+@noindent
+the initial rule is completed (the start symbol and the end
+of input were read), the parsing exits successfully.
+
+The interpretation of states 4 to 7 is straightforward, and is left to
+the reader.
+
+@example
+state 4
+
+ exp -> exp '+' . exp (rule 1)
+
+ NUM shift, and go to state 1
+
+ exp go to state 8
+
+state 5
+
+ exp -> exp '-' . exp (rule 2)
+
+ NUM shift, and go to state 1
+
+ exp go to state 9
+
+state 6
+
+ exp -> exp '*' . exp (rule 3)
+
+ NUM shift, and go to state 1
+
+ exp go to state 10
+
+state 7
+
+ exp -> exp '/' . exp (rule 4)
+
+ NUM shift, and go to state 1
+
+ exp go to state 11
+@end example
+
+As was announced in beginning of the report, @samp{State 8 conflicts:
+1 shift/reduce}:
+
+@example
+state 8
+
+ exp -> exp . '+' exp (rule 1)
+ exp -> exp '+' exp . (rule 1)
+ exp -> exp . '-' exp (rule 2)
+ exp -> exp . '*' exp (rule 3)
+ exp -> exp . '/' exp (rule 4)
+
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
+
+ '/' [reduce using rule 1 (exp)]
+ $default reduce using rule 1 (exp)
+@end example
+
+Indeed, there are two actions associated to the lookahead @samp{/}:
+either shifting (and going to state 7), or reducing rule 1. The
+conflict means that either the grammar is ambiguous, or the parser lacks
+information to make the right decision. Indeed the grammar is
+ambiguous, as, since we did not specify the precedence of @samp{/}, the
+sentence @samp{NUM + NUM / NUM} can be parsed as @samp{NUM + (NUM /
+NUM)}, which corresponds to shifting @samp{/}, or as @samp{(NUM + NUM) /
+NUM}, which corresponds to reducing rule 1.
+
+Because in @acronym{LALR}(1) parsing a single decision can be made, Bison
+arbitrarily chose to disable the reduction, see @ref{Shift/Reduce, ,
+Shift/Reduce Conflicts}. Discarded actions are reported in between
+square brackets.
+
+Note that all the previous states had a single possible action: either
+shifting the next token and going to the corresponding state, or
+reducing a single rule. In the other cases, i.e., when shifting
+@emph{and} reducing is possible or when @emph{several} reductions are
+possible, the lookahead is required to select the action. State 8 is
+one such state: if the lookahead is @samp{*} or @samp{/} then the action
+is shifting, otherwise the action is reducing rule 1. In other words,
+the first two items, corresponding to rule 1, are not eligible when the
+lookahead is @samp{*}, since we specified that @samp{*} has higher
+precedence that @samp{+}. More generally, some items are eligible only
+with some set of possible lookaheads. When run with
+@option{--report=lookahead}, Bison specifies these lookaheads:
+
+@example
+state 8
+
+ exp -> exp . '+' exp [$, '+', '-', '/'] (rule 1)
+ exp -> exp '+' exp . [$, '+', '-', '/'] (rule 1)
+ exp -> exp . '-' exp (rule 2)
+ exp -> exp . '*' exp (rule 3)
+ exp -> exp . '/' exp (rule 4)
+
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
+
+ '/' [reduce using rule 1 (exp)]
+ $default reduce using rule 1 (exp)
+@end example
+
+The remaining states are similar:
+
+@example
+state 9
+
+ exp -> exp . '+' exp (rule 1)
+ exp -> exp . '-' exp (rule 2)
+ exp -> exp '-' exp . (rule 2)
+ exp -> exp . '*' exp (rule 3)
+ exp -> exp . '/' exp (rule 4)
+
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
+
+ '/' [reduce using rule 2 (exp)]
+ $default reduce using rule 2 (exp)
+
+state 10
+
+ exp -> exp . '+' exp (rule 1)
+ exp -> exp . '-' exp (rule 2)
+ exp -> exp . '*' exp (rule 3)
+ exp -> exp '*' exp . (rule 3)
+ exp -> exp . '/' exp (rule 4)
+
+ '/' shift, and go to state 7
+
+ '/' [reduce using rule 3 (exp)]
+ $default reduce using rule 3 (exp)
+
+state 11
+
+ exp -> exp . '+' exp (rule 1)
+ exp -> exp . '-' exp (rule 2)
+ exp -> exp . '*' exp (rule 3)
+ exp -> exp . '/' exp (rule 4)
+ exp -> exp '/' exp . (rule 4)
+
+ '+' shift, and go to state 4
+ '-' shift, and go to state 5
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
+
+ '+' [reduce using rule 4 (exp)]
+ '-' [reduce using rule 4 (exp)]
+ '*' [reduce using rule 4 (exp)]
+ '/' [reduce using rule 4 (exp)]
+ $default reduce using rule 4 (exp)
+@end example
+
+@noindent
+Observe that state 11 contains conflicts due to the lack of precedence
+of @samp{/} wrt @samp{+}, @samp{-}, and @samp{*}, but also because the
+associativity of @samp{/} is not specified.
+
+
+@node Tracing
+@section Tracing Your Parser
+@findex yydebug
+@cindex debugging
+@cindex tracing the parser
+
+If a Bison grammar compiles properly but doesn't do what you want when it
+runs, the @code{yydebug} parser-trace feature can help you figure out why.
+
+There are several means to enable compilation of trace facilities:
+
+@table @asis
+@item the macro @code{YYDEBUG}
+@findex YYDEBUG
+Define the macro @code{YYDEBUG} to a nonzero value when you compile the
+parser. This is compliant with @acronym{POSIX} Yacc. You could use
+@samp{-DYYDEBUG=1} as a compiler option or you could put @samp{#define
+YYDEBUG 1} in the prologue of the grammar file (@pxref{Prologue, , The
+Prologue}).
+
+@item the option @option{-t}, @option{--debug}
+Use the @samp{-t} option when you run Bison (@pxref{Invocation,
+,Invoking Bison}). This is @acronym{POSIX} compliant too.
+
+@item the directive @samp{%debug}
+@findex %debug
+Add the @code{%debug} directive (@pxref{Decl Summary, ,Bison
+Declaration Summary}). This is a Bison extension, which will prove
+useful when Bison will output parsers for languages that don't use a
+preprocessor. Unless @acronym{POSIX} and Yacc portability matter to
+you, this is
+the preferred solution.
+@end table
+
+We suggest that you always enable the debug option so that debugging is
+always possible.
+
+The trace facility outputs messages with macro calls of the form
+@code{YYFPRINTF (stderr, @var{format}, @var{args})} where
+@var{format} and @var{args} are the usual @code{printf} format and
+arguments. If you define @code{YYDEBUG} to a nonzero value but do not
+define @code{YYFPRINTF}, @code{<stdio.h>} is automatically included
+and @code{YYPRINTF} is defined to @code{fprintf}.
+
+Once you have compiled the program with trace facilities, the way to
+request a trace is to store a nonzero value in the variable @code{yydebug}.
+You can do this by making the C code do it (in @code{main}, perhaps), or
+you can alter the value with a C debugger.
+
+Each step taken by the parser when @code{yydebug} is nonzero produces a
+line or two of trace information, written on @code{stderr}. The trace
+messages tell you these things:
+
+@itemize @bullet
+@item
+Each time the parser calls @code{yylex}, what kind of token was read.
+
+@item
+Each time a token is shifted, the depth and complete contents of the
+state stack (@pxref{Parser States}).
+
+@item
+Each time a rule is reduced, which rule it is, and the complete contents
+of the state stack afterward.
+@end itemize
+
+To make sense of this information, it helps to refer to the listing file
+produced by the Bison @samp{-v} option (@pxref{Invocation, ,Invoking
+Bison}). This file shows the meaning of each state in terms of
+positions in various rules, and also what each state will do with each
+possible input token. As you read the successive trace messages, you
+can see that the parser is functioning according to its specification in
+the listing file. Eventually you will arrive at the place where
+something undesirable happens, and you will see which parts of the
+grammar are to blame.
+
+The parser file is a C program and you can use C debuggers on it, but it's
+not easy to interpret what it is doing. The parser function is a
+finite-state machine interpreter, and aside from the actions it executes
+the same code over and over. Only the values of variables show where in
+the grammar it is working.
+
+@findex YYPRINT
+The debugging information normally gives the token type of each token
+read, but not its semantic value. You can optionally define a macro
+named @code{YYPRINT} to provide a way to print the value. If you define
+@code{YYPRINT}, it should take three arguments. The parser will pass a
+standard I/O stream, the numeric code for the token type, and the token
+value (from @code{yylval}).
+
+Here is an example of @code{YYPRINT} suitable for the multi-function
+calculator (@pxref{Mfcalc Decl, ,Declarations for @code{mfcalc}}):
+
+@smallexample
+%@{
+ static void print_token_value (FILE *, int, YYSTYPE);
+ #define YYPRINT(file, type, value) print_token_value (file, type, value)
+%@}
+
+@dots{} %% @dots{} %% @dots{}
+
+static void
+print_token_value (FILE *file, int type, YYSTYPE value)
+@{
+ if (type == VAR)
+ fprintf (file, "%s", value.tptr->name);
+ else if (type == NUM)
+ fprintf (file, "%d", value.val);
+@}
+@end smallexample
+
+@c ================================================= Invoking Bison
+
+@node Invocation
+@chapter Invoking Bison
+@cindex invoking Bison
+@cindex Bison invocation
+@cindex options for invoking Bison
+
+The usual way to invoke Bison is as follows:
+
+@example
+bison @var{infile}
+@end example
+
+Here @var{infile} is the grammar file name, which usually ends in
+@samp{.y}. The parser file's name is made by replacing the @samp{.y}
+with @samp{.tab.c}. Thus, the @samp{bison foo.y} filename yields
+@file{foo.tab.c}, and the @samp{bison hack/foo.y} filename yields
+@file{hack/foo.tab.c}. It's also possible, in case you are writing
+C++ code instead of C in your grammar file, to name it @file{foo.ypp}
+or @file{foo.y++}. Then, the output files will take an extension like
+the given one as input (respectively @file{foo.tab.cpp} and
+@file{foo.tab.c++}).
+This feature takes effect with all options that manipulate filenames like
+@samp{-o} or @samp{-d}.
+
+For example :
+
+@example
+bison -d @var{infile.yxx}
+@end example
+@noindent
+will produce @file{infile.tab.cxx} and @file{infile.tab.hxx}, and
+
+@example
+bison -d -o @var{output.c++} @var{infile.y}
+@end example
+@noindent
+will produce @file{output.c++} and @file{outfile.h++}.
+
+For compatibility with @acronym{POSIX}, the standard Bison
+distribution also contains a shell script called @command{yacc} that
+invokes Bison with the @option{-y} option.
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