PLY (Python Lex-Yacc)

Documentation version: $Header: /cvs/projects/PLY/doc/ply.html,v 1.7 2001/06/18 21:48:15 beazley Exp $

Introduction

Early versions of PLY were developed to support the Introduction to Compilers Course at the University of Chicago. In this course, students built a fully functional compiler for a simple Pascal-like language. Their compiler, implemented entirely in Python, had to include lexical analysis, parsing, type checking, type inference, nested scoping, and code generation for the SPARC processor. Approximately 30 different compiler implementations were completed in this course. Most of PLY's interface and operation has been motivated by common usability problems encountered by students.

Because PLY was primarily developed as an instructional tool, you will find it to be MUCH more picky about token and grammar rule specification than most other Python parsing tools. In part, this added formality is meant to catch common programming mistakes made by novice users. However, advanced users will also find such features to be useful when building complicated grammars for real programming languages. It should also be noted that PLY does not provide much in the way of bells and whistles (e.g., automatic construction of abstract syntax trees, tree traversal, etc.). Instead, you will find a bare-bones, yet fully capable lex/yacc implementation written entirely in Python.

The rest of this document assumes that you are somewhat familar with parsing theory, syntax directed translation, and automatic tools such as lex and yacc. If you are unfamilar with these topics, you will probably want to consult an introductory text such as "Compilers: Principles, Techniques, and Tools", by Aho, Sethi, and Ullman. "Lex and Yacc" by John Levine may also be handy.

PLY Overview

The two tools are meant to work together. Specifically, lex.py provides an external interface in the form of a token() function that returns the next valid token on the input stream. yacc.py calls this repeatedly to retrieve tokens and invoke grammar rules. The output of yacc.py is often an Asbtract Syntax Tree (AST). However, this is entirely up to the user. If desired, yacc.py can also be used to implement simple one-pass compilers.

Like its Unix counterpart, yacc.py provides most of the features you expect including extensive error checking, grammar validation, support for empty productions, error tokens, and ambiguity resolution via precedence rules. The primary difference between yacc.py and yacc is the use of SLR parsing instead of LALR(1). Although this slightly restricts the types of grammars than can be successfully parsed, it is sufficiently powerful to handle most kinds of normal programming language constructs.

Finally, it is important to note that PLY relies on reflection (introspection) to build its lexers and parsers. Unlike traditional lex/yacc which require a special input file that is converted into a separate source file, the specifications given to PLY are valid Python programs. This means that there are no extra source files nor is there a special compiler construction step (e.g., running yacc to generate Python code for the compiler).

Lex Example

# ------------------------------------------------------------
# calclex.py
#
# tokenizer for a simple expression evaluator for
# numbers and +,-,*,/
# ------------------------------------------------------------
import lex

# List of token names.   This is always required
tokens = (
   'NUMBER',
   'PLUS',
   'MINUS',
   'TIMES',
   'DIVIDE',
   'LPAREN',
   'RPAREN',
)

# Regular expression rules for simple tokens
t_PLUS    = r'\+'
t_MINUS   = r'-'
t_TIMES   = r'\*'
t_DIVIDE  = r'/'
t_LPAREN  = r'\('
t_RPAREN  = r'\)'

# A regular expression rule with some action code
def t_NUMBER(t):
    r'\d+'
    try:
         t.value = int(t.value)    
    except ValueError:
         print "Line %d: Number %s is too large!" % (t.lineno,t.value)
	 t.value = 0
    return t

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

# A string containing ignored characters (spaces and tabs)
t_ignore  = ' \t'

# Error handling rule
def t_error(t):
    print "Illegal character '%s'" % t.value[0]
    t.skip(1)

# Build the lexer
lex.lex()

# Test it out
data = '''
3 + 4 * 10
  + -20 *2
'''

# Give the lexer some input
lex.input(data)

# Tokenize
while 1:
    tok = lex.token()
    if not tok: break      # No more input
    print tok

t_PLUS = r'\+'

def t_NUMBER(t):
    r'\d+'
    try:
         t.value = int(t.value)
    except ValueError:
         print "Number %s is too large!" % t.value
	 t.value = 0
    return t

The rule t_newline() illustrates a regular expression rule for a discarded token. In this case, a rule is written to match newlines so that proper line number tracking can be performed. By returning no value, the function causes the newline character to be discarded.

The special t_ignore rule is reserved by lex.py for characters that should be completely ignored in the input stream. Usually this is used to skip over whitespace and other non-essential characters. Although it is possible to define a regular expression rule for whitespace in a manner similar to t_newline(), the use of t_ignore provides substantially better lexing performance because it is handled as a special case and is checked in a much more efficient manner than the normal regular expression rules.

Finally, the t_error() function is used to handle lexing errors that occur when illegal characters are detected. In this case, the t.value attribute contains the rest of the input string that has not been tokenized. In the example, we simply print the offending character and skip ahead one character by calling t.skip(1).

To build the lexer, the function lex.lex() is used. This function uses Python reflection (or introspection) to read the the regular expression rules out of the calling context and build the lexer. Once the lexer has been built, two functions can be used to control the lexer.

• lex.input(data). Reset the lexer and store a new input string.
• lex.token(). Return the next token. Returns a special LexToken instance on success or None if the end of the input text has been reached.

$ python example.py
LexToken(NUMBER,3,2)
LexToken(PLUS,'+',2)
LexToken(NUMBER,4,2)
LexToken(TIMES,'*',2)
LexToken(NUMBER,10,2)
LexToken(PLUS,'+',3)
LexToken(MINUS,'-',3)
LexToken(NUMBER,20,3)
LexToken(TIMES,'*',3)
LexToken(NUMBER,2,3)

Lex Implementation Notes

• lex.py uses the re module to do its patten matching. When building the master regular expression, rules are added in the following order:
  1. All tokens defined by functions are added in the same order as they appear in the lexer file.
  2. Tokens defined by strings are added by sorting them in order of decreasing regular expression length (longer expressions are added first).

  Without this ordering, it can be difficult to correctly match certain types of tokens. For example, if you wanted to have separate tokens for "=" and "==", you need to make sure that "==" is checked first. By sorting regular expressions in order of decreasing length, this problem is solved for rules defined as strings. For functions, the order can be explicitly controlled since rules appearing first are checked first.

• The lexer requires input to be supplied as a single input string. Since most machines have more than enough memory, this rarely presents a performance concern. However, it means that the lexer currently can't be used with streaming data such as open files or sockets. This limitation is primarily a side-effect of using the re module.

• To handle reserved words, it is usually easier to just match an identifier and do a special name lookup in a function like this:

  reserved = {
     'if' : 'IF',
     'then' : 'THEN',
     'else' : 'ELSE',
     'while' : 'WHILE',
     ...
  }
  
  def t_ID(t):
      r'[a-zA-Z_][a-zA-Z_0-9]*'
      t.type = reserved.get(t.value,'ID')    # Check for reserved words
      return t
  

• The lexer requires tokens to be defined as class instances with t.type, t.value, and t.lineno attributes. By default, tokens are created as instances of the LexToken class defined internally to lex.py. If desired, you can create new kinds of tokens provided that they have the three required attributes. However, in practice, it is probably safer to stick with the default.

• The only safe attribute for assigning token properties is t.value. In some cases, you may want to attach a number of different properties to a token (e.g., symbol table entries for identifiers). To do this, replace t.value with a tuple or class instance. For example:

  def t_ID(t):
      ...
      # For identifiers, create a (lexeme, symtab) tuple
      t.value = (t.value, symbol_lookup(t.value))
      ...
      return t
  

  Although allowed, do NOT assign additional attributes to the token object. For example,

  def t_ID(t):
      ...
      # Bad implementation of above
      t.symtab = symbol_lookup(t.value)
      ...
  

  The reason you don't want to do this is that the yacc.py module only provides public access to the t.value attribute of each token. Therefore, any other attributes you assign are inaccessible (if you are familiar with the internals of C lex/yacc, t.value is the same as yylval.tok).

• To track line numbers, the lexer internally maintains a line number variable. Each token automatically gets the value of the current line number in the t.lineno attribute. To modify the current line number, simply change the t.lineno attribute in a function rule (as previously shown for t_newline()). Even if the resulting token is discarded, changes to the line number remain in effect for subsequent tokens.

• To support multiple scanners in the same application, the lex.lex() function actually returns a special Lexer object. This object has two methods input() and token() that can be used to supply input and get tokens. For example:

  lexer = lex.lex()
  lexer.input(sometext)
  while 1:
      tok = lexer.token()
      if not tok: break
      print tok
  

  The functions lex.input() and lex.token() are bound to the input() and token() methods of the last lexer created by the lex module.

• To reduce compiler startup time and improve performance, the lexer can be built in optimized mode as follows:

  lex.lex(optimize=1)
  

  When used, most error checking and validation is disabled. This provides a slight performance gain while tokenizing and tends to chop a few tenths of a second off startup time. Since it disables error checking, this mode is not the default and is not recommended during development. However, once you have your compiler fully working, it is usually safe to disable the error checks.

• You can enable some additional debugging by building the lexer like this:

  lex.lex(debug=1)
  

• To help you debug your lexer, lex.py comes with a simple main program which will either tokenize input read from standard input or from a file. To use it, simply put this in your lexer:

  if __name__ == '__main__':
       lex.runmain()
  

  Then, run you lexer as a main program such as python mylex.py

• Since the lexer is written entirely in Python, its performance is largely determined by that of the Python re module. Although the lexer has been written to be as efficient as possible, it's not blazingly fast when used on very large input files. Sorry. If performance is concern, you might consider upgrading to the most recent version of Python, creating a hand-written lexer, or offloading the lexer into a C extension module. In defense of lex.py, it's performance is not that bad when used on reasonably sized input files. For instance, lexing a 4700 line C program with 32000 input tokens takes about 20 seconds on a 200 Mhz PC. Obviously, it will run much faster on a more speedy machine.

Parsing basics

 
expression : expression + term
           | expression - term
           | term

term       : term * factor
           | term / factor
           | factor

factor     : NUMBER
           | ( expression )

 
Grammar                             Action
--------------------------------    -------------------------------------------- 
expression0 : expression1 + term    expression0.val = expression1.val + term.val
            | expression1 - term    expression0.val = expression1.val - term.val
            | term                  expression0.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.lexval)
            | ( expression )        factor.val = expression.val

LR parsing is commonly implemented by shifting grammar symbols onto a stack and looking at the stack and the next input token for patterns. The details of the algorithm can be found in a compiler text, but the following example illustrates the steps that are performed if you wanted to parse the expression 3 + 5 * (10 - 20) using the grammar defined above:

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!

It is important to note that the underlying implementation is actually built around a large finite-state machine and some tables. The construction of these tables is quite complicated 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.

Yacc example

# Yacc example

import yacc

# Get the token map from the lexer.  This is required.
from calclex import tokens

def p_expression_plus(t):
    'expression : expression PLUS term'
    t[0] = t[1] + t[3]

def p_expression_minus(t):
    'expression : expression MINUS term'
    t[0] = t[1] - t[3]

def p_expression_term(t):
    'expression : term'
    t[0] = t[1]

def p_term_times(t):
    'term : term TIMES factor'
    t[0] = t[1] * t[3]

def p_term_div(t):
    'term : term DIVIDE factor'
    t[0] = t[1] / t[3]

def p_term_factor(t):
    'term : factor'
    t[0] = t[1]

def p_factor_num(t):
    'factor : NUMBER'
    t[0] = t[1]

def p_factor_expr(t):
    'factor : LPAREN expression RPAREN'
    t[0] = t[2]

# Error rule for syntax errors
def p_error(t):
    print "Syntax error in input!"

# Build the parser
yacc.yacc()

while 1:
   try:
       s = raw_input('calc > ')
   except EOFError:
       break
   if not s: continue
   result = yacc.parse(s)
   print result

def p_expression_plus(t):
    'expression : expression PLUS term'
    #   ^            ^        ^    ^
    #  t[0]         t[1]     t[2] t[3]

    t[0] = t[1] + t[3]

The first rule defined in the yacc specification determines the starting grammar symbol (in this case, a rule for expression appears first). Whenever the starting rule is reduced by the parser and no more input is available, parsing stops and the final value is returned (this value will be whatever the top-most rule placed in t[0]).

The p_error(t) rule is defined to catch syntax errors. See the error handling section below for more detail.

To build the parser, call the yacc.yacc() function. This function looks at the module and attempts to construct all of the LR parsing tables for the grammar you have specified. The first time yacc.yacc() is invoked, you will get a message such as this:

$ python calcparse.py
yacc: Generating SLR parsing table...  
calc > 

If any errors are detected in your grammar specification, yacc.py will produce diagnostic messages and possibly raise an exception. Some of the errors that can be detected include:

• Duplicated function names (if more than one rule function have the same name in the grammar file).
• Shift/reduce and reduce/reduce conflicts generated by ambiguous grammars.
• Badly specified grammar rules.
• Infinite recursion (rules that can never terminate).
• Unused rules and tokens
• Undefined rules and tokens

Combining Grammar Rule Functions

def p_expression_plus(t):
    'expression : expression PLUS term'
    t[0] = t[1] + t[3]

def p_expression_minus(t):
    'expression : expression MINUS term'
    t[0] = t[1] - t[3]

def p_expression(t):
    '''expression : expression PLUS term
                  | expression MINUS term'''
    if t[2] == '+':
        t[0] = t[1] + t[3]
    elif t[2] == '-':
        t[0] = t[1] - t[3]

def p_binary_operators(t):
    '''expression : expression PLUS term
                  | expression MINUS term
       term       : term TIMES factor
                  | term DIVIDE factor'''
    if t[2] == '+':
        t[0] = t[1] + t[3]
    elif t[2] == '-':
        t[0] = t[1] - t[3]
    elif t[2] == '*':
        t[0] = t[1] * t[3]
    elif t[2] == '/':
        t[0] = t[1] / t[3]

Empty Productions

def p_empty(t):
    'empty :'
    pass

def p_optitem(t):
    'optitem : item'
    '        | empty'
    ...

Dealing With Ambiguous Grammars

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

When an ambiguous grammar is given to yacc.py it will print messages about "shift/reduce conflicts" or a "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 : expression : NUMBER
3    $ expr                             * 4 + 5$    Shift *
4    $ expr *                             4 + 5$    Shift 4
5    $ expr * 4                             + 5$    Reduce: expression : NUMBER
6    $ expr * expr                          + 5$    SHIFT/REDUCE CONFLICT ????

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 (including the ambiguous 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 precedence than addition.

To resolve ambiguity, especially in expression grammars, yacc.py allows individual tokens to be assigned a precedence level and associativity. This is done by adding a variable precedence to the grammar file like this:

precedence = (
    ('left', 'PLUS', 'MINUS'),
    ('left', 'TIMES', 'DIVIDE'),
)

The precedence specification is used to attach a numerical precedence value and associativity direction to each grammar rule. This is always determined by the precedence of the right-most terminal symbol. Therefore, if PLUS/MINUS had a precedence of 1 and TIMES/DIVIDE had a precedence of 2, the grammar rules would have precedence values as follows:

expression : expression PLUS expression                 # prec = 1, left
           | expression MINUS expression                # prec = 1, left
           | expression TIMES expression                # prec = 2, left
           | expression DIVIDE expression               # prec = 2, left
           | LPAREN expression RPAREN                   # prec = unknown
           | NUMBER                                     # prec = unknown

1. If the current token has higher precedence, 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).

When shift/reduce conflicts are resolved using the first three techniques (with the help of precedence rules), yacc.py 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 contents. For example, consider a unary-minus operator in "3 + 4 * -5". Normally, unary minus has 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 fictitious tokens like this:

precedence = (
    ('left', 'PLUS', 'MINUS'),
    ('left', 'TIMES', 'DIVIDE'),
    ('right', 'UMINUS'),            # Unary minus operator
)

def p_expr_uminus(t):
    'expression : MINUS expression %prec UMINUS'
    t[0] = -t[2]

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

assignment  : ID EQUALS NUMBER
expression  : NUMBER

The parser.out file

Unused terminals:


Grammar

Rule 1     expression -> expression PLUS expression
Rule 2     expression -> expression MINUS expression
Rule 3     expression -> expression TIMES expression
Rule 4     expression -> expression DIVIDE expression
Rule 5     expression -> NUMBER
Rule 6     expression -> LPAREN expression RPAREN

Terminals, with rules where they appear

TIMES                : 3
error                : 
MINUS                : 2
RPAREN               : 6
LPAREN               : 6
DIVIDE               : 4
PLUS                 : 1
NUMBER               : 5

Nonterminals, with rules where they appear

expression           : 1 1 2 2 3 3 4 4 6 0


Parsing method: SLR


state 0

    S' -> . expression
    expression -> . expression PLUS expression
    expression -> . expression MINUS expression
    expression -> . expression TIMES expression
    expression -> . expression DIVIDE expression
    expression -> . NUMBER
    expression -> . LPAREN expression RPAREN

    NUMBER          shift and go to state 3
    LPAREN          shift and go to state 2


state 1

    S' -> expression .
    expression -> expression . PLUS expression
    expression -> expression . MINUS expression
    expression -> expression . TIMES expression
    expression -> expression . DIVIDE expression

    PLUS            shift and go to state 6
    MINUS           shift and go to state 5
    TIMES           shift and go to state 4
    DIVIDE          shift and go to state 7


state 2

    expression -> LPAREN . expression RPAREN
    expression -> . expression PLUS expression
    expression -> . expression MINUS expression
    expression -> . expression TIMES expression
    expression -> . expression DIVIDE expression
    expression -> . NUMBER
    expression -> . LPAREN expression RPAREN

    NUMBER          shift and go to state 3
    LPAREN          shift and go to state 2


state 3

    expression -> NUMBER .

    $               reduce using rule 5
    PLUS            reduce using rule 5
    MINUS           reduce using rule 5
    TIMES           reduce using rule 5
    DIVIDE          reduce using rule 5
    RPAREN          reduce using rule 5


state 4

    expression -> expression TIMES . expression
    expression -> . expression PLUS expression
    expression -> . expression MINUS expression
    expression -> . expression TIMES expression
    expression -> . expression DIVIDE expression
    expression -> . NUMBER
    expression -> . LPAREN expression RPAREN

    NUMBER          shift and go to state 3
    LPAREN          shift and go to state 2


state 5

    expression -> expression MINUS . expression
    expression -> . expression PLUS expression
    expression -> . expression MINUS expression
    expression -> . expression TIMES expression
    expression -> . expression DIVIDE expression
    expression -> . NUMBER
    expression -> . LPAREN expression RPAREN

    NUMBER          shift and go to state 3
    LPAREN          shift and go to state 2


state 6

    expression -> expression PLUS . expression
    expression -> . expression PLUS expression
    expression -> . expression MINUS expression
    expression -> . expression TIMES expression
    expression -> . expression DIVIDE expression
    expression -> . NUMBER
    expression -> . LPAREN expression RPAREN

    NUMBER          shift and go to state 3
    LPAREN          shift and go to state 2


state 7

    expression -> expression DIVIDE . expression
    expression -> . expression PLUS expression
    expression -> . expression MINUS expression
    expression -> . expression TIMES expression
    expression -> . expression DIVIDE expression
    expression -> . NUMBER
    expression -> . LPAREN expression RPAREN

    NUMBER          shift and go to state 3
    LPAREN          shift and go to state 2


state 8

    expression -> LPAREN expression . RPAREN
    expression -> expression . PLUS expression
    expression -> expression . MINUS expression
    expression -> expression . TIMES expression
    expression -> expression . DIVIDE expression

    RPAREN          shift and go to state 13
    PLUS            shift and go to state 6
    MINUS           shift and go to state 5
    TIMES           shift and go to state 4
    DIVIDE          shift and go to state 7


state 9

    expression -> expression TIMES expression .
    expression -> expression . PLUS expression
    expression -> expression . MINUS expression
    expression -> expression . TIMES expression
    expression -> expression . DIVIDE expression

    $               reduce using rule 3
    PLUS            reduce using rule 3
    MINUS           reduce using rule 3
    TIMES           reduce using rule 3
    DIVIDE          reduce using rule 3
    RPAREN          reduce using rule 3

  ! PLUS            [ shift and go to state 6 ]
  ! MINUS           [ shift and go to state 5 ]
  ! TIMES           [ shift and go to state 4 ]
  ! DIVIDE          [ shift and go to state 7 ]

state 10

    expression -> expression MINUS expression .
    expression -> expression . PLUS expression
    expression -> expression . MINUS expression
    expression -> expression . TIMES expression
    expression -> expression . DIVIDE expression

    $               reduce using rule 2
    PLUS            reduce using rule 2
    MINUS           reduce using rule 2
    RPAREN          reduce using rule 2
    TIMES           shift and go to state 4
    DIVIDE          shift and go to state 7

  ! TIMES           [ reduce using rule 2 ]
  ! DIVIDE          [ reduce using rule 2 ]
  ! PLUS            [ shift and go to state 6 ]
  ! MINUS           [ shift and go to state 5 ]

state 11

    expression -> expression PLUS expression .
    expression -> expression . PLUS expression
    expression -> expression . MINUS expression
    expression -> expression . TIMES expression
    expression -> expression . DIVIDE expression

    $               reduce using rule 1
    PLUS            reduce using rule 1
    MINUS           reduce using rule 1
    RPAREN          reduce using rule 1
    TIMES           shift and go to state 4
    DIVIDE          shift and go to state 7

  ! TIMES           [ reduce using rule 1 ]
  ! DIVIDE          [ reduce using rule 1 ]
  ! PLUS            [ shift and go to state 6 ]
  ! MINUS           [ shift and go to state 5 ]

state 12

    expression -> expression DIVIDE expression .
    expression -> expression . PLUS expression
    expression -> expression . MINUS expression
    expression -> expression . TIMES expression
    expression -> expression . DIVIDE expression

    $               reduce using rule 4
    PLUS            reduce using rule 4
    MINUS           reduce using rule 4
    TIMES           reduce using rule 4
    DIVIDE          reduce using rule 4
    RPAREN          reduce using rule 4

  ! PLUS            [ shift and go to state 6 ]
  ! MINUS           [ shift and go to state 5 ]
  ! TIMES           [ shift and go to state 4 ]
  ! DIVIDE          [ shift and go to state 7 ]

state 13

    expression -> LPAREN expression RPAREN .

    $               reduce using rule 6
    PLUS            reduce using rule 6
    MINUS           reduce using rule 6
    TIMES           reduce using rule 6
    DIVIDE          reduce using rule 6
    RPAREN          reduce using rule 6

  ! TIMES           [ reduce using rule 2 ]
  ! DIVIDE          [ reduce using rule 2 ]
  ! PLUS            [ shift and go to state 6 ]
  ! MINUS           [ shift and go to state 5 ]

Syntax Error Handling

When a syntax error occurs, yacc.py performs the following steps:

1. On the first occurrence of an error, the user-defined p_error() function is called with the offending token as an argument. Afterwards, the parser enters an "error-recovery" mode in which it will not make future calls to p_error() until it has successfully shifted at least 3 tokens onto the parsing stack.

2. If no recovery action is taken in p_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

def p_statement_print(t):
     'statement : PRINT expr SEMI'
     ...

def p_statement_print_error(t):
     'statement : PRINT error SEMI'
     print "Syntax error in print statement. Bad expression"

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:

def p_statement_print_error(t):
    'statement : PRINT error'
    print "Syntax error in print statement. Bad expression"

Panic mode recovery

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

def p_error(t):
    print "Whoa. You are seriously hosed."
    # Read ahead looking for a closing '}'
    while 1:
        tok = yacc.token()             # Get the next token
        if not tok or tok.type == 'RBRACE': break
    yacc.restart()

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

def p_error(t):
    print "Syntax error at token", t.type
    # Just discard the token and tell the parser it's okay.
    yacc.errok()

Within the p_error() function, three functions are available to control the behavior of the parser:

• yacc.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 p_error() again.

• yacc.token(). This returns the next token on the input stream.

• yacc.restart(). This discards the entire parsing stack and resets the parser to its initial state.

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

def p_error(t):
    # Read ahead looking for a terminating ";"
    while 1:
        tok = yacc.token()             # Get the next token
        if not tok or tok.type == 'SEMI': break
    yacc.errok()

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

General comments on error handling

Line Number Tracking

• t.lineno(num). Return the starting line number for symbol num
• t.linespan(num). Return a tuple (startline,endline) with the starting and ending line number for symbol num.

def t_expression(t):
    'expression : expression PLUS expression'
    t.lineno(1)        # Line number of the left expression
    t.lineno(2)        # line number of the PLUS operator
    t.lineno(3)        # line number of the right expression
    ...
    start,end = t.linespan(3)    # Start,end lines of the right expression

AST Construction

class Expr: pass

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

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

def p_expression_binop(t):
    '''expression : expression PLUS expression
                  | expression MINUS expression
                  | expression TIMES expression
                  | expression DIVIDE expression'''

    t[0] = BinOp(t[1],t[2],t[3])

def p_expression_group(t):
    'expression : LPAREN expression RPAREN'
    t[0] = t[2]

def p_expression_number(t):
    'expression : NUMBER'
    t[0] = Number(t[1])

class Node:
    def __init__(self,type,children=None,leaf=None):
         self.type = type
         if children:
              self.children = children
         else:
              self.children = [ ]
         self.leaf = leaf
	 
def p_expression_binop(t):
    '''expression : expression PLUS expression
                  | expression MINUS expression
                  | expression TIMES expression
                  | expression DIVIDE expression'''

    t[0] = Node("binop", [t[1],t[3]], t[2])

Yacc implementation notes

• By default, yacc.py relies on lex.py for tokenizing. However, an alternative tokenizer can be supplied as follows:

  yacc.parse(lexer=x)
  

  in this case, x must be a Lexer object that minimally has a x.token() method for retrieving the next token. If an input string is given to yacc.parse(), the lexer must also have an x.input() method.

• By default, the yacc generates tables in debugging mode (which produces the parser.out file and other output). To disable this, use

  yacc.yacc(debug=0)
  

• To change the name of the parsetab.py file, use:

  yacc.yacc(tabmodule="foo")
  

• To print copious amounts of debugging during parsing, use:

  yacc.parse(debug=1)
  

• The yacc.yacc() function really returns a parser object. If you want to support multiple parsers in the same application, do this:

  p = yacc.yacc()
  ...
  p.parse()
  

  Note: The function yacc.parse() is bound to the last parser that was generated.

• Since the generation of the SLR tables is relatively expensive, previously generated tables are cached and reused if possible. The decision to regenerate the tables is determined by taking an MD5 checksum of all grammar rules and precedence rules. Only in the event of a mismatch are the tables regenerated.

  It should be noted that table generation is reasonably efficient, even for grammars that involve around a 100 rules and several hundred states. For more complex languages such as C, table generation may take 30-60 seconds on a slow machine. Please be patient.

• Since LR parsing is mostly driven by tables, the performance of the parser is largely independent of the size of the grammar. The biggest bottlenecks will be the lexer and the complexity of your grammar rules.

Where to go from here?