order of the output and the exact presentation might vary, but the
interpretation is the same.
-The first section includes details on conflicts that were solved thanks
-to precedence and/or associativity:
-
-@example
-Conflict in state 8 between rule 2 and token '+' resolved as reduce.
-Conflict in state 8 between rule 2 and token '-' resolved as reduce.
-Conflict in state 8 between rule 2 and token '*' resolved as shift.
-@exdent @dots{}
-@end example
-
-@noindent
-The next section lists states that still have conflicts.
-
-@example
-State 8 conflicts: 1 shift/reduce
-State 9 conflicts: 1 shift/reduce
-State 10 conflicts: 1 shift/reduce
-State 11 conflicts: 4 shift/reduce
-@end example
-
@noindent
@cindex token, useless
@cindex useless token
@cindex useless nonterminal
@cindex rule, useless
@cindex useless rule
-The next section reports useless tokens, nonterminal and rules. Useless
-nonterminals and rules are removed in order to produce a smaller parser,
-but useless tokens are preserved, since they might be used by the
-scanner (note the difference between ``useless'' and ``unused''
-below):
+The first section reports useless tokens, nonterminals and rules. Useless
+nonterminals and rules are removed in order to produce a smaller parser, but
+useless tokens are preserved, since they might be used by the scanner (note
+the difference between ``useless'' and ``unused'' below):
@example
-Nonterminals useless in grammar:
+Nonterminals useless in grammar
useless
-Terminals unused in grammar:
+Terminals unused in grammar
STR
-Rules useless in grammar:
-#6 useless: STR;
+Rules useless in grammar
+ 6 useless: STR
@end example
@noindent
-The next section reproduces the exact grammar that Bison used:
+The next section lists states that still have conflicts.
+
+@example
+State 8 conflicts: 1 shift/reduce
+State 9 conflicts: 1 shift/reduce
+State 10 conflicts: 1 shift/reduce
+State 11 conflicts: 4 shift/reduce
+@end example
+
+@noindent
+Then Bison reproduces the exact grammar it used:
@example
Grammar
- Number, Line, Rule
- 0 5 $accept -> exp $end
- 1 5 exp -> exp '+' exp
- 2 6 exp -> exp '-' exp
- 3 7 exp -> exp '*' exp
- 4 8 exp -> exp '/' exp
- 5 9 exp -> NUM
+ 0 $accept: exp $end
+
+ 1 exp: exp '+' exp
+ 2 | exp '-' exp
+ 3 | exp '*' exp
+ 4 | exp '/' exp
+ 5 | NUM
@end example
@noindent
'/' (47) 4
error (256)
NUM (258) 5
+STR (259)
@end group
@group
Nonterminals, with rules where they appear
-$accept (8)
+$accept (9)
on left: 0
-exp (9)
+exp (10)
on left: 1 2 3 4 5, on right: 0 1 2 3 4
@end group
@end example
@example
state 0
- $accept -> . exp $ (rule 0)
+ 0 $accept: . exp $end
- NUM shift, and go to state 1
+ NUM shift, and go to state 1
- exp go to state 2
+ exp go to state 2
@end example
This reads as follows: ``state 0 corresponds to being at the very
@example
state 0
- $accept -> . exp $ (rule 0)
- exp -> . exp '+' exp (rule 1)
- exp -> . exp '-' exp (rule 2)
- exp -> . exp '*' exp (rule 3)
- exp -> . exp '/' exp (rule 4)
- exp -> . NUM (rule 5)
+ 0 $accept: . exp $end
+ 1 exp: . exp '+' exp
+ 2 | . exp '-' exp
+ 3 | . exp '*' exp
+ 4 | . exp '/' exp
+ 5 | . NUM
- NUM shift, and go to state 1
+ NUM shift, and go to state 1
- exp go to state 2
+ exp go to state 2
@end example
@noindent
-In the state 1...
+In the state 1@dots{}
@example
state 1
- exp -> NUM . (rule 5)
+ 5 exp: NUM .
- $default reduce using rule 5 (exp)
+ $default reduce using rule 5 (exp)
@end example
@noindent
@example
state 2
- $accept -> exp . $ (rule 0)
- exp -> exp . '+' exp (rule 1)
- exp -> exp . '-' exp (rule 2)
- exp -> exp . '*' exp (rule 3)
- exp -> exp . '/' exp (rule 4)
+ 0 $accept: exp . $end
+ 1 exp: exp . '+' exp
+ 2 | exp . '-' exp
+ 3 | exp . '*' exp
+ 4 | exp . '/' exp
- $ shift, and go to state 3
- '+' shift, and go to state 4
- '-' shift, and go to state 5
- '*' shift, and go to state 6
- '/' shift, and go to state 7
+ $end shift, and go to state 3
+ '+' shift, and go to state 4
+ '-' shift, and go to state 5
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
@end example
@noindent
In state 2, the automaton can only shift a symbol. For instance,
-because of the item @samp{exp -> exp . '+' exp}, if the lookahead is
+because of the item @samp{exp: exp . '+' exp}, if the lookahead is
@samp{+} it is shifted onto the parse stack, and the automaton
-jumps to state 4, corresponding to the item @samp{exp -> exp '+' . exp}.
+jumps to state 4, corresponding to the item @samp{exp: exp '+' . exp}.
Since there is no default action, any lookahead not listed triggers a syntax
error.
@example
state 3
- $accept -> exp $ . (rule 0)
+ 0 $accept: exp $end .
- $default accept
+ $default accept
@end example
@noindent
-the initial rule is completed (the start symbol and the end
-of input were read), the parsing exits successfully.
+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)
+ 1 exp: exp '+' . exp
- NUM shift, and go to state 1
+ NUM shift, and go to state 1
+
+ exp go to state 8
- exp go to state 8
state 5
- exp -> exp '-' . exp (rule 2)
+ 2 exp: exp '-' . exp
+
+ NUM shift, and go to state 1
- NUM shift, and go to state 1
+ exp go to state 9
- exp go to state 9
state 6
- exp -> exp '*' . exp (rule 3)
+ 3 exp: exp '*' . exp
- NUM shift, and go to state 1
+ NUM shift, and go to state 1
+
+ exp go to state 10
- exp go to state 10
state 7
- exp -> exp '/' . exp (rule 4)
+ 4 exp: exp '/' . exp
- NUM shift, and go to state 1
+ NUM shift, and go to state 1
- exp go to state 11
+ exp go to state 11
@end example
As was announced in beginning of the report, @samp{State 8 conflicts:
@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)
+ 1 exp: exp . '+' exp
+ 1 | exp '+' exp .
+ 2 | exp . '-' exp
+ 3 | exp . '*' exp
+ 4 | exp . '/' exp
- '*' shift, and go to state 6
- '/' shift, and go to state 7
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
- '/' [reduce using rule 1 (exp)]
- $default reduce using rule 1 (exp)
+ '/' [reduce using rule 1 (exp)]
+ $default reduce using rule 1 (exp)
@end example
Indeed, there are two actions associated to the lookahead @samp{/}:
Because in deterministic parsing a single decision can be made, Bison
arbitrarily chose to disable the reduction, see @ref{Shift/Reduce, ,
-Shift/Reduce Conflicts}. Discarded actions are reported in between
+Shift/Reduce Conflicts}. Discarded actions are reported between
square brackets.
Note that all the previous states had a single possible action: either
@example
state 8
- exp -> exp . '+' exp (rule 1)
- exp -> exp '+' exp . [$, '+', '-', '/'] (rule 1)
- exp -> exp . '-' exp (rule 2)
- exp -> exp . '*' exp (rule 3)
- exp -> exp . '/' exp (rule 4)
+ 1 exp: exp . '+' exp
+ 1 | exp '+' exp . [$end, '+', '-', '/']
+ 2 | exp . '-' exp
+ 3 | exp . '*' exp
+ 4 | exp . '/' exp
+
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
- '*' 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
+
+Note however that while @samp{NUM + NUM / NUM} is ambiguous (which results in
+the conflicts on @samp{/}), @samp{NUM + NUM * NUM} is not: the conflict was
+solved thanks to associativity and precedence directives. If invoked with
+@option{--report=solved}, Bison includes information about the solved
+conflicts in the report:
- '/' [reduce using rule 1 (exp)]
- $default reduce using rule 1 (exp)
+@example
+Conflict between rule 1 and token '+' resolved as reduce (%left '+').
+Conflict between rule 1 and token '-' resolved as reduce (%left '-').
+Conflict between rule 1 and token '*' resolved as shift ('+' < '*').
@end example
+
The remaining states are similar:
@example
@group
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)
+ 1 exp: exp . '+' exp
+ 2 | exp . '-' exp
+ 2 | exp '-' exp .
+ 3 | exp . '*' exp
+ 4 | exp . '/' exp
- '*' shift, and go to state 6
- '/' shift, and go to state 7
+ '*' shift, and go to state 6
+ '/' shift, and go to state 7
- '/' [reduce using rule 2 (exp)]
- $default reduce using rule 2 (exp)
+ '/' [reduce using rule 2 (exp)]
+ $default reduce using rule 2 (exp)
@end group
@group
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)
+ 1 exp: exp . '+' exp
+ 2 | exp . '-' exp
+ 3 | exp . '*' exp
+ 3 | exp '*' exp .
+ 4 | exp . '/' exp
- '/' shift, and go to state 7
+ '/' shift, and go to state 7
- '/' [reduce using rule 3 (exp)]
- $default reduce using rule 3 (exp)
+ '/' [reduce using rule 3 (exp)]
+ $default reduce using rule 3 (exp)
@end group
@group
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)
+ 1 exp: exp . '+' exp
+ 2 | exp . '-' exp
+ 3 | exp . '*' exp
+ 4 | exp . '/' exp
+ 4 | exp '/' exp .
+
+ '+' 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 group
@end example
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