 oo (gen_have_thmss_i have_lemss o Comment.ignore);
val have_facts = ProofHistory.apply o local_have_thmss (Proof.have_thmss []) o Comment.ignore;
val have_facts_i = ProofHistory.apply o gen_have_thmss_i (Proof.have_thmss []) o Comment.ignore;


(* forward chaining *)

fun gen_from_facts f = ProofHistory.apply o (Proof.chain oo curry f ("", []));

fun add_thmss name atts ths_atts state =
  Proof.have_thmss (Proof.the_facts state) name atts ths_atts state;

val from_facts = gen_from_facts (local_have_thmss (Proof.have_thmss [])) o Comment.ignore;
val from_facts_i = gen_from_facts (gen_have_thmss_i (Proof.have_thmss [])) o Comment.ignore;
val with_facts = gen_from_facts (local_have_thmss add_thmss) o Comment.ignore;
val with_facts_i = gen_from_facts (gen_have_thmss_i add_thmss) o Comment.ignore;

fun chain comment_ignore = ProofHistory.apply Proof.chain;
fun export_chain comment_ignore = ProofHistory.applys Proof.export_chain;


(* context *)

val fix = ProofHistory.apply o Proof.fix o map Comment.ignore;
val fix_i = ProofHistory.apply o Proof.fix_i o map Comment.ignore;
val match_bind = ProofHistory.apply o Proof.match_bind o map Comment.ignore;
val match_bind_i = ProofHistory.apply o Proof.match_bind_i o map Comment.ignore;


(* statements *)

local

fun global_statement f (name, src, s) int thy =
  ProofHistory.init (Toplevel.undo_limit int)
    (f name (map (Attrib.global_attribute thy) src) s thy);

fun global_statement_i f (name, atts, t) int thy =
  ProofHistory.init (Toplevel.undo_limit int) (f name atts t thy);

fun local_statement f g (name, src, s) = ProofHistory.apply (fn state =>
  f name (map (Attrib.local_attribute (Proof.theory_of state)) src) s (g state));

fun local_statement_i f g (name, atts, t) = ProofHistory.apply (f name atts t o g);

fun multi_statement f args = ProofHistory.apply (fn state =>
  f (map (fn (name, src, s) =>
      (name, map (Attrib.local_attribute (Proof.theory_of state)) src, s)) args) state);

fun multi_statement_i f args = ProofHistory.apply (f args);

in

val theorem     = global_statement Proof.theorem o Comment.ignore;
val theorem_i   = global_statement_i Proof.theorem_i o Comment.ignore;
val lemma       = global_statement Proof.lemma o Comment.ignore;
val lemma_i     = global_statement_i Proof.lemma_i o Comment.ignore;
val assume      = multi_statement Proof.assume o map Comment.ignore;
val assume_i    = multi_statement_i Proof.assume_i o map Comment.ignore;
val presume     = multi_statement Proof.presume o map Comment.ignore;
val presume_i   = multi_statement_i Proof.presume_i o map Comment.ignore;
val local_def   = local_statement LocalDefs.def I o Comment.ignore;
val local_def_i = local_statement LocalDefs.def_i I o Comment.ignore;
val show        = local_statement (Proof.show Seq.single) I o Comment.ignore;
val show_i      = local_statement_i (Proof.show_i Seq.single) I o Comment.ignore;
val have        = local_statement (Proof.have Seq.single) I o Comment.ignore;
val have_i      = local_statement_i (Proof.have_i Seq.single) I o Comment.ignore;
val thus        = local_statement (Proof.show Seq.single) Proof.chain o Comment.ignore;
val thus_i      = local_statement_i (Proof.show_i Seq.single) Proof.chain o Comment.ignore;
val hence       = local_statement (Proof.have Seq.single) Proof.chain o Comment.ignore;
val hence_i     = local_statement_i (Proof.have_i Seq.single) Proof.chain o Comment.ignore;

end;


(* blocks *)

val begin_block = ProofHistory.apply Proof.begin_block;
val next_block = ProofHistory.apply Proof.next_block;
val end_block = ProofHistory.applys Proof.end_block;


(* backward steps *)

val tac = ProofHistory.applys o Method.refine_no_facts;
val then_tac = ProofHistory.applys o Method.refine;

val proof = ProofHistory.applys o Method.proof o
  apsome Comment.ignore_interest o Comment.ignore_interest' o Comment.ignore;


(* print result *)

local

fun pretty_result {kind, name, thm} =
  Pretty.block [Pretty.str (kind ^ (if name = "" then "" else " " ^ name ^ ":")),
    Pretty.fbrk, Proof.pretty_thm thm];

fun pretty_rule thm =
  Pretty.block [Pretty.str "trying to solve goal by rule:", Pretty.fbrk, Proof.pretty_thm thm];

in

val print_result = Pretty.writeln o pretty_result;

fun cond_print_result_rule int =
  if int then (print_result, Pretty.writeln o pretty_rule)
  else (K (), K ());

fun proof'' f = Toplevel.proof' (f o cond_print_result_rule);

end;


(* local endings *)

val local_qed =
  proof'' o (ProofHistory.applys oo Method.local_qed) o apsome Comment.ignore_interest;

fun ignore_interests (x, y) = (Comment.ignore_interest x, apsome Comment.ignore_interest y);

val local_terminal_proof =
  proof'' o (ProofHistory.applys oo Method.local_terminal_proof) o ignore_interests;

val local_immediate_proof = proof'' (ProofHistory.applys o Method.local_immediate_proof);
val local_default_proof = proof'' (ProofHistory.applys o Method.local_default_proof);
val local_skip_proof = proof'' (ProofHistory.applys o SkipProof.local_skip_proof);


(* global endings *)

val kill_proof = Proof.theory_of o ProofHistory.current;

fun global_result finish = Toplevel.proof_to_theory (fn prf =>
  let
    val state = ProofHistory.current prf;
    val _ = if Proof.at_bottom state then () else raise Toplevel.UNDEF;
    val (thy, res as {kind, name, thm}) = finish state;
  in print_result res; Context.setmp (Some thy) (Present.result kind name) thm; thy end);

val global_qed = global_result o Method.global_qed o apsome Comment.ignore_interest;
val global_terminal_proof = global_result o Method.global_terminal_proof o ignore_interests;
val global_immediate_proof = global_result Method.global_immediate_proof;
val global_default_proof = global_result Method.global_default_proof;
val global_skip_proof = global_result SkipProof.global_skip_proof;


(* common endings *)

fun qed (meth, comment) = local_qed meth o global_qed meth;
fun terminal_proof (meths, comment) = local_terminal_proof meths o global_terminal_proof meths;
fun immediate_proof comment = local_immediate_proof o global_immediate_proof;
fun default_proof comment = local_default_proof o global_default_proof;
fun skip_proof comment = local_skip_proof o global_skip_proof;


(* calculational proof commands *)

local

fun cond_print_calc int thms =
  if int then Pretty.writeln (Pretty.big_list "calculation:" (map Proof.pretty_thm thms))
  else ();

fun proof''' f = Toplevel.proof' (f o cond_print_calc);

fun gen_calc get f (args, _) prt state =
  f (apsome (fn (srcs, _) => get srcs state) args) prt state;

in

fun get_thmss srcs = Proof.the_facts o local_have_thmss (Proof.have_thmss []) (("", []), srcs); 
fun get_thmss_i thms _ = thms;

fun also x = proof''' (ProofHistory.applys o gen_calc get_thmss Calculation.also x);
fun also_i x = proof''' (ProofHistory.applys o gen_calc get_thmss_i Calculation.also x);
fun finally x = proof''' (ProofHistory.applys o gen_calc get_thmss Calculation.finally x);
fun finally_i x = proof''' (ProofHistory.applys o gen_calc get_thmss_i Calculation.finally x);

end;


(* use ML text *)

fun use_mltext txt opt_thy = #2 (Context.pass opt_thy (use_text false) txt);
fun use_mltext_theory txt thy = #2 (Context.pass_theory thy (use_text false) txt);

fun use_context txt = use_mltext_theory ("Context.>> (" ^ txt ^ ");");

fun use_let name body txt =
  use_context ("let val " ^ name ^ " = " ^ txt ^ " in\n" ^ body ^ " end");

val use_setup =
  use_let "setup: (theory -> theory) list" "Library.apply setup";


(* translation functions *)

val parse_ast_translation =
  use_let "parse_ast_translation: (string * (Syntax.ast list -> Syntax.ast)) list"
    "Theory.add_trfuns (parse_ast_translation, [], [], [])";

val parse_translation =
  use_let "parse_translation: (string * (term list -> term)) list"
    "Theory.add_trfuns ([], parse_translation, [], [])";

val print_translation =
  use_let "print_translation: (string * (term list -> term)) list"
    "Theory.add_trfuns ([], [], print_translation, [])";

val print_ast_translation =
  use_let "print_ast_translation: (string * (Syntax.ast list -> Syntax.ast)) list"
    "Theory.add_trfuns ([], [], [], print_ast_translation)";

val typed_print_translation =
  use_let "typed_print_translation: (string * (bool -> typ -> term list -> term)) list"
    "Theory.add_trfunsT typed_print_translation";

val token_translation =
  use_let "token_translation: (string * string * (string -> string * int)) list"
    "Theory.add_tokentrfuns token_translation";


(* add_oracle *)

fun add_oracle ((name, txt), comment_ignore) =
  use_let
    "oracle: bstring * (Sign.sg * Object.T -> term)"
    "Theory.add_oracle oracle"
    ("(" ^ quote name ^ ", " ^ txt ^ ")");


(* theory init and exit *)

fun gen_begin_theory bg name parents files =
  let
    val paths = map (apfst Path.unpack) files;
    val thy = bg name parents paths;
  in Present.begin_theory name parents paths thy end;

val begin_theory = gen_begin_theory ThyInfo.begin_theory;
val begin_update_theory = gen_begin_theory ThyInfo.begin_update_theory;

fun end_theory thy =
  (Present.end_theory (PureThy.get_name thy); ThyInfo.end_theory thy);

fun kill_theory thy = ThyInfo.remove_thy (PureThy.get_name thy);


fun bg_theory (name, parents, files) int =
  (if int then begin_update_theory else begin_theory) name parents files;

fun en_theory thy = (end_theory thy; ());

fun theory spec = Toplevel.init_theory (bg_theory spec) en_theory kill_theory;


(* context switch *)

fun context name =
  Toplevel.init_theory (fn _ => (the (#2 (Context.pass None ThyInfo.quiet_update_thy name))))
  (K ()) (K ());


end;