sly/docs/sly.rst

SLY (Sly Lex Yacc)
==================

This document provides an overview of lexing and parsing with SLY.
Given the intrinsic complexity of parsing, I would strongly advise
that you read (or at least skim) this entire document before jumping
into a big development project with SLY.

SLY requires Python 3.6 or newer.  If you're using an older version,
you're out of luck. Sorry.

Introduction
------------
SLY is library for writing parsers and compilers.  It is loosely
based on the traditional compiler construction tools lex and yacc
and implements the same LALR(1) parsing algorithm.  Most of the
features available in lex and yacc are also available in SLY.
It should also be noted that SLY does not provide much in
the way of bells and whistles (e.g., automatic construction of
abstract syntax trees, tree traversal, etc.). Nor should you view it
as a parsing framework. Instead, you will find a bare-bones, yet
fully capable library for writing parsers in Python.

The rest of this document assumes that you are somewhat familiar with
parsing theory, syntax directed translation, and the use of compiler
construction tools such as lex and yacc in other programming
languages. If you are unfamiliar with these topics, you will probably
want to consult an introductory text such as "Compilers: Principles,
Techniques, and Tools", by Aho, Sethi, and Ullman.  O'Reilly's "Lex
and Yacc" by John Levine may also be handy.  In fact, the O'Reilly book can be
used as a reference for SLY as the concepts are virtually identical.

SLY Overview
------------

SLY provides two separate classes ``Lexer`` and ``Parser``.  The
``Lexer`` class is used to break input text into a collection of
tokens specified by a collection of regular expression rules.  The
``Parser`` class is used to recognize language syntax that has been
specified in the form of a context free grammar.    The two classes
are typically used together to make a parser.  However, this is not
a strict requirement--there is a great deal of flexibility allowed.
The next two parts describe the basics.

Writing a Lexer
---------------

Suppose you're writing a programming language and you wanted to parse the
following input string::

    x = 3 + 42 * (s - t)

The first step of parsing is to break the text into tokens where
each token has a type and value. For example, the above text might be
described by the following list of token tuples::

    [ ('ID','x'), ('EQUALS','='), ('NUMBER','3'),
      ('PLUS','+'), ('NUMBER','42'), ('TIMES','*'),
      ('LPAREN','('), ('ID','s'), ('MINUS','-'),
      ('ID','t'), ('RPAREN',')') ]

The SLY ``Lexer`` class is used to do this.   Here is a sample of a simple
lexer that tokenizes the above text::

    # calclex.py

    from sly import Lexer

    class CalcLexer(Lexer):
        # Set of token names.   This is always required
        tokens = { ID, NUMBER, PLUS, MINUS, TIMES,
                   DIVIDE, ASSIGN, LPAREN, RPAREN }

        # String containing ignored characters between tokens
        ignore = ' \t'

        # Regular expression rules for tokens
        ID      = r'[a-zA-Z_][a-zA-Z0-9_]*'
        NUMBER  = r'\d+'
        PLUS    = r'\+'
        MINUS   = r'-'
        TIMES   = r'\*'
        DIVIDE  = r'/'
        ASSIGN  = r'='
        LPAREN  = r'\('
        RPAREN  = r'\)'

    if __name__ == '__main__':
        data = 'x = 3 + 42 * (s - t)'
        lexer = CalcLexer()
        for tok in lexer.tokenize(data):
            print('type=%r, value=%r' % (tok.type, tok.value))

When executed, the example will produce the following output::

    type='ID', value='x'
    type='ASSIGN', value='='
    type='NUMBER', value='3'
    type='PLUS', value='+'
    type='NUMBER', value='42'
    type='TIMES', value='*'
    type='LPAREN', value='('
    type='ID', value='s'
    type='MINUS', value='-'
    type='ID', value='t'
    type='RPAREN', value=')'

A lexer only has one public method ``tokenize()``.  This is a generator
function that produces a stream of ``Token`` instances.
The ``type`` and ``value`` attributes of ``Token`` contain the
token type name and value respectively.

The tokens set
^^^^^^^^^^^^^^^

Lexers must specify a ``tokens`` set that defines all of the possible
token type names that can be produced by the lexer.  This is always
required and is used to perform a variety of validation checks.

In the example, the following code specified the token names::

    class CalcLexer(Lexer):
        ...
        # Set of token names.   This is always required
        tokens = { ID, NUMBER, PLUS, MINUS, TIMES,
                   DIVIDE, ASSIGN, LPAREN, RPAREN }
        ...

Token names should be specified using all-caps as shown.

Specification of token match patterns
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Tokens are specified by writing a regular expression rule compatible
with the ``re`` module.  The name of each rule must match one of the
names of the tokens provided in the ``tokens`` set.  For example::

    PLUS = r'\+'
    MINUS = r'-'

Tokens are matched in the same order that patterns are listed in the
``Lexer`` class.  Longer tokens always need to be specified before
short tokens.  For example, if you wanted to have separate tokens for
``=`` and ``==``, you need to make sure that ``==`` is listed first.  For
example::

    class MyLexer(Lexer):
        tokens = { ASSIGN, EQ, ...}
        ...
        EQ     = r'=='       # MUST APPEAR FIRST! (LONGER)
        ASSIGN = r'='

Discarded text
^^^^^^^^^^^^^^

The special ``ignore`` specification is reserved for single characters
that should be completely ignored between tokens in the input stream.
Usually this is used to skip over whitespace and other non-essential
characters.  The characters given in ``ignore`` are not ignored when
such characters are part of other regular expression patterns.  For
example, if you had a rule to capture quoted text, that pattern can
include the ignored characters (which will be captured in the normal
way).  The main purpose of ``ignore`` is to ignore whitespace and
other padding between the tokens that you actually want to parse.

You can also discard more specialized text patterns by writing special
regular expression rules with a name that includes the prefix
``ignore_``.  For example, this lexer includes rules to ignore
comments and newlines::

    # calclex.py

    from sly import Lexer

    class CalcLexer(Lexer):
        ...
        # String containing ignored characters (between tokens)
        ignore = ' \t'

        # Other ignored patterns
        ignore_comment = r'\#.*'
        ignore_newline = r'\n+'
        ...

    if __name__ == '__main__':
        data = '''x = 3 + 42
                    * (s    # This is a comment
                        - t)'''
        lexer = CalcLexer()
        for tok in lexer.tokenize(data):
            print('type=%r, value=%r' % (tok.type, tok.value))


Adding Match Actions
^^^^^^^^^^^^^^^^^^^^

When certain tokens are matched, you may want to trigger some kind of
action that performs extra processing.  For example, converting
a numeric value or looking up language keywords.  One way to do this
is to write your action as a method and give the associated regular
expression using the ``@_()`` decorator like this::

    @_(r'\d+')
    def NUMBER(self, t):
        t.value = int(t.value)   # Convert to a numeric value
        return t

The method always takes a single argument which is an instance of
type ``Token``.  By default, ``t.type`` is set to the name of the token
(e.g., ``'NUMBER'``).  The function can change the token type and
value as it sees appropriate.  When finished, the resulting token
object should be returned as a result. If no value is returned by the
function, the token is discarded and the next token read.

The ``@_()`` decorator is defined automatically within the ``Lexer``
class--you don't need to do any kind of special import for it.
It can also accept multiple regular expression rules. For example::

    @_(r'0x[0-9a-fA-F]+',
       r'\d+')
    def NUMBER(self, t):
        if t.value.startswith('0x'):
            t.value = int(t.value[2:], 16)
        else:
            t.value = int(t.value)
        return t

Instead of using the ``@_()`` decorator, you can also write a method
that matches the same name as a token previously specified as a
string. For example::

    NUMBER = r'\d+'
    ...
    def NUMBER(self, t):
        t.value = int(t.value)
        return t

This is potentially useful trick for debugging a lexer.  You can temporarily
attach a method a token and have it execute when the token is encountered.
If you later take the method away, the lexer will revert back to its original
behavior.

Token Remapping
^^^^^^^^^^^^^^^

Occasionally, you might need to remap tokens based on special cases.
Consider the case of matching identifiers such as "abc", "python", or "guido".
Certain identifiers such as "if", "else", and "while" might need to be
treated as special keywords.  To handle this, include token remapping rules when
writing the lexer like this::

    # calclex.py

    from sly import Lexer

    class CalcLexer(Lexer):
        tokens = { ID, IF, ELSE, WHILE }
        # String containing ignored characters (between tokens)
        ignore = ' \t'

        # Base ID rule
        ID = r'[a-zA-Z_][a-zA-Z0-9_]*'

        # Special cases
        ID['if'] = IF
        ID['else'] = ELSE
        ID['while'] = WHILE

When parsing an identifier, the special cases will remap certain matching
values to a new token type.  For example, if the value of an identifier is
"if" above, an ``IF`` token will be generated.

Line numbers and position tracking
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

By default, lexers know nothing about line numbers.  This is because
they don't know anything about what constitutes a "line" of input
(e.g., the newline character or even if the input is textual data).
To update this information, you need to add a special rule for newlines.
Promote the ``ignore_newline`` rule to a method like this::

    # Define a rule so we can track line numbers
    @_(r'\n+')
    def ignore_newline(self, t):
        self.lineno += len(t.value)

Within the rule, the lineno attribute of the lexer is now updated.
After the line number is updated, the token is discarded since nothing
is returned.

Lexers do not perform and kind of automatic column tracking.  However,
it does record positional information related to each token in the token's
``index`` attribute.  Using this, it is usually possible to compute
column information as a separate step.  For instance, you can search
backwards until you reach the previous newline::

    # Compute column.
    #     input is the input text string
    #     token is a token instance
    def find_column(text, token):
        last_cr = text.rfind('\n', 0, token.index)
        if last_cr < 0:
            last_cr = 0
        column = (token.index - last_cr) + 1
        return column

Since column information is often only useful in the context of error
handling, calculating the column position can be performed when needed
as opposed to including it on each token.

Literal characters
^^^^^^^^^^^^^^^^^^

Literal characters can be specified by defining a set
``literals`` in the class.  For example::

     class MyLexer(Lexer):
         ...
         literals = { '+','-','*','/' }
         ...

A literal character is a *single character* that is returned "as
is" when encountered by the lexer.  Literals are checked after all of
the defined regular expression rules.  Thus, if a rule starts with one
of the literal characters, it will always take precedence.

When a literal token is returned, both its ``type`` and ``value``
attributes are set to the character itself. For example, ``'+'``.

It's possible to write token methods that perform additional actions
when literals are matched.  However, you'll need to set the token type
appropriately. For example::

     class MyLexer(Lexer):

          literals = { '{', '}' }

          def __init__(self):
              self.nesting_level = 0

          @_(r'\{')
          def lbrace(self, t):
              t.type = '{'      # Set token type to the expected literal
	      self.nesting_level += 1
              return t

          @_(r'\}')
          def rbrace(t):
              t.type = '}'      # Set token type to the expected literal
	      self.nesting_level -=1
              return t

Error handling
^^^^^^^^^^^^^^

If a bad character is encountered while lexing, tokenizing will stop.
However, you can add an ``error()`` method to handle lexing errors
that occur when illegal characters are detected.  The error method
receives a ``Token`` where the ``value`` attribute contains all
remaining untokenized text.  A typical handler might look at this text
and skip ahead in some manner.  For example::

    class MyLexer(Lexer):
        ...
        # Error handling rule
        def error(self, t):
            print("Illegal character '%s'" % t.value[0])
            self.index += 1

In this case, we print the offending character and skip ahead
one character by updating the lexer position.   Error handling in a
parser is often a hard problem.  An error handler might scan ahead
to a logical synchronization point such as a semicolon, a blank line,
or similar landmark.

If the ``error()`` method also returns the passed token, it will
show up as an ``ERROR`` token in the resulting token stream. This
might be useful if the parser wants to see error tokens for some
reason--perhaps for the purposes of improved error messages or
some other kind of error handling.

Third-Party Regex Module
^^^^^^^^^^^^^^^^^^^^^^^^

.. versionadded:: 0.4

The third-party `regex <https://pypi.org/project/regex/>`_ module can be used
with sly. Like this::

    from sly import Lexer
    import regex

    class MyLexer(Lexer):
        regex_module = regex
        ...

Now all regular expressions that ``MyLexer`` uses will be handled with the
``regex`` module. The ``regex_module`` can be set to any module that is
compatible with Python's standard library ``re``.


A More Complete Example
^^^^^^^^^^^^^^^^^^^^^^^

Here is a more complete example that puts many of these concepts
into practice::

    # calclex.py

    from sly import Lexer

    class CalcLexer(Lexer):
        # Set of token names.   This is always required
        tokens = { NUMBER, ID, WHILE, IF, ELSE, PRINT,
                   PLUS, MINUS, TIMES, DIVIDE, ASSIGN,
                   EQ, LT, LE, GT, GE, NE }


        literals = { '(', ')', '{', '}', ';' }

        # String containing ignored characters
        ignore = ' \t'

        # Regular expression rules for tokens
        PLUS    = r'\+'
        MINUS   = r'-'
        TIMES   = r'\*'
        DIVIDE  = r'/'
        EQ      = r'=='
        ASSIGN  = r'='
        LE      = r'<='
        LT      = r'<'
        GE      = r'>='
        GT      = r'>'
        NE      = r'!='

        @_(r'\d+')
        def NUMBER(self, t):
            t.value = int(t.value)
            return t

        # Identifiers and keywords
        ID = r'[a-zA-Z_][a-zA-Z0-9_]*'
        ID['if'] = IF
        ID['else'] = ELSE
        ID['while'] = WHILE
        ID['print'] = PRINT

        ignore_comment = r'\#.*'

        # Line number tracking
        @_(r'\n+')
        def ignore_newline(self, t):
            self.lineno += t.value.count('\n')

        def error(self, t):
            print('Line %d: Bad character %r' % (self.lineno, t.value[0]))
            self.index += 1

    if __name__ == '__main__':
        data = '''
    # Counting
    x = 0;
    while (x < 10) {
        print x:
        x = x + 1;
    }
    '''
        lexer = CalcLexer()
        for tok in lexer.tokenize(data):
            print(tok)

If you run this code, you'll get output that looks like this::

    Token(type='ID', value='x', lineno=3, index=20)
    Token(type='ASSIGN', value='=', lineno=3, index=22)
    Token(type='NUMBER', value=0, lineno=3, index=24)
    Token(type=';', value=';', lineno=3, index=25)
    Token(type='WHILE', value='while', lineno=4, index=31)
    Token(type='(', value='(', lineno=4, index=37)
    Token(type='ID', value='x', lineno=4, index=38)
    Token(type='LT', value='<', lineno=4, index=40)
    Token(type='NUMBER', value=10, lineno=4, index=42)
    Token(type=')', value=')', lineno=4, index=44)
    Token(type='{', value='{', lineno=4, index=46)
    Token(type='PRINT', value='print', lineno=5, index=56)
    Token(type='ID', value='x', lineno=5, index=62)
    Line 5: Bad character ':'
    Token(type='ID', value='x', lineno=6, index=73)
    Token(type='ASSIGN', value='=', lineno=6, index=75)
    Token(type='ID', value='x', lineno=6, index=77)
    Token(type='PLUS', value='+', lineno=6, index=79)
    Token(type='NUMBER', value=1, lineno=6, index=81)
    Token(type=';', value=';', lineno=6, index=82)
    Token(type='}', value='}', lineno=7, index=88)

Study this example closely.  It might take a bit to digest, but all of the
essential parts of writing a lexer are there. Tokens have to be specified
with regular expression rules. You can optionally attach actions that
execute when certain patterns are encountered.  Certain features such as
character literals are there mainly for convenience, saving you the trouble
of writing separate regular expression rules. You can also add error handling.

Writing a Parser
----------------

The ``Parser`` class is used to parse language syntax.  Before showing
an example, there are a few important bits of background that must be
covered.

Parsing Background
^^^^^^^^^^^^^^^^^^
When writing a parser, *syntax* is usually specified in terms of a BNF
grammar.  For example, if you wanted to parse simple arithmetic
expressions, you might first write an unambiguous grammar
specification like this::

    expr       : expr + term
               | expr - term
               | term

    term       : term * factor
               | term / factor
               | factor

    factor     : NUMBER
               | ( expr )

In the grammar, symbols such as ``NUMBER``, ``+``, ``-``, ``*``, and
``/`` are known as *terminals* and correspond to raw input tokens.
Identifiers such as ``term`` and ``factor`` refer to grammar rules
comprised of a collection of terminals and other rules.  These
identifiers are known as *non-terminals*.  The separation of the
grammar into different levels (e.g., ``expr`` and ``term``) encodes
the operator precedence rules for the different operations. In this
case, multiplication and division have higher precedence than addition
and subtraction.

The semantics of what happens during parsing is often specified using
a technique known as syntax directed translation.  In syntax directed
translation, the symbols in the grammar become a kind of
object. Values can be attached each symbol and operations carried out
on those values when different grammar rules are recognized.  For
example, given the expression grammar above, you might write the
specification for the operation of a simple calculator like this::

    Grammar                   Action
    ------------------------  --------------------------------
    expr0   : expr1 + term    expr0.val = expr1.val + term.val
            | expr1 - term    expr0.val = expr1.val - term.val
            | term            expr0.val = term.val

    term0   : term1 * factor  term0.val = term1.val * factor.val
            | term1 / factor  term0.val = term1.val / factor.val
            | factor          term0.val = factor.val

    factor  : NUMBER          factor.val = int(NUMBER.val)
            | ( expr )        factor.val = expr.val

In this grammar, new values enter via the ``NUMBER`` token.  Those
values then propagate according to the actions described above.  For
example, ``factor.val = int(NUMBER.val)`` propagates the value from
``NUMBER`` to ``factor``.  ``term0.val = factor.val`` propagates the
value from ``factor`` to ``term``.  Rules such as ``expr0.val =
expr1.val + term1.val`` combine and propagate values further. Just to
illustrate, here is how values propagate in the expression ``2 + 3 * 4``::

     NUMBER.val=2 + NUMBER.val=3 * NUMBER.val=4    # NUMBER -> factor
     factor.val=2 + NUMBER.val=3 * NUMBER.val=4    # factor -> term
     term.val=2 + NUMBER.val=3 * NUMBER.val=4      # term -> expr
     expr.val=2 + NUMBER.val=3 * NUMBER.val=4      # NUMBER -> factor
     expr.val=2 + factor.val=3 * NUMBER.val=4      # factor -> term
     expr.val=2 + term.val=3 * NUMBER.val=4        # NUMBER -> factor
     expr.val=2 + term.val=3 * factor.val=4        # term * factor -> term
     expr.val=2 + term.val=12                      # expr + term -> expr
     expr.val=14

SLY uses a parsing technique known as LR-parsing or shift-reduce
parsing.  LR parsing is a bottom up technique that tries to recognize
the right-hand-side of various grammar rules.  Whenever a valid
right-hand-side is found in the input, the appropriate action method
is triggered and the grammar symbols on right hand side are replaced
by the grammar symbol on the left-hand-side.

LR parsing is commonly implemented by shifting grammar symbols onto a
stack and looking at the stack and the next input token for patterns
that match one of the grammar rules.  The details of the algorithm can
be found in a compiler textbook, but the following example illustrates
the steps that are performed when parsing the expression ``3 + 5 * (10
- 20)`` using the grammar defined above.  In the example, the special
symbol ``$`` represents the end of input::

    Step Symbol Stack           Input Tokens            Action
    ---- ---------------------  ---------------------   -------------------------------
    1                           3 + 5 * ( 10 - 20 )$    Shift 3
    2    3                        + 5 * ( 10 - 20 )$    Reduce factor : NUMBER
    3    factor                   + 5 * ( 10 - 20 )$    Reduce term   : factor
    4    term                     + 5 * ( 10 - 20 )$    Reduce expr : term
    5    expr                     + 5 * ( 10 - 20 )$    Shift +
    6    expr +                     5 * ( 10 - 20 )$    Shift 5
    7    expr + 5                     * ( 10 - 20 )$    Reduce factor : NUMBER
    8    expr + factor                * ( 10 - 20 )$    Reduce term   : factor
    9    expr + term                  * ( 10 - 20 )$    Shift *
    10   expr + term *                  ( 10 - 20 )$    Shift (
    11   expr + term * (                  10 - 20 )$    Shift 10
    12   expr + term * ( 10                  - 20 )$    Reduce factor : NUMBER
    13   expr + term * ( factor              - 20 )$    Reduce term : factor
    14   expr + term * ( term                - 20 )$    Reduce expr : term
    15   expr + term * ( expr                - 20 )$    Shift -
    16   expr + term * ( expr -                20 )$    Shift 20
    17   expr + term * ( expr - 20                )$    Reduce factor : NUMBER
    18   expr + term * ( expr - factor            )$    Reduce term : factor
    19   expr + term * ( expr - term              )$    Reduce expr : expr - term
    20   expr + term * ( expr                     )$    Shift )
    21   expr + term * ( expr )                    $    Reduce factor : (expr)
    22   expr + term * factor                      $    Reduce term : term * factor
    23   expr + term                               $    Reduce expr : expr + term
    24   expr                                      $    Reduce expr
    25                                             $    Success!

When parsing the expression, an underlying state machine and the
current input token determine what happens next.  If the next token
looks like part of a valid grammar rule (based on other items on the
stack), it is generally shifted onto the stack.  If the top of the
stack contains a valid right-hand-side of a grammar rule, it is
usually "reduced" and the symbols replaced with the symbol on the
left-hand-side.  When this reduction occurs, the appropriate action is
triggered (if defined).  If the input token can't be shifted and the
top of stack doesn't match any grammar rules, a syntax error has
occurred and the parser must take some kind of recovery step (or bail
out).  A parse is only successful if the parser reaches a state where
the symbol stack is empty and there are no more input tokens.

It is important to note that the underlying implementation is built
around a large finite-state machine that is encoded in a collection of
tables. The construction of these tables is non-trivial and
beyond the scope of this discussion.  However, subtle details of this
process explain why, in the example above, the parser chooses to shift
a token onto the stack in step 9 rather than reducing the
rule ``expr : expr + term``.

Parsing Example
^^^^^^^^^^^^^^^
Suppose you wanted to make a grammar for evaluating simple arithmetic
expressions as previously described.  Here is how you would do it with
SLY::

    from sly import Parser
    from calclex import CalcLexer

    class CalcParser(Parser):
        # Get the token list from the lexer (required)
        tokens = CalcLexer.tokens

        # Grammar rules and actions
        @_('expr PLUS term')
        def expr(self, p):
            return p.expr + p.term

        @_('expr MINUS term')
        def expr(self, p):
            return p.expr - p.term

        @_('term')
        def expr(self, p):
            return p.term

        @_('term TIMES factor')
        def term(self, p):
            return p.term * p.factor

        @_('term DIVIDE factor')
        def term(self, p):
            return p.term / p.factor

        @_('factor')
        def term(self, p):
            return p.factor

        @_('NUMBER')
        def factor(self, p):
            return p.NUMBER

        @_('LPAREN expr RPAREN')
        def factor(self, p):
            return p.expr

    if __name__ == '__main__':
        lexer = CalcLexer()
        parser = CalcParser()

        while True:
            try:
                text = input('calc > ')
                result = parser.parse(lexer.tokenize(text))
                print(result)
            except EOFError:
                break

In this example, each grammar rule is defined by a method that's been
decorated by ``@_(rule)`` decorator.  The very first grammar rule
defines the top of the parse (the first rule listed in a BNF grammar).
The name of each method must match the name of the grammar rule being
parsed.  The argument to the ``@_()`` decorator is a string describing
the right-hand-side of the grammar.  Thus, a grammar rule like this::

    expr : expr PLUS term

becomes a method like this::

    @_('expr PLUS term')
    def expr(self, p):
        ...

The method is triggered when that grammar rule is recognized on the
input.  As an argument, the method receives a sequence of grammar symbol
values in ``p``.  There are two ways to access these symbols. First, you
can use symbol names as shown::

    @_('expr PLUS term')
    def expr(self, p):
        return p.expr + p.term

Alternatively, you can also index ``p`` like an array::

    @_('expr PLUS term')
    def expr(self, p):
        return p[0] + p[2]

For tokens, the value of the corresponding ``p.symbol`` or ``p[i]`` is
the *same* as the ``p.value`` attribute assigned to tokens in the
lexer module.  For non-terminals, the value is whatever was returned
by the methods defined for that rule.

If a grammar rule includes the same symbol name more than once, you
need to append a numeric suffix to disambiguate the symbol name when
you're accessing values.  For example::

    @_('expr PLUS expr')
    def expr(self, p):
        return p.expr0 + p.expr1

Finally, within each rule, you always return a value that becomes
associated with that grammar symbol elsewhere. This is how values
propagate within the grammar.

There are many other kinds of things that might happen in a rule
though. For example, a rule might construct part of a parse tree
instead::

    @_('expr PLUS term')
    def expr(self, p):
        return ('+', p.expr, p.term)

or it might create an instance related to an abstract syntax tree::

    class BinOp(object):
        def __init__(self, op, left, right):
            self.op = op
            self.left = left
            self.right = right

    @_('expr PLUS term')
    def expr(self, p):
        return BinOp('+', p.expr, p.term)

The key thing is that the method returns the value that's going to
be attached to the symbol "expr" in this case.  This is the propagation
of values that was described in the previous section.

Combining Grammar Rule Functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

When grammar rules are similar, they can be combined into a single method.
For example, suppose you had two rules that were constructing a parse tree::

    @_('expr PLUS term')
    def expr(self, p):
        return ('+', p.expr, p.term)

    @_('expr MINUS term')
    def expr(self, p):
        return ('-', p.expr, p.term)

Instead of writing two functions, you might write a single function like this::

    @_('expr PLUS term',
       'expr MINUS term')
    def expr(self, p):
        return (p[1], p.expr, p.term)

In this example, the operator could be ``PLUS`` or ``MINUS``.  Thus,
we can't use the symbolic name to refer to its value. Instead, use the array
index ``p[1]`` to get it as shown.

In general, the ``@_()`` decorator for any given method can list
multiple grammar rules.  When combining grammar rules into a single
function though, all of the rules should have a similar structure
(e.g., the same number of terms and consistent symbol names).
Otherwise, the corresponding action code may end up being more
complicated than necessary.

Character Literals
^^^^^^^^^^^^^^^^^^

If desired, a grammar may contain tokens defined as single character
literals.  For example::

    @_('expr "+" term')
    def expr(self, p):
        return p.expr + p.term

    @_('expr "-" term')
    def expr(self, p):
        return p.expr - p.term

A character literal must be enclosed in quotes such as ``"+"``.  In
addition, if literals are used, they must be declared in the
corresponding lexer class through the use of a special ``literals``
declaration::

    class CalcLexer(Lexer):
        ...
        literals = { '+','-','*','/' }
        ...

Character literals are limited to a single character.  Thus, it is not
legal to specify literals such as ``<=`` or ``==``.  For this, use the
normal lexing rules (e.g., define a rule such as ``LE = r'<='``).

Empty Productions
^^^^^^^^^^^^^^^^^

If you need an empty production, define a special rule like this::

    @_('')
    def empty(self, p):
        pass

Now to use the empty production elsewhere, use the name 'empty' as a symbol.  For
example, suppose you need to encode a rule that involved an optional item like this::

    spam : optitem grok

    optitem : item
            | empty


You would encode the rules in SLY as follows::

    @_('optitem grok')
    def spam(self, p):
        ...

    @_('item')
    def optitem(self, p):
        ...

    @_('empty')
    def optitem(self, p):
        ...

Note: You could write empty rules anywhere by specifying an empty
string. However,writing an "empty" rule and using "empty" to denote an
empty production may be easier to read and more clearly state your
intention.

EBNF Features (Optionals and Repeats)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Certain grammar features occur with some frequency.  For example, suppose you want to
have an optional item as shown in the previous section.  An alternate way to specify
it is to enclose one more more symbols in [ ] like this::

    @_('[ item ] grok')
    def spam(self, p):
        if p.item is not None:
             print("item was given and has value", p.item)
	else:
             print("item was not given")

    @_('whatever')
    def item(self, p):
        ...

In this case, the value of ``p.item`` is set to ``None`` if the value wasn't supplied.
Otherwise, it will have the value returned by the ``item`` rule below.

You can also encode repetitions.  For example, a common construction is a 
list of comma separated expressions.  To parse that, you could write::

    @_('expr { COMMA expr }')
    def exprlist(self, p):
        return [p.expr0] + p.expr1

In this example, the ``{ COMMA expr }`` represents zero or more repetitions
of a rule.  The value of all symbols inside is now a list.  So, ``p.expr1``
is a list of all expressions matched.   Note, when duplicate symbol names 
appear in a rule, they are distinguished by appending a numeric index as shown. 

Dealing With Ambiguous Grammars
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The expression grammar given in the earlier example has been written
in a special format to eliminate ambiguity.  However, in many
situations, it is extremely difficult or awkward to write grammars in
this format.  A much more natural way to express the grammar is in a
more compact form like this::

    expr : expr PLUS expr
         | expr MINUS expr
         | expr TIMES expr
         | expr DIVIDE expr
         | LPAREN expr RPAREN
         | NUMBER

Unfortunately, this grammar specification is ambiguous.  For example,
if you are parsing the string "3 * 4 + 5", there is no way to tell how
the operators are supposed to be grouped.  For example, does the
expression mean "(3 * 4) + 5" or is it "3 * (4+5)"?

When an ambiguous grammar is given, you will get messages about
"shift/reduce conflicts" or "reduce/reduce conflicts".  A shift/reduce
conflict is caused when the parser generator can't decide whether or
not to reduce a rule or shift a symbol on the parsing stack.  For
example, consider the string "3 * 4 + 5" and the internal parsing
stack::

    Step Symbol Stack  Input Tokens       Action
    ---- ------------- ----------------   -------------------------------
    1    $                   3 * 4 + 5$   Shift 3
    2    $ 3                   * 4 + 5$   Reduce : expr : NUMBER
    3    $ expr                * 4 + 5$   Shift *
    4    $ expr *                4 + 5$   Shift 4
    5    $ expr * 4                + 5$   Reduce: expr : NUMBER
    6    $ expr * expr             + 5$   SHIFT/REDUCE CONFLICT ????

In this case, when the parser reaches step 6, it has two options.  One
is to reduce the rule ``expr : expr * expr`` on the stack.  The other
option is to shift the token ``+`` on the stack.  Both options are
perfectly legal from the rules of the context-free-grammar.

By default, all shift/reduce conflicts are resolved in favor of
shifting.  Therefore, in the above example, the parser will always
shift the ``+`` instead of reducing.  Although this strategy works in
many cases (for example, the case of "if-then" versus "if-then-else"),
it is not enough for arithmetic expressions.  In fact, in the above
example, the decision to shift ``+`` is completely wrong---we should
have reduced ``expr * expr`` since multiplication has higher
mathematical precedence than addition.

To resolve ambiguity, especially in expression grammars, SLY allows
individual tokens to be assigned a precedence level and associativity.
This is done by adding a variable ``precedence`` to the parser class
like this::

    class CalcParser(Parser):
        ...
        precedence = (
           ('left', PLUS, MINUS),
           ('left', TIMES, DIVIDE),
        )

        # Rules where precedence is applied
	@_('expr PLUS expr')
 	def expr(self, p):
            return p.expr0 + p.expr1

	@_('expr MINUS expr')
 	def expr(self, p):
            return p.expr0 - p.expr1

	@_('expr TIMES expr')
 	def expr(self, p):
            return p.expr0 * p.expr1

	@_('expr DIVIDE expr')
 	def expr(self, p):
            return p.expr0 / p.expr1
        ...

This ``precedence`` declaration specifies that ``PLUS``/``MINUS`` have
the same precedence level and are left-associative and that
``TIMES``/``DIVIDE`` have the same precedence and are
left-associative.  Within the ``precedence`` declaration, tokens are
ordered from lowest to highest precedence. Thus, this declaration
specifies that ``TIMES``/``DIVIDE`` have higher precedence than
``PLUS``/``MINUS`` (since they appear later in the precedence
specification).

The precedence specification works by associating a numerical
precedence level value and associativity direction to the listed
tokens.  For example, in the above example you get::

    PLUS      : level = 1,  assoc = 'left'
    MINUS     : level = 1,  assoc = 'left'
    TIMES     : level = 2,  assoc = 'left'
    DIVIDE    : level = 2,  assoc = 'left'

These values are then used to attach a numerical precedence value and
associativity direction to each grammar rule. *This is always
determined by looking at the precedence of the right-most terminal
symbol.*  For example::

    expr : expr PLUS expr           # level = 1, left
         | expr MINUS expr          # level = 1, left
         | expr TIMES expr          # level = 2, left
         | expr DIVIDE expr         # level = 2, left
         | LPAREN expr RPAREN       # level = None (not specified)
         | NUMBER                   # level = None (not specified)

When shift/reduce conflicts are encountered, the parser generator
resolves the conflict by looking at the precedence rules and
associativity specifiers.

1. If the current token has higher precedence than the rule on the stack, it is shifted.

2. If the grammar rule on the stack has higher precedence, the rule is reduced.

3. If the current token and the grammar rule have the same precedence,
   the rule is reduced for left associativity, whereas the token is
   shifted for right associativity.

4. If nothing is known about the precedence, shift/reduce conflicts
   are resolved in favor of shifting (the default).

For example, if ``expr PLUS expr`` has been parsed and the
next token is ``TIMES``, the action is going to be a shift because
``TIMES`` has a higher precedence level than ``PLUS``.  On the other hand,
if ``expr TIMES expr`` has been parsed and the next token is
``PLUS``, the action is going to be reduce because ``PLUS`` has a lower
precedence than ``TIMES.``

When shift/reduce conflicts are resolved using the first three
techniques (with the help of precedence rules), SLY will
report no errors or conflicts in the grammar.

One problem with the precedence specifier technique is that it is
sometimes necessary to change the precedence of an operator in certain
contexts.  For example, consider a unary-minus operator in ``3 + 4 *
-5``.  Mathematically, the unary minus is normally given a very high
precedence--being evaluated before the multiply.  However, in our
precedence specifier, ``MINUS`` has a lower precedence than ``TIMES``.  To
deal with this, precedence rules can be given for so-called "fictitious tokens"
like this::

    class CalcParser(Parser):
        ...
        precedence = (
            ('left', PLUS, MINUS),
            ('left', TIMES, DIVIDE),
            ('right', UMINUS),            # Unary minus operator
        )

Now, in the grammar file, you write the unary minus rule like this::

        @_('MINUS expr %prec UMINUS')
        def expr(p):
           return -p.expr

In this case, ``%prec UMINUS`` overrides the default rule precedence--setting it to that
of ``UMINUS`` in the precedence specifier.

At first, the use of ``UMINUS`` in this example may appear very confusing.
``UMINUS`` is not an input token or a grammar rule.  Instead, you should
think of it as the name of a special marker in the precedence table.
When you use the ``%prec`` qualifier, you're telling SLY
that you want the precedence of the expression to be the same as for
this special marker instead of the usual precedence.

It is also possible to specify non-associativity in the ``precedence``
table. This is used when you *don't* want operations to chain
together.  For example, suppose you wanted to support comparison
operators like ``<`` and ``>`` but you didn't want combinations like
``a < b < c``.  To do this, specify the precedence rules like this::

    class MyParser(Parser):
         ...
         precedence = (
              ('nonassoc', LESSTHAN, GREATERTHAN),  # Nonassociative operators
              ('left', PLUS, MINUS),
              ('left', TIMES, DIVIDE),
              ('right', UMINUS),            # Unary minus operator
         )

If you do this, the occurrence of input text such as ``a < b < c``
will result in a syntax error.  However, simple expressions such as
``a < b`` will still be fine.

Reduce/reduce conflicts are caused when there are multiple grammar
rules that can be applied to a given set of symbols.  This kind of
conflict is almost always bad and is always resolved by picking the
rule that appears first in the grammar file.   Reduce/reduce conflicts
are almost always caused when different sets of grammar rules somehow
generate the same set of symbols.  For example::

    assignment :  ID EQUALS NUMBER
               |  ID EQUALS expr

    expr       : expr PLUS expr
               | expr MINUS expr
               | expr TIMES expr
               | expr DIVIDE expr
               | LPAREN expr RPAREN
               | NUMBER

In this case, a reduce/reduce conflict exists between these two rules::

    assignment  : ID EQUALS NUMBER
    expr        : NUMBER

For example, if you're parsing ``a = 5``, the parser can't figure out if this
is supposed to be reduced as ``assignment : ID EQUALS NUMBER`` or
whether it's supposed to reduce the 5 as an expression and then reduce
the rule ``assignment : ID EQUALS expr``.

It should be noted that reduce/reduce conflicts are notoriously
difficult to spot simply looking at the input grammar.  When a
reduce/reduce conflict occurs, SLY will try to help by
printing a warning message such as this::

    WARNING: 1 reduce/reduce conflict
    WARNING: reduce/reduce conflict in state 15 resolved using rule (assignment -> ID EQUALS NUMBER)
    WARNING: rejected rule (expression -> NUMBER)

This message identifies the two rules that are in conflict.  However,
it may not tell you how the parser arrived at such a state.  To try
and figure it out, you'll probably have to look at your grammar and
the contents of the parser debugging file with an appropriately high
level of caffeination (see the next section).

Parser Debugging
^^^^^^^^^^^^^^^^

Tracking down shift/reduce and reduce/reduce conflicts is one of the
finer pleasures of using an LR parsing algorithm.  To assist in
debugging, you can have SLY produce a debugging file when it
constructs the parsing tables.  Add a ``debugfile`` attribute to your
class like this::

    class CalcParser(Parser):
        debugfile = 'parser.out'
        ...

When present, this will write the entire grammar along with all parsing
states to the file you specify.  Each state of the parser is shown
as output that looks something like this::

    state 2

        (7) factor -> LPAREN . expr RPAREN
        (1) expr -> . term
        (2) expr -> . expr MINUS term
        (3) expr -> . expr PLUS term
        (4) term -> . factor
        (5) term -> . term DIVIDE factor
        (6) term -> . term TIMES factor
        (7) factor -> . LPAREN expr RPAREN
        (8) factor -> . NUMBER
        LPAREN          shift and go to state 2
        NUMBER          shift and go to state 3

        factor                         shift and go to state 1
        term                           shift and go to state 4
        expr                           shift and go to state 6

Each state keeps track of the grammar rules that might be in the
process of being matched at that point.  Within each rule, the "."
character indicates the current location of the parse within that
rule.  In addition, the actions for each valid input token are listed.
By looking at these rules (and with a little practice), you can
usually track down the source of most parsing conflicts.  It should
also be stressed that not all shift-reduce conflicts are bad.
However, the only way to be sure that they are resolved correctly is
to look at the debugging file.

Syntax Error Handling
^^^^^^^^^^^^^^^^^^^^^

If you are creating a parser for production use, the handling of
syntax errors is important.  As a general rule, you don't want a
parser to simply throw up its hands and stop at the first sign of
trouble.  Instead, you want it to report the error, recover if
possible, and continue parsing so that all of the errors in the input
get reported to the user at once.  This is the standard behavior found
in compilers for languages such as C, C++, and Java.

In SLY, when a syntax error occurs during parsing, the error is immediately
detected (i.e., the parser does not read any more tokens beyond the
source of the error).  However, at this point, the parser enters a
recovery mode that can be used to try and continue further parsing.
As a general rule, error recovery in LR parsers is a delicate
topic that involves ancient rituals and black-magic.   The recovery mechanism
provided by SLY is comparable to Unix yacc so you may want
consult a book like O'Reilly's "Lex and Yacc" for some of the finer details.

When a syntax error occurs, SLY performs the following steps:

1. On the first occurrence of an error, the user-defined ``error()``
   method is called with the offending token as an argument. However, if
   the syntax error is due to reaching the end-of-file, an argument of
   ``None`` is passed.  Afterwards, the parser enters an "error-recovery"
   mode in which it will not make future calls to ``error()`` until it
   has successfully shifted at least 3 tokens onto the parsing stack.

2. If no recovery action is taken in ``error()``, the offending
   lookahead token is replaced with a special ``error`` token.

3. If the offending lookahead token is already set to ``error``,
   the top item of the parsing stack is deleted.

4. If the entire parsing stack is unwound, the parser enters a restart
   state and attempts to start parsing from its initial state.

5. If a grammar rule accepts ``error`` as a token, it will be
   shifted onto the parsing stack.

6. If the top item of the parsing stack is ``error``, lookahead tokens
   will be discarded until the parser can successfully shift a new
   symbol or reduce a rule involving ``error``.

Recovery and resynchronization with error rules
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The most well-behaved approach for handling syntax errors is to write
grammar rules that include the ``error`` token.  For example,
suppose your language had a grammar rule for a print statement like
this::

    @_('PRINT expr SEMI')
    def statement(self, p):
        ...

To account for the possibility of a bad expression, you might write an
additional grammar rule like this::

    @_('PRINT error SEMI')
    def statement(self, p):
        print("Syntax error in print statement. Bad expression")

In this case, the ``error`` token will match any sequence of
tokens that might appear up to the first semicolon that is
encountered.  Once the semicolon is reached, the rule will be
invoked and the ``error`` token will go away.

This type of recovery is sometimes known as parser resynchronization.
The ``error`` token acts as a wildcard for any bad input text and
the token immediately following ``error`` acts as a
synchronization token.

It is important to note that the ``error`` token usually does not
appear as the last token on the right in an error rule.  For example::

    @_('PRINT error')
    def statement(self, p):
        print("Syntax error in print statement. Bad expression")

This is because the first bad token encountered will cause the rule to
be reduced--which may make it difficult to recover if more bad tokens
immediately follow.    It's better to have some kind of landmark such as
a semicolon, closing parentheses, or other token that can be used as
a synchronization point.

Panic mode recovery
~~~~~~~~~~~~~~~~~~~

An alternative error recovery scheme is to enter a panic mode recovery
in which tokens are discarded to a point where the parser might be
able to recover in some sensible manner.

Panic mode recovery is implemented entirely in the ``error()``
function.  For example, this function starts discarding tokens until
it reaches a closing '}'.  Then, it restarts the parser in its initial
state::

    def error(self, p):
        print("Whoa. You are seriously hosed.")
        if not p:
            print("End of File!")
            return

        # Read ahead looking for a closing '}'
        while True:
            tok = next(self.tokens, None)
            if not tok or tok.type == 'RBRACE':
                break
        self.restart()

This function discards the bad token and tells the parser that
the error was ok::

    def error(self, p):
        if p:
             print("Syntax error at token", p.type)
             # Just discard the token and tell the parser it's okay.
             self.errok()
         else:
             print("Syntax error at EOF")

A few additional details about some of the attributes and methods being used:

- ``self.errok()``.  This resets the parser state so it doesn't think
  it's in error-recovery mode.  This will prevent an ``error`` token
  from being generated and will reset the internal error counters so
  that the next syntax error will call ``error()`` again.

- ``self.tokens``. This is the iterable sequence of tokens being parsed. Calling
  ``next(self.tokens)`` will force it to advance by one token.

- ``self.restart()``.  This discards the entire parsing stack and
  resets the parser to its initial state.

To supply the next lookahead token to the parser, ``error()`` can return a token.  This might be
useful if trying to synchronize on special characters.  For example::

    def error(self, tok):
        # Read ahead looking for a terminating ";"
        while True:
            tok = next(self.tokens, None)           # Get the next token
            if not tok or tok.type == 'SEMI':
                break
            self.errok()

        # Return SEMI to the parser as the next lookahead token
        return tok

When Do Syntax Errors Get Reported?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In most cases, SLY will handle errors as soon as a bad input token is
detected on the input.  However, be aware that SLY may choose to delay
error handling until after it has reduced one or more grammar rules
first.  This behavior might be unexpected, but it's related to special
states in the underlying parsing table known as "defaulted states."  A
defaulted state is parsing condition where the same grammar rule will
be reduced regardless of what valid token comes next on the input.
For such states, SLY chooses to go ahead and reduce the grammar rule
*without reading the next input token*.  If the next token is bad, SLY
will eventually get around to reading it and report a syntax error.
It's just a little unusual in that you might see some of your grammar
rules firing immediately prior to the syntax error.

General comments on error handling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For normal types of languages, error recovery with error rules and
resynchronization characters is probably the most reliable
technique. This is because you can instrument the grammar to catch
errors at selected places where it is relatively easy to recover and
continue parsing.  Panic mode recovery is really only useful in
certain specialized applications where you might want to discard huge
portions of the input text to find a valid restart point.

Line Number and Position Tracking
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Position tracking is often a tricky problem when writing compilers.
By default, SLY tracks the line number and position of all tokens.
The following attributes may be useful in a production rule:

- ``p.lineno``. Line number of the left-most terminal in a production.
- ``p.index``. Lexing index of the left-most terminal in a production.

For example::

    @_('expr PLUS expr')
    def expr(self, p):
        line   = p.lineno      # line number of the PLUS token
        index  = p.index       # Index of the PLUS token in input text


SLY doesn't propagate line number information to non-terminals. If you need
this, you'll need to store line number information yourself and propagate it
in AST nodes or some other data structure.

AST Construction
^^^^^^^^^^^^^^^^

SLY provides no special functions for constructing an abstract syntax
tree.  However, such construction is easy enough to do on your own.

A minimal way to construct a tree is to create and
propagate a tuple or list in each grammar rule function.   There
are many possible ways to do this, but one example is something
like this::

    @_('expr PLUS expr',
       'expr MINUS expr',
       'expr TIMES expr',
       'expr DIVIDE expr')
    def expr(self, p):
        return ('binary-expression', p[1], p.expr0, p.expr1)

    @_('LPAREN expr RPAREN')
    def expr(self, p):
        return ('group-expression', p.expr)

    @_('NUMBER')
    def expr(self, p):
        return ('number-expression', p.NUMBER)

Another approach is to create a set of data structures for different
kinds of abstract syntax tree nodes and create different node types
in each rule::

    class Expr:
        pass

    class BinOp(Expr):
        def __init__(self, op, left, right)
            self.op = op
            self.left = left
            self.right = right

    class Number(Expr):
        def __init__(self, value):
            self.value = value

    @_('expr PLUS expr',
       'expr MINUS expr',
       'expr TIMES expr',
       'expr DIVIDE expr')
    def expr(self, p):
        return BinOp(p[1], p.expr0, p.expr1)

    @_('LPAREN expr RPAREN')
    def expr(self, p):
        return p.expr

    @_('NUMBER')
    def expr(self, p):
        return Number(p.NUMBER)

The advantage to this approach is that it may make it easier to attach
more complicated semantics, type checking, code generation, and other
features to the node classes.

Changing the starting symbol
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Normally, the first rule found in a parser class defines the starting
grammar rule (top level rule).  To change this, supply a ``start``
specifier in your class.  For example::

    class CalcParser(Parser):
        start = 'foo'

        @_('A B')
        def bar(self, p):
            ...

        @_('bar X')
        def foo(self, p):     # Parsing starts here (start symbol above)
            ...

The use of a ``start`` specifier may be useful during debugging
since you can use it to work with a subset of a larger grammar.

Embedded Actions
^^^^^^^^^^^^^^^^

The parsing technique used by SLY only allows actions to be executed
at the end of a rule.  For example, suppose you have a rule like this::

    @_('A B C D')
    def foo(self, p):
        print("Parsed a foo", p.A, p.B, p.C, p.D)

In this case, the supplied action code only executes after all of the
symbols ``A``, ``B``, ``C``, and ``D`` have been
parsed. Sometimes, however, it is useful to execute small code
fragments during intermediate stages of parsing.  For example, suppose
you wanted to perform some action immediately after ``A`` has
been parsed. To do this, write an empty rule like this::

    @_('A seen_A B C D')
    def foo(self, p):
        print("Parsed a foo", p.A, p.B, p.C, p.D)
        print("seen_A returned", p.seen_A])

    @_('')
    def seen_A(self, p):
        print("Saw an A = ", p[-1])   # Access grammar symbol to the left
        return 'some_value'           # Assign value to seen_A

In this example, the empty ``seen_A`` rule executes immediately after
``A`` is shifted onto the parsing stack.  Within this rule, ``p[-1]``
refers to the symbol on the stack that appears immediately to the left
of the ``seen_A`` symbol.  In this case, it would be the value of
``A`` in the ``foo`` rule immediately above.  Like other rules, a
value can be returned from an embedded action by returning it.

The use of embedded actions can sometimes introduce extra shift/reduce
conflicts.  For example, this grammar has no conflicts::

    @_('abcd',
       'abcx')
    def foo(self, p):
        pass

    @_('A B C D')
    def abcd(self, p):
        pass

    @_('A B C X')
    def abcx(self, p):
        pass

However, if you insert an embedded action into one of the rules like this::

    @_('abcd',
       'abcx')
    def foo(self, p):
        pass

    @_('A B C D')
    def abcd(self, p):
        pass

    @_('A B seen_AB C X')
    def abcx(self, p):
        pass

    @_('')
    def seen_AB(self, p):
        pass

an extra shift-reduce conflict will be introduced.  This conflict is
caused by the fact that the same symbol ``C`` appears next in
both the ``abcd`` and ``abcx`` rules.  The parser can either
shift the symbol (``abcd`` rule) or reduce the empty
rule ``seen_AB`` (``abcx`` rule).

A common use of embedded rules is to control other aspects of parsing
such as scoping of local variables.  For example, if you were parsing
C code, you might write code like this::

    @_('LBRACE new_scope statements RBRACE')
    def statements(self, p):
        # Action code
        ...
        pop_scope()        # Return to previous scope

    @_('')
    def new_scope(self, p):
        # Create a new scope for local variables
        create_scope()
        ...

In this case, the embedded action ``new_scope`` executes
immediately after a ``LBRACE`` (``{``) symbol is parsed.
This might adjust internal symbol tables and other aspects of the
parser.  Upon completion of the rule ``statements``, code
undos the operations performed in the embedded action
(e.g., ``pop_scope()``).