This manual (@value{UPDATED}) is for GNU Bison (version
@value{VERSION}), the GNU parser generator.
-Copyright @copyright{} 1988-1993, 1995, 1998-2011 Free Software
+Copyright @copyright{} 1988-1993, 1995, 1998-2012 Free Software
Foundation, Inc.
@quotation
the name of an identifier, etc.).
* Semantic Actions:: Each rule can have an action containing C code.
* GLR Parsers:: Writing parsers for general context-free languages.
-* Locations Overview:: Tracking Locations.
+* Locations:: Overview of location tracking.
* Bison Parser:: What are Bison's input and output,
how is the output used?
* Stages:: Stages in writing and running Bison grammars.
Bison Grammar Files
-* Grammar Outline:: Overall layout of the grammar file.
-* Symbols:: Terminal and nonterminal symbols.
-* Rules:: How to write grammar rules.
-* Recursion:: Writing recursive rules.
-* Semantics:: Semantic values and actions.
-* Locations:: Locations and actions.
-* Named References:: Using named references in actions.
-* Declarations:: All kinds of Bison declarations are described here.
-* Multiple Parsers:: Putting more than one Bison parser in one program.
+* Grammar Outline:: Overall layout of the grammar file.
+* Symbols:: Terminal and nonterminal symbols.
+* Rules:: How to write grammar rules.
+* Recursion:: Writing recursive rules.
+* Semantics:: Semantic values and actions.
+* Tracking Locations:: Locations and actions.
+* Named References:: Using named references in actions.
+* Declarations:: All kinds of Bison declarations are described here.
+* Multiple Parsers:: Putting more than one Bison parser in one program.
Outline of a Bison Grammar
the name of an identifier, etc.).
* Semantic Actions:: Each rule can have an action containing C code.
* GLR Parsers:: Writing parsers for general context-free languages.
-* Locations Overview:: Tracking Locations.
+* Locations:: Overview of location tracking.
* Bison Parser:: What are Bison's input and output,
how is the output used?
* Stages:: Stages in writing and running Bison grammars.
%@}
@end example
-@node Locations Overview
+@node Locations
@section Locations
@cindex location
@cindex textual location
Bison provides a mechanism for handling these locations.
Each token has a semantic value. In a similar fashion, each token has an
-associated location, but the type of locations is the same for all tokens and
-groupings. Moreover, the output parser is equipped with a default data
-structure for storing locations (@pxref{Locations}, for more details).
+associated location, but the type of locations is the same for all tokens
+and groupings. Moreover, the output parser is equipped with a default data
+structure for storing locations (@pxref{Tracking Locations}, for more
+details).
Like semantic values, locations can be reached in actions using a dedicated
set of constructs. In the example above, the location of the whole grouping
/* Skip white space. */
while ((c = getchar ()) == ' ' || c == '\t')
- ;
+ continue;
@end group
@group
/* Process numbers. */
if (c == EOF)
return 0;
+@group
/* Return a single char, and update location. */
if (c == '\n')
@{
++yylloc.last_column;
return c;
@}
+@end group
@end example
Basically, the lexical analyzer performs the same processing as before:
found, a pointer to that symbol is returned; otherwise zero is returned.
@smallexample
+#include <stdlib.h> /* malloc. */
+#include <string.h> /* strlen. */
+
+@group
symrec *
putsym (char const *sym_name, int sym_type)
@{
sym_table = ptr;
return ptr;
@}
+@end group
+@group
symrec *
getsym (char const *sym_name)
@{
return ptr;
return 0;
@}
+@end group
@end smallexample
The function @code{yylex} must now recognize variables, numeric values, and
int c;
/* Ignore white space, get first nonwhite character. */
- while ((c = getchar ()) == ' ' || c == '\t');
+ while ((c = getchar ()) == ' ' || c == '\t')
+ continue;
if (c == EOF)
return 0;
@xref{Invocation, ,Invoking Bison}.
@menu
-* Grammar Outline:: Overall layout of the grammar file.
-* Symbols:: Terminal and nonterminal symbols.
-* Rules:: How to write grammar rules.
-* Recursion:: Writing recursive rules.
-* Semantics:: Semantic values and actions.
-* Locations:: Locations and actions.
-* Named References:: Using named references in actions.
-* Declarations:: All kinds of Bison declarations are described here.
-* Multiple Parsers:: Putting more than one Bison parser in one program.
+* Grammar Outline:: Overall layout of the grammar file.
+* Symbols:: Terminal and nonterminal symbols.
+* Rules:: How to write grammar rules.
+* Recursion:: Writing recursive rules.
+* Semantics:: Semantic values and actions.
+* Tracking Locations:: Locations and actions.
+* Named References:: Using named references in actions.
+* Declarations:: All kinds of Bison declarations are described here.
+* Multiple Parsers:: Putting more than one Bison parser in one program.
@end menu
@node Grammar Outline
Thus, they belong in one or more @code{%code requires}:
@smallexample
+@group
%code top @{
#define _GNU_SOURCE
#include <stdio.h>
@}
+@end group
+@group
%code requires @{
#include "ptypes.h"
@}
+@end group
+@group
%union @{
long int n;
tree t; /* @r{@code{tree} is defined in @file{ptypes.h}.} */
@}
+@end group
+@group
%code requires @{
#define YYLTYPE YYLTYPE
typedef struct YYLTYPE
char *filename;
@} YYLTYPE;
@}
+@end group
+@group
%code @{
static void print_token_value (FILE *, int, YYSTYPE);
#define YYPRINT(F, N, L) print_token_value (F, N, L)
static void trace_token (enum yytokentype token, YYLTYPE loc);
@}
+@end group
@dots{}
@end smallexample
@code{%code} to a @code{%code provides}:
@smallexample
+@group
%code top @{
#define _GNU_SOURCE
#include <stdio.h>
@}
+@end group
+@group
%code requires @{
#include "ptypes.h"
@}
+@end group
+@group
%union @{
long int n;
tree t; /* @r{@code{tree} is defined in @file{ptypes.h}.} */
@}
+@end group
+@group
%code requires @{
#define YYLTYPE YYLTYPE
typedef struct YYLTYPE
char *filename;
@} YYLTYPE;
@}
+@end group
+@group
%code provides @{
void trace_token (enum yytokentype token, YYLTYPE loc);
@}
+@end group
+@group
%code @{
static void print_token_value (FILE *, int, YYSTYPE);
#define YYPRINT(F, N, L) print_token_value (F, N, L)
@}
+@end group
@dots{}
@end smallexample
type:
@smallexample
+@group
%code requires @{ #include "type1.h" @}
%union @{ type1 field1; @}
%destructor @{ type1_free ($$); @} <field1>
%printer @{ type1_print ($$); @} <field1>
+@end group
+@group
%code requires @{ #include "type2.h" @}
%union @{ type2 field2; @}
%destructor @{ type2_free ($$); @} <field2>
%printer @{ type2_print ($$); @} <field2>
+@end group
@end smallexample
@noindent
useful semantic value associated with the @samp{+} token, it could be
referred to as @code{$2}.
-@xref{Named References,,Using Named References}, for more information
-about using the named references construct.
+@xref{Named References}, for more information about using the named
+references construct.
Note that the vertical-bar character @samp{|} is really a rule
separator, and actions are attached to a single rule. This is a
Now Bison can execute the action in the rule for @code{subroutine} without
deciding which rule for @code{compound} it will eventually use.
-@node Locations
+@node Tracking Locations
@section Tracking Locations
@cindex location
@cindex textual location
In addition, the named references construct @code{@@@var{name}} and
@code{@@[@var{name}]} may also be used to address the symbol locations.
-@xref{Named References,,Using Named References}, for more information
-about using the named references construct.
+@xref{Named References}, for more information about using the named
+references construct.
Here is a basic example using the default data type for locations:
@end itemize
@node Named References
-@section Using Named References
+@section Named References
@cindex named references
-While every semantic value can be accessed with positional references
-@code{$@var{n}} and @code{$$}, it's often much more convenient to refer to
-them by name. First of all, original symbol names may be used as named
-references. For example:
+As described in the preceding sections, the traditional way to refer to any
+semantic value or location is a @dfn{positional reference}, which takes the
+form @code{$@var{n}}, @code{$$}, @code{@@@var{n}}, and @code{@@$}. However,
+such a reference is not very descriptive. Moreover, if you later decide to
+insert or remove symbols in the right-hand side of a grammar rule, the need
+to renumber such references can be tedious and error-prone.
+
+To avoid these issues, you can also refer to a semantic value or location
+using a @dfn{named reference}. First of all, original symbol names may be
+used as named references. For example:
@example
@group
@end example
@noindent
-The positional @code{$$}, @code{@@$}, @code{$n}, and @code{@@n} can be
-mixed with @code{$name} and @code{@@name} arbitrarily. For example:
+Positional and named references can be mixed arbitrarily. For example:
@example
@group
@end example
@noindent
-Explicit names may be declared for RHS and for LHS symbols as well. In order
-to access a semantic value generated by a mid-rule action, an explicit name
-may also be declared by putting a bracketed name after the closing brace of
-the mid-rule action code:
+In order to access a semantic value generated by a mid-rule action, an
+explicit name may also be declared by putting a bracketed name after the
+closing brace of the mid-rule action code:
@example
@group
exp[res]: exp[x] '+' @{$left = $x;@}[left] exp[right]
bracketed syntax @code{$[name]} and @code{@@[name]} must be used:
@example
@group
-if-stmt: IF '(' expr ')' THEN then.stmt ';'
+if-stmt: "if" '(' expr ')' "then" then.stmt ';'
@{ $[if-stmt] = new_if_stmt ($expr, $[then.stmt]); @}
@end group
@end example
It often happens that named references are followed by a dot, dash or other
C punctuation marks and operators. By default, Bison will read
-@code{$name.suffix} as a reference to symbol value @code{$name} followed by
-@samp{.suffix}, i.e., an access to the @samp{suffix} field of the semantic
-value. In order to force Bison to recognize @code{name.suffix} in its entirety
-as the name of a semantic value, bracketed syntax @code{$[name.suffix]}
-must be used.
+@samp{$name.suffix} as a reference to symbol value @code{$name} followed by
+@samp{.suffix}, i.e., an access to the @code{suffix} field of the semantic
+value. In order to force Bison to recognize @samp{name.suffix} in its
+entirety as the name of a semantic value, the bracketed syntax
+@samp{$[name.suffix]} must be used.
+
+The named references feature is experimental. More user feedback will help
+to stabilize it.
@node Declarations
@section Bison Declarations
@cindex mid-rule actions
Finally, Bison will never invoke a @code{%destructor} for an unreferenced
mid-rule semantic value (@pxref{Mid-Rule Actions,,Actions in Mid-Rule}).
-That is, Bison does not consider a mid-rule to have a semantic value if you do
-not reference @code{$$} in the mid-rule's action or @code{$@var{n}} (where
-@var{n} is the RHS symbol position of the mid-rule) in any later action in that
-rule.
-However, if you do reference either, the Bison-generated parser will invoke the
-@code{<>} @code{%destructor} whenever it discards the mid-rule symbol.
+That is, Bison does not consider a mid-rule to have a semantic value if you
+do not reference @code{$$} in the mid-rule's action or @code{$@var{n}}
+(where @var{n} is the right-hand side symbol position of the mid-rule) in
+any later action in that rule. However, if you do reference either, the
+Bison-generated parser will invoke the @code{<>} @code{%destructor} whenever
+it discards the mid-rule symbol.
@ignore
@noindent
(Reentrant) Parser}.
If you have also used locations, the parser header file declares
-@code{YYLTYPE} and @code{yylloc} using a protocol similar to that of
-the @code{YYSTYPE} macro and @code{yylval}. @xref{Locations,
-,Tracking Locations}.
+@code{YYLTYPE} and @code{yylloc} using a protocol similar to that of the
+@code{YYSTYPE} macro and @code{yylval}. @xref{Tracking Locations}.
This parser header file is normally essential if you wish to put the
definition of @code{yylex} in a separate source file, because
@subsection Textual Locations of Tokens
@vindex yylloc
-If you are using the @samp{@@@var{n}}-feature (@pxref{Locations, ,
-Tracking Locations}) in actions to keep track of the textual locations
-of tokens and groupings, then you must provide this information in
-@code{yylex}. The function @code{yyparse} expects to find the textual
-location of a token just parsed in the global variable @code{yylloc}.
-So @code{yylex} must store the proper data in that variable.
+If you are using the @samp{@@@var{n}}-feature (@pxref{Tracking Locations})
+in actions to keep track of the textual locations of tokens and groupings,
+then you must provide this information in @code{yylex}. The function
+@code{yyparse} expects to find the textual location of a token just parsed
+in the global variable @code{yylloc}. So @code{yylex} must store the proper
+data in that variable.
By default, the value of @code{yylloc} is a structure and you need only
initialize the members that are going to be used by the actions. The
@deffn {Value} @@$
@findex @@$
-Acts like a structure variable containing information on the textual location
-of the grouping made by the current rule. @xref{Locations, ,
-Tracking Locations}.
+Acts like a structure variable containing information on the textual
+location of the grouping made by the current rule. @xref{Tracking
+Locations}.
@c Check if those paragraphs are still useful or not.
@deffn {Value} @@@var{n}
@findex @@@var{n}
-Acts like a structure variable containing information on the textual location
-of the @var{n}th component of the current rule. @xref{Locations, ,
-Tracking Locations}.
+Acts like a structure variable containing information on the textual
+location of the @var{n}th component of the current rule. @xref{Tracking
+Locations}.
@end deffn
@node Internationalization
of zero or more @code{word} groupings.
@example
+@group
sequence: /* empty */
@{ printf ("empty sequence\n"); @}
| maybeword
| sequence word
@{ printf ("added word %s\n", $2); @}
;
+@end group
+@group
maybeword: /* empty */
@{ printf ("empty maybeword\n"); @}
| word
@{ printf ("single word %s\n", $1); @}
;
+@end group
@end example
@noindent
from being empty:
@example
+@group
sequence: /* empty */
| sequence words
| sequence redirects
;
+@end group
+@group
words: word
| words word
;
+@end group
+@group
redirects:redirect
| redirects redirect
;
+@end group
@end example
@node Mysterious Conflicts
@example
typedef int foo, bar;
int baz (void)
+@group
@{
static bar (bar); /* @r{redeclare @code{bar} as static variable} */
extern foo foo (foo); /* @r{redeclare @code{foo} as function} */
return foo (bar);
@}
+@end group
@end example
Unfortunately, the name being declared is separated from the declaration
duplication, with actions omitted for brevity:
@example
+@group
initdcl:
declarator maybeasm '='
init
| declarator maybeasm
;
+@end group
+@group
notype_initdcl:
notype_declarator maybeasm '='
init
| notype_declarator maybeasm
;
+@end group
@end example
@noindent
and reports the uses of the symbols:
@example
+@group
Terminals, with rules where they appear
$end (0) 0
'/' (47) 4
error (256)
NUM (258) 5
+@end group
+@group
Nonterminals, with rules where they appear
$accept (8)
on left: 0
exp (9)
on left: 1 2 3 4 5, on right: 0 1 2 3 4
+@end group
@end example
@noindent
The remaining states are similar:
@example
+@group
state 9
exp -> exp . '+' exp (rule 1)
'/' [reduce using rule 2 (exp)]
$default reduce using rule 2 (exp)
+@end group
+@group
state 10
exp -> exp . '+' exp (rule 1)
'/' [reduce using rule 3 (exp)]
$default reduce using rule 3 (exp)
+@end group
+@group
state 11
exp -> exp . '+' exp (rule 1)
'*' [reduce using rule 4 (exp)]
'/' [reduce using rule 4 (exp)]
$default reduce using rule 4 (exp)
+@end group
@end example
@noindent
@c - %define filename_type "const symbol::Symbol"
When the directive @code{%locations} is used, the C++ parser supports
-location tracking, see @ref{Locations, , Locations Overview}. Two
-auxiliary classes define a @code{position}, a single point in a file,
-and a @code{location}, a range composed of a pair of
-@code{position}s (possibly spanning several files).
+location tracking, see @ref{Tracking Locations}. Two auxiliary classes
+define a @code{position}, a single point in a file, and a @code{location}, a
+range composed of a pair of @code{position}s (possibly spanning several
+files).
@deftypemethod {position} {std::string*} file
The name of the file. It will always be handled as a pointer, the
@comment file: calc++-scanner.ll
@example
+@group
%@{
# define YY_USER_ACTION yylloc->columns (yyleng);
%@}
+@end group
%%
%@{
yylloc->step ();
@comment file: calc++-scanner.ll
@example
+@group
void
calcxx_driver::scan_begin ()
@{
yyin = stdin;
else if (!(yyin = fopen (file.c_str (), "r")))
@{
- error (std::string ("cannot open ") + file);
- exit (1);
+ error (std::string ("cannot open ") + file + ": " + strerror(errno));
+ exit (EXIT_FAILURE);
@}
@}
+@end group
+@group
void
calcxx_driver::scan_end ()
@{
fclose (yyin);
@}
+@end group
@end example
@node Calc++ Top Level
#include <iostream>
#include "calc++-driver.hh"
+@group
int
main (int argc, char *argv[])
@{
else if (!driver.parse (*argv))
std::cout << driver.result << std::endl;
@}
+@end group
@end example
@node Java Parsers
@c - class Position
@c - class Location
-When the directive @code{%locations} is used, the Java parser
-supports location tracking, see @ref{Locations, , Locations Overview}.
-An auxiliary user-defined class defines a @dfn{position}, a single point
-in a file; Bison itself defines a class representing a @dfn{location},
-a range composed of a pair of positions (possibly spanning several
-files). The location class is an inner class of the parser; the name
-is @code{Location} by default, and may also be renamed using
-@code{%define location_type "@var{class-name}"}.
+When the directive @code{%locations} is used, the Java parser supports
+location tracking, see @ref{Tracking Locations}. An auxiliary user-defined
+class defines a @dfn{position}, a single point in a file; Bison itself
+defines a class representing a @dfn{location}, a range composed of a pair of
+positions (possibly spanning several files). The location class is an inner
+class of the parser; the name is @code{Location} by default, and may also be
+renamed using @code{%define location_type "@var{class-name}"}.
The location class treats the position as a completely opaque value.
By default, the class name is @code{Position}, but this can be changed
@node Memory Exhausted
@section Memory Exhausted
-@display
+@quotation
My parser returns with error with a @samp{memory exhausted}
message. What can I do?
-@end display
+@end quotation
This question is already addressed elsewhere, @xref{Recursion,
,Recursive Rules}.
The following phenomenon has several symptoms, resulting in the
following typical questions:
-@display
+@quotation
I invoke @code{yyparse} several times, and on correct input it works
properly; but when a parse error is found, all the other calls fail
too. How can I reset the error flag of @code{yyparse}?
-@end display
+@end quotation
@noindent
or
-@display
+@quotation
My parser includes support for an @samp{#include}-like feature, in
which case I run @code{yyparse} from @code{yyparse}. This fails
-although I did specify @code{%define api.pure}.
-@end display
+although I did specify @samp{%define api.pure}.
+@end quotation
These problems typically come not from Bison itself, but from
Lex-generated scanners. Because these scanners use large buffers for
demonstration, consider the following source file,
@file{first-line.l}:
-@verbatim
-%{
+@example
+@group
+%@{
#include <stdio.h>
#include <stdlib.h>
-%}
+%@}
+@end group
%%
.*\n ECHO; return 1;
%%
+@group
int
yyparse (char const *file)
-{
+@{
yyin = fopen (file, "r");
if (!yyin)
- exit (2);
+ @{
+ perror ("fopen");
+ exit (EXIT_FAILURE);
+ @}
+@end group
+@group
/* One token only. */
yylex ();
if (fclose (yyin) != 0)
- exit (3);
+ @{
+ perror ("fclose");
+ exit (EXIT_FAILURE);
+ @}
return 0;
-}
+@}
+@end group
+@group
int
main (void)
-{
+@{
yyparse ("input");
yyparse ("input");
return 0;
-}
-@end verbatim
+@}
+@end group
+@end example
@noindent
If the file @file{input} contains
-@verbatim
+@example
input:1: Hello,
input:2: World!
-@end verbatim
+@end example
@noindent
then instead of getting the first line twice, you get:
@node Strings are Destroyed
@section Strings are Destroyed
-@display
+@quotation
My parser seems to destroy old strings, or maybe it loses track of
them. Instead of reporting @samp{"foo", "bar"}, it reports
@samp{"bar", "bar"}, or even @samp{"foo\nbar", "bar"}.
-@end display
+@end quotation
This error is probably the single most frequent ``bug report'' sent to
Bison lists, but is only concerned with a misunderstanding of the role
of the scanner. Consider the following Lex code:
-@verbatim
-%{
+@example
+@group
+%@{
#include <stdio.h>
char *yylval = NULL;
-%}
+%@}
+@end group
+@group
%%
.* yylval = yytext; return 1;
\n /* IGNORE */
%%
+@end group
+@group
int
main ()
-{
+@{
/* Similar to using $1, $2 in a Bison action. */
char *fst = (yylex (), yylval);
char *snd = (yylex (), yylval);
printf ("\"%s\", \"%s\"\n", fst, snd);
return 0;
-}
-@end verbatim
+@}
+@end group
+@end example
If you compile and run this code, you get:
@node Implementing Gotos/Loops
@section Implementing Gotos/Loops
-@display
+@quotation
My simple calculator supports variables, assignments, and functions,
but how can I implement gotos, or loops?
-@end display
+@end quotation
Although very pedagogical, the examples included in the document blur
the distinction to make between the parser---whose job is to recover
@node Multiple start-symbols
@section Multiple start-symbols
-@display
+@quotation
I have several closely related grammars, and I would like to share their
implementations. In fact, I could use a single grammar but with
multiple entry points.
-@end display
+@end quotation
Bison does not support multiple start-symbols, but there is a very
simple means to simulate them. If @code{foo} and @code{bar} are the two
@node Secure? Conform?
@section Secure? Conform?
-@display
+@quotation
Is Bison secure? Does it conform to POSIX?
-@end display
+@end quotation
If you're looking for a guarantee or certification, we don't provide it.
However, Bison is intended to be a reliable program that conforms to the
@node I can't build Bison
@section I can't build Bison
-@display
+@quotation
I can't build Bison because @command{make} complains that
@code{msgfmt} is not found.
What should I do?
-@end display
+@end quotation
Like most GNU packages with internationalization support, that feature
is turned on by default. If you have problems building in the @file{po}
@node Where can I find help?
@section Where can I find help?
-@display
+@quotation
I'm having trouble using Bison. Where can I find help?
-@end display
+@end quotation
First, read this fine manual. Beyond that, you can send mail to
@email{help-bison@@gnu.org}. This mailing list is intended to be
@node Bug Reports
@section Bug Reports
-@display
+@quotation
I found a bug. What should I include in the bug report?
-@end display
+@end quotation
Before you send a bug report, make sure you are using the latest
version. Check @url{ftp://ftp.gnu.org/pub/gnu/bison/} or one of its
send additional files as well (such as `config.h' or `config.cache').
Patches are most welcome, but not required. That is, do not hesitate to
-send a bug report just because you can not provide a fix.
+send a bug report just because you cannot provide a fix.
Send bug reports to @email{bug-bison@@gnu.org}.
@node More Languages
@section More Languages
-@display
+@quotation
Will Bison ever have C++ and Java support? How about @var{insert your
favorite language here}?
-@end display
+@end quotation
C++ and Java support is there now, and is documented. We'd love to add other
languages; contributions are welcome.
@node Beta Testing
@section Beta Testing
-@display
+@quotation
What is involved in being a beta tester?
-@end display
+@end quotation
It's not terribly involved. Basically, you would download a test
release, compile it, and use it to build and run a parser or two. After
@node Mailing Lists
@section Mailing Lists
-@display
+@quotation
How do I join the help-bison and bug-bison mailing lists?
-@end display
+@end quotation
See @url{http://lists.gnu.org/}.
@deffn {Variable} @@$
In an action, the location of the left-hand side of the rule.
-@xref{Locations, , Locations Overview}.
+@xref{Tracking Locations}.
@end deffn
@deffn {Variable} @@@var{n}
-In an action, the location of the @var{n}-th symbol of the right-hand
-side of the rule. @xref{Locations, , Locations Overview}.
+In an action, the location of the @var{n}-th symbol of the right-hand side
+of the rule. @xref{Tracking Locations}.
@end deffn
@deffn {Variable} @@@var{name}
-In an action, the location of a symbol addressed by name.
-@xref{Locations, , Locations Overview}.
+In an action, the location of a symbol addressed by name. @xref{Tracking
+Locations}.
@end deffn
@deffn {Variable} @@[@var{name}]
-In an action, the location of a symbol addressed by name.
-@xref{Locations, , Locations Overview}.
+In an action, the location of a symbol addressed by name. @xref{Tracking
+Locations}.
@end deffn
@deffn {Variable} $$