Documentation version: $Header: /cvs/projects/PLY/doc/ply.html,v 1.7 2001/06/18 21:48:15 beazley Exp $
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.
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).
# ------------------------------------------------------------
# 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
In the example, the tokens list defines all of the possible
token names that can be produced by the lexer. This list is always required
and is used to perform a variety of validation checks. Following the tokens
list, regular expressions are written for each token. Each of these
rules are defined by making declarations with a special prefix t_ to indicate that it
defines a token. For simple tokens, the regular expression can
be specified as strings such as this (note: Python raw strings are used since they are the
most convenient way to write regular expression strings):
In this case, the name following the t_ must exactly match one of the names supplied in tokens. If some kind of action needs to be performed, a token rule can be specified as a function. For example: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
In this case, the regular expression rule is specified in the function documentation string.
The function always takes a single argument which is an instance of
LexToken. This object has attributes of t.type which is the token type,
t.value which is the lexeme, and t.lineno which is the current line number.
By default, t.type is set to the name following the t_ prefix. The action
function can modify the contents of the LexToken object as appropriate. However,
when it is done, the resulting token should be returned. If no value is returned by the action
function, the token is simply discarded and the next token read.
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.
$ 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)
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.
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
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).
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.
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.lex.lex(optimize=1)
lex.lex(debug=1)
if __name__ == '__main__':
lex.runmain()
Then, run you lexer as a main program such as python mylex.py
expression : expression + term
| expression - term
| term
term : term * factor
| term / factor
| factor
factor : NUMBER
| ( expression )
Next, the semantic behavior of a language is often specified using a
technique known as syntax directed translation. In syntax directed
translation, attributes are attached to each symbol in a given grammar
rule along with an action. Whenever a particular grammar rule is
recognized, the action describes what to do. For example, given the
expression grammar above, you might write the specification for a
simple calculator like this:
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
Finally, Yacc 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 code is triggered and the
grammar symbols 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. 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:
When parsing the expression, an underlying state machine and the current input token determine what to do 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).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
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
In this example, each grammar rule is defined by a Python function where the docstring to that function contains the
appropriate context-free grammar specification (an idea borrowed from John Aycock's SPARK toolkit). Each function accepts a single
argument t that is a sequence containing the values of each grammar symbol in the corresponding rule. The values of
t[i] are mapped to grammar symbols as shown here:
def p_expression_plus(t):
'expression : expression PLUS term'
# ^ ^ ^ ^
# t[0] t[1] t[2] t[3]
t[0] = t[1] + t[3]
For tokens, the "value" in the corresponding t[i] is the
same as the value of the t.value attribute assigned
in the lexer module. For non-terminals, the value is determined by
whatever is placed in t[0] when rules are reduced. This
value can be anything at all. However, it probably most common for
the value to be a simple Python type, a tuple, or an instance. In this example, we
are relying on the fact that the NUMBER token stores an integer value in its value
field. All of the other rules simply perform various types of integer operations and store
the result.
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:
Since table construction is relatively expensive (especially for large grammars), the resulting parsing table is written to the current directory in a file called parsetab.py. In addition, a debugging file called parser.out is created. On subsequent executions, yacc will reload the table from parsetab.py unless it has detected a change in the underlying grammar (in which case the tables and parsetab.py file are regenerated).$ 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:
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]
Instead of writing two functions, you might write a single function like this:
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]
In general, the doc string for any given function can contain multiple grammar rules. So, it would
have also been legal (although possibly confusing) to write this:
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]
When combining grammar rules into a single function, it is usually a good idea for all of the rules to have
a similar structure (e.g., the same number of terms). Otherwise, the corresponding action code may be more
complicated than necessary.
def p_empty(t):
'empty :'
pass
Now to use the empty production, simply use 'empty' as a symbol. For example:
def p_optitem(t):
'optitem : item'
' | empty'
...
expression : expression PLUS expression
| expression MINUS expression
| expression TIMES expression
| expression DIVIDE expression
| LPAREN expression 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 this expression mean "(3 * 4) + 5" or is it "3 * (4+5)"?
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:
In this case, when the parser reaches step 6, it has two options. One is the 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.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'),
)
This 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.
Furthermore, the declaration specifies that TIMES/DIVIDE have higher
precedence than PLUS/MINUS (since they appear later in the
precedence specification).
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
When shift/reduce conflicts are encountered, the parser generator resolves the conflict by
looking at the precedence rules and associativity specifiers.
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
)
Now, in the grammar file, we can write our unary minus rule like this:
def p_expr_uminus(t):
'expression : MINUS expression %prec UMINUS'
t[0] = -t[2]
In this case, %prec UMINUS overrides the default rule precedence--setting it to that
of UMINUS in the precedence specifier.
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
In this case, a reduce/reduce conflict exists between these two rules:
For example, if you wrote "a = 5", the parser can't figure out if this is supposed to 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 expression.assignment : ID EQUALS NUMBER expression : NUMBER
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
In the file, each state of the grammar is described. Within each state the "." indicates the current
location of the parse within any applicable grammar rules. In addition, the actions for each valid
input token are listed. When a shift/reduce or reduce/reduce conflict arises, rules not selected
are prefixed with an !. For example:
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 parser.out.! TIMES [ reduce using rule 2 ] ! DIVIDE [ reduce using rule 2 ] ! PLUS [ shift and go to state 6 ] ! MINUS [ shift and go to state 5 ]
When a syntax error occurs, yacc.py performs the following steps:
def p_statement_print(t):
'statement : PRINT expr SEMI'
...
To account for the possibility of a bad expression, you might write an additional grammar rule like this:
def p_statement_print_error(t):
'statement : PRINT error SEMI'
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:
def p_statement_print_error(t):
'statement : PRINT error'
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.
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:
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
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
Since line numbers are managed internally by the parser, there is usually no need to modify the line
numbers. However, if you want to save the line numbers in a parse-tree node, you will need to make your own
private copy.
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])
To simplify tree traversal, it may make sense to pick a very generic tree structure for your parse tree nodes.
For example:
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])
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.yacc.parse(lexer=x)
yacc.yacc(debug=0)
yacc.yacc(tabmodule="foo")
yacc.parse(debug=1)
Note: The function yacc.parse() is bound to the last parser that was generated.p = yacc.yacc() ... p.parse()
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.