8.2 Understanding Your Parser

Bison parsers are shift/reduce automata (see The Bison Parser Algorithm). In some cases (much more frequent than one would hope), looking at this automaton is required to tune or simply fix a parser.

The textual file is generated when the options --report or --verbose are specified, see Invoking Bison. Its name is made by removing ‘.tab.c’ or ‘.c’ from the parser implementation file name, and adding ‘.output’ instead. Therefore, if the grammar file is foo.y, then the parser implementation file is called foo.tab.c by default. As a consequence, the verbose output file is called foo.output.

The following grammar file, calc.y, will be used in the sequel:

%union
{
  int ival;
  const char *sval;
}

%token <ival> NUM
%nterm <ival> exp

%token <sval> STR
%nterm <sval> useless

%left '+' '-'
%left '*'

%%

exp:
  exp '+' exp
| exp '-' exp
| exp '*' exp
| exp '/' exp
| NUM
;

useless: STR;
%%

bison reports:

calc.y: warning: 1 nonterminal useless in grammar [-Wother]
calc.y: warning: 1 rule useless in grammar [-Wother]
calc.y:19.1-7: warning: nonterminal useless in grammar: useless [-Wother]
   19 | useless: STR;
      | ^~~~~~~
calc.y: warning: 7 shift/reduce conflicts [-Wconflicts-sr]
calc.y: note: rerun with option '-Wcounterexamples' to generate conflict counterexamples

Going back to the calc example, when given --report=state, in addition to calc.tab.c, it creates a file calc.output with contents detailed below. The order of the output and the exact presentation might vary, but the interpretation is the same.

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):

Nonterminals useless in grammar
   useless

Terminals unused in grammar
   STR

Rules useless in grammar
    6 useless: STR

The next section lists states that still have conflicts.

State 8 conflicts: 1 shift/reduce
State 9 conflicts: 1 shift/reduce
State 10 conflicts: 1 shift/reduce
State 11 conflicts: 4 shift/reduce

Then Bison reproduces the exact grammar it used:

Grammar

    0 $accept: exp $end

    1 exp: exp '+' exp
    2    | exp '-' exp
    3    | exp '*' exp
    4    | exp '/' exp
    5    | NUM

and reports the uses of the symbols:

Terminals, with rules where they appear

    $end (0) 0
    '*' (42) 3
    '+' (43) 1
    '-' (45) 2
    '/' (47) 4
    error (256)
    NUM <ival> (258) 5
    STR <sval> (259)

Nonterminals, with rules where they appear

    $accept (9)
        on left: 0
    exp <ival> (10)
        on left: 1 2 3 4 5
        on right: 0 1 2 3 4

Bison then proceeds onto the automaton itself, describing each state with its set of items, also known as dotted rules. Each item is a production rule together with a point (‘.’) marking the location of the input cursor.

State 0

    0 $accept: • exp $end

    NUM  shift, and go to state 1

    exp  go to state 2

This reads as follows: “state 0 corresponds to being at the very beginning of the parsing, in the initial rule, right before the start symbol (here, exp). When the parser returns to this state right after having reduced a rule that produced an exp, the control flow jumps to state 2. If there is no such transition on a nonterminal symbol, and the lookahead is a NUM, then this token is shifted onto the parse stack, and the control flow jumps to state 1. Any other lookahead triggers a syntax error.”

Even though the only active rule in state 0 seems to be rule 0, the report lists NUM as a lookahead token because NUM can be at the beginning of any rule deriving an exp. By default Bison reports the so-called core or kernel of the item set, but if you want to see more detail you can invoke bison with --report=itemset to list the derived items as well:

State 0

    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

    exp  go to state 2

In the state 1…

State 1

    5 exp: NUM •

    $default  reduce using rule 5 (exp)

the rule 5, ‘exp: NUM;’, is completed. Whatever the lookahead token (‘$default’), the parser will reduce it. If it was coming from State 0, then, after this reduction it will return to state 0, and will jump to state 2 (‘exp: go to state 2’).

State 2

    0 $accept: exp • $end
    1 exp: exp • '+' exp
    2    | exp • '-' exp
    3    | exp • '*' exp
    4    | exp • '/' exp

    $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

In state 2, the automaton can only shift a symbol. For instance, because of the item ‘exp: exp • '+' exp’, if the lookahead is ‘+’ it is shifted onto the parse stack, and the automaton jumps to state 4, corresponding to the item ‘exp: exp '+' • exp’. Since there is no default action, any lookahead not listed triggers a syntax error.

The state 3 is named the final state, or the accepting state:

State 3

    0 $accept: exp $end •

    $default  accept

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.

State 4

    1 exp: exp '+' • exp

    NUM  shift, and go to state 1

    exp  go to state 8


State 5

    2 exp: exp '-' • exp

    NUM  shift, and go to state 1

    exp  go to state 9


State 6

    3 exp: exp '*' • exp

    NUM  shift, and go to state 1

    exp  go to state 10


State 7

    4 exp: exp '/' • exp

    NUM  shift, and go to state 1

    exp  go to state 11

As was announced in beginning of the report, ‘State 8 conflicts: 1 shift/reduce’:

State 8

    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

    '/'       [reduce using rule 1 (exp)]
    $default  reduce using rule 1 (exp)

Indeed, there are two actions associated to the lookahead ‘/’: 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 ‘/’, the sentence ‘NUM + NUM / NUM’ can be parsed as ‘NUM + (NUM / NUM)’, which corresponds to shifting ‘/’, or as ‘(NUM + NUM) / NUM’, which corresponds to reducing rule 1.

Because in deterministic parsing a single decision can be made, Bison arbitrarily chose to disable the reduction, see Shift/Reduce Conflicts. Discarded actions are reported 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 and reducing is possible or when several reductions are possible, the lookahead is required to select the action. State 8 is one such state: if the lookahead is ‘*’ or ‘/’ 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 token is ‘*’, since we specified that ‘*’ has higher precedence than ‘+’. More generally, some items are eligible only with some set of possible lookahead tokens. When run with --report=lookahead, Bison specifies these lookahead tokens:

State 8

    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

    '/'       [reduce using rule 1 (exp)]
    $default  reduce using rule 1 (exp)

Note however that while ‘NUM + NUM / NUM’ is ambiguous (which results in the conflicts on ‘/’), ‘NUM + NUM * NUM’ is not: the conflict was solved thanks to associativity and precedence directives. If invoked with --report=solved, Bison includes information about the solved conflicts in the report:

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 ('+' < '*').

When given --report=counterexamples, bison will generate counterexamples within the report, augmented with the corresponding items (see Generation of Counterexamples).

shift/reduce conflict on token '/':
    1 exp: exp '+' exp •
    4 exp: exp • '/' exp

  Example: exp '+' exp • '/' exp
  Shift derivation
    exp
    ↳ 1: exp '+' exp
                 ↳ 4: exp • '/' exp
  Example: exp '+' exp • '/' exp
  Reduce derivation
    exp
    ↳ 4: exp                 '/' exp
         ↳ 1: exp '+' exp •

This shows two separate derivations in the grammar for the same exp: ‘e1 + e2 / e3’. The derivations show how your rules would parse the given example. Here, the first derivation completes a reduction when seeing ‘/’, causing ‘e1 + e2’ to be grouped as an exp. The second derivation shifts on ‘/’, resulting in ‘e2 / e3’ being grouped as an exp. Therefore, it is easy to see that adding precedence/associativity directives would fix this conflict.

The remaining states are similar:

State 9

    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

    '/'       [reduce using rule 2 (exp)]
    $default  reduce using rule 2 (exp)

State 10

    1 exp: exp • '+' exp
    2    | exp • '-' exp
    3    | exp • '*' exp
    3    | exp '*' exp •
    4    | exp • '/' exp

    '/'  shift, and go to state 7

    '/'       [reduce using rule 3 (exp)]
    $default  reduce using rule 3 (exp)

State 11

    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)

Observe that state 11 contains conflicts not only due to the lack of precedence of ‘/’ with respect to ‘+’, ‘-’, and ‘*’, but also because the associativity of ‘/’ is not specified.

Bison may also produce an HTML version of this output, via an XML file and XSLT processing (see Visualizing your parser in multiple formats).