SysIII/usr/src/man/docs/yacc
.ds :? YACC
.de PT
.lt \\n(LLu
.pc %
.nr PN \\n%
.if \\n%-1 .if o .tl '\s9\f2\*(:?\fP''\\n(PN\s0'
.if \\n%-1 .if e .tl '\s9\\n(PN''\f2\*(:?\^\fP\s0'
.lt \\n(.lu
..
'\" .RP
'\" .ND "July 31, 1978"
.TL
Yacc:
Yet Another Compiler-Compiler
.AU "MH 2C-559" 3968
Stephen C. Johnson
.AI
.MH
.AB
.PP
Computer program input generally has some structure;
in fact, every computer program that does input can be thought of as defining
an ``input language'' which it accepts.
An input language may be as complex as a programming language, or as simple as
a sequence of numbers.
Unfortunately, usual input facilities
are limited, difficult to use,
and often are lax about checking their inputs for validity.
.PP
Yacc provides a general tool for describing
the input to a computer program.
The Yacc user specifies the structures
of his input, together with code to be invoked as
each such structure is recognized.
Yacc turns such a specification into a subroutine that
handles the input process;
frequently, it is convenient and appropriate to have most
of the flow of control in the user's application
handled by this subroutine.
.PP
The input subroutine produced by Yacc calls a user-supplied routine to
return the next basic input item.
Thus, the user can specify his input in terms of individual input characters, or
in terms of higher level constructs such as names and numbers.
The user-supplied routine may also handle idiomatic features such as
comment and continuation conventions, which typically defy easy grammatical specification.
.PP
Yacc is written in portable C.
The class of specifications accepted is a very general one: LALR(1)
grammars with disambiguating rules.
.PP
In addition to compilers for C, APL, Pascal, RATFOR, etc., Yacc
has also been used for less conventional languages,
including a phototypesetter language, several desk calculator languages, a document retrieval system,
and a Fortran debugging system.
.AE
.OK
Computer Languages
Compilers
Formal Language Theory
.CS 23 11 34 0 0 8
.SH
0: Introduction
.PP
Yacc provides a general tool for imposing structure on the input to a computer program.
The Yacc user prepares a
specification of the input process; this includes rules
describing the input structure, code to be invoked when these
rules are recognized, and a low-level routine to do the
basic input.
Yacc then generates a function to control the input process.
This function, called a
.I parser ,
calls the user-supplied low-level input routine
(the
.I "lexical analyzer" )
to pick up the basic items
(called
.I tokens )
from the input stream.
These tokens are organized according to the input structure rules,
called
.I "grammar rules" \|;
when one of these rules has been recognized,
then user code supplied for this rule, an
.I action ,
is invoked; actions have the ability to return values and
make use of the values of other actions.
.PP
Yacc is written in a portable dialect of C\*([.1\*(.]
and the actions, and output subroutine, are in C as well.
Moreover, many of the syntactic conventions of Yacc follow C.
.PP
The heart of the input specification is a collection of grammar rules.
Each rule describes an allowable structure and gives it a name.
For example, one grammar rule might be
.DS
date : month\_name day \',\' year ;
.DE
Here,
.I date ,
.I month\_name ,
.I day ,
and
.I year
represent structures of interest in the input process;
presumably,
.I month\_name ,
.I day ,
and
.I year
are defined elsewhere.
The comma ``,'' is enclosed in single quotes; this implies that the
comma is to appear literally in the input.
The colon and semicolon merely serve as punctuation in the rule, and have
no significance in controlling the input.
Thus, with proper definitions, the input
.DS
July 4, 1776
.DE
might be matched by the above rule.
.PP
An important part of the input process is carried out by the
lexical analyzer.
This user routine reads the input stream, recognizing the lower level structures,
and communicates these tokens
to the parser.
For historical reasons, a structure recognized by the lexical analyzer is called a
.I "terminal symbol" ,
while the structure recognized by the parser is called a
.I "nonterminal symbol" .
To avoid confusion, terminal symbols will usually be referred to as
.I tokens .
.PP
There is considerable leeway in deciding whether to recognize structures using the lexical
analyzer or grammar rules.
For example, the rules
.DS
month\_name : \'J\' \'a\' \'n\' ;
month\_name : \'F\' \'e\' \'b\' ;
. . .
month\_name : \'D\' \'e\' \'c\' ;
.DE
might be used in the above example.
The lexical analyzer would only need to recognize individual letters, and
.I month\_name
would be a nonterminal symbol.
Such low-level rules tend to waste time and space, and may
complicate the specification beyond Yacc's ability to deal with it.
Usually, the lexical analyzer would
recognize the month names,
and return an indication that a
.I month\_name
was seen; in this case,
.I month\_name
would be a token.
.PP
Literal characters such as ``,'' must also be passed through the lexical
analyzer, and are also considered tokens.
.PP
Specification files are very flexible.
It is realively easy to add to the above example the rule
.DS
date : month \'/\' day \'/\' year ;
.DE
allowing
.DS
7 / 4 / 1776
.DE
as a synonym for
.DS
July 4, 1776
.DE
In most cases, this new rule could be ``slipped in'' to a working system with minimal effort,
and little danger of disrupting existing input.
.PP
The input being read may not conform to the
specifications.
These input errors are detected as early as is theoretically possible with a
left-to-right scan;
thus, not only is the chance of reading and computing with bad
input data substantially reduced, but the bad data can usually be quickly found.
Error handling,
provided as part of the input specifications,
permits the reentry of bad data,
or the continuation of the input process after skipping over the bad data.
.PP
In some cases, Yacc fails to produce a parser when given a set of
specifications.
For example, the specifications may be self contradictory, or they may
require a more powerful recognition mechanism than that available to Yacc.
The former cases represent design errors;
the latter cases
can often be corrected
by making
the lexical analyzer
more powerful, or by rewriting some of the grammar rules.
While Yacc cannot handle all possible specifications, its power
compares favorably with similar systems;
moreover, the
constructions which are difficult for Yacc to handle are
also frequently difficult for human beings to handle.
Some users have reported that the discipline of formulating valid
Yacc specifications for their input revealed errors of
conception or design early in the program development.
.PP
The theory underlying Yacc has been described elsewhere\*(<.\*([.2,\|3,\|4\*(.]\*(>.
Yacc has been extensively used in numerous practical applications,
including
.I lint \*(<,\*([.5\*(.]\*(>,
the Portable C Compiler\*(<,\*([.6\*(.]\*(>,
and a system for typesetting mathematics\*(<.\*([.7\*(.]\*(>.
.PP
The next several sections describe the
basic process of preparing a Yacc specification;
Section 1 describes the preparation of grammar rules,
Section 2 the preparation of the user supplied actions associated with these rules,
and Section 3 the preparation of lexical analyzers.
Section 4 describes the operation of the parser.
Section 5 discusses various reasons why Yacc may be unable to produce a
parser from a specification, and what to do about it.
Section 6 describes a simple mechanism for
handling operator precedences in arithmetic expressions.
Section 7 discusses error detection and recovery.
Section 8 discusses the operating environment and special features
of the parsers Yacc produces.
Section 9 gives some suggestions which should improve the
style and efficiency of the specifications.
Section 10 discusses some advanced topics, and Section 11 gives
acknowledgements.
Appendix A has a brief example, and Appendix B gives a
summary of the Yacc input syntax.
Appendix C gives an example using some of the more advanced
features of Yacc, and, finally,
Appendix D describes mechanisms and syntax
no longer actively supported, but
provided for historical continuity with older versions of Yacc.
.tr *\(**
.tr |\(or
.SH
1: Basic Specifications
.PP
Names refer to either tokens or nonterminal symbols.
Yacc requires
token names to be declared as such.
In addition, for reasons discussed in Section 3, it is often desirable
to include the lexical analyzer as part of the specification file;
it may be useful to include other programs as well.
Thus, every specification file consists of three sections:
the
.I declarations ,
.I "(grammar) rules" ,
and
.I programs .
The sections are separated by double percent ``%%'' marks.
(The percent ``%'' is generally used in Yacc specifications as an escape character.)
.PP
In other words, a full specification file looks like
.DS
declarations
%%
rules
%%
programs
.DE
.PP
The declaration section may be empty.
Moreover, if the programs section is omitted, the second %% mark may be omitted also;
thus, the smallest legal Yacc specification is
.DS
%%
rules
.DE
.PP
Blanks, tabs, and newlines are ignored except
that they may not appear in names or multi-character reserved symbols.
Comments may appear wherever a name is legal; they are enclosed
in /* . . . */, as in C and PL/I.
.PP
The rules section is made up of one or more grammar rules.
A grammar rule has the form:
.DS
A : BODY ;
.DE
A represents a nonterminal name, and BODY represents a sequence of zero or more names and literals.
The colon and the semicolon are Yacc punctuation.
.PP
Names may be of arbitrary length, and may be made up of letters, dot ``.'', underscore ``\_'', and
non-initial digits.
Upper and lower case letters are distinct.
The names used in the body of a grammar rule may represent tokens or nonterminal symbols.
.PP
A literal consists of a character enclosed in single quotes ``\'''.
As in C, the backslash ``\e'' is an escape character within literals, and all the C escapes
are recognized.
Thus
.DS
\'\en\' newline
\'\er\' return
\'\e\'\' single quote ``\'''
\'\e\e\' backslash ``\e''
\'\et\' tab
\'\eb\' backspace
\'\ef\' form feed
\'\exxx\' ``xxx'' in octal
.DE
For a number of technical reasons, the
\s-2NUL\s0
character (\'\e0\' or 0) should never
be used in grammar rules.
.PP
If there are several grammar rules with the same left hand side, the vertical bar ``|''
can be used to avoid rewriting the left hand side.
In addition,
the semicolon at the end of a rule can be dropped before a vertical bar.
Thus the grammar rules
.DS
A : B C D ;
A : E F ;
A : G ;
.DE
can be given to Yacc as
.DS
A : B C D
| E F
| G
;
.DE
It is not necessary that all grammar rules with the same left side appear together in the grammar rules section,
although it makes the input much more readable, and easier to change.
.PP
If a nonterminal symbol matches the empty string, this can be indicated in the obvious way:
.DS
empty : ;
.DE
.PP
Names representing tokens must be declared; this is most simply done by writing
.DS
%token name1 name2 . . .
.DE
in the declarations section.
(See Sections 3 , 5, and 6 for much more discussion).
Every name not defined in the declarations section is assumed to represent a nonterminal symbol.
Every nonterminal symbol must appear on the left side of at least one rule.
.PP
Of all the nonterminal symbols, one, called the
.I "start symbol" ,
has particular importance.
The parser is designed to recognize the start symbol; thus,
this symbol represents the largest,
most general structure described by the grammar rules.
By default,
the start symbol is taken to be the left hand side of the first
grammar rule in the rules section.
It is possible, and in fact desirable, to declare the start
symbol explicitly in the declarations section using the %start keyword:
.DS
%start symbol
.DE
.PP
The end of the input to the parser is signaled by a special token, called the
.I endmarker .
If the tokens up to, but not including, the endmarker form a structure
which matches the start symbol, the parser function returns to its caller
after the endmarker is seen; it
.I accepts
the input.
If the endmarker is seen in any other context, it is an error.
.PP
It is the job of the user-supplied lexical analyzer
to return the endmarker when appropriate; see section 3, below.
Usually the endmarker represents some reasonably obvious
I/O status, such as ``end-of-file'' or ``end-of-record''.
.SH
2: Actions
.PP
With each grammar rule, the user may associate actions to be performed each time
the rule is recognized in the input process.
These actions may return values, and may obtain the values returned by previous
actions.
Moreover, the lexical analyzer can return values
for tokens, if desired.
.PP
An action is an arbitrary C statement, and as such can do
input and output, call subprograms, and alter
external vectors and variables.
An action is specified by
one or more statements, enclosed in curly braces ``{'' and ``}''.
For example,
.DS
A : \'(\' B \')\'
{ hello( 1, "abc" ); }
.DE
and
.DS
XXX : YYY ZZZ
{ printf("a message\en");
flag = 25; }
.DE
are grammar rules with actions.
.PP
To facilitate easy communication between the actions and the parser, the action statements are altered
slightly.
The symbol ``dollar sign'' ``$'' is used as a signal to Yacc in this context.
.PP
To return a value, the action normally sets the
pseudo-variable ``$$'' to some value.
For example, an action that does nothing but return the value 1 is
.DS
{ $$ = 1; }
.DE
.PP
To obtain the values returned by previous actions and the lexical analyzer, the
action may use the pseudo-variables $1, $2, . . .,
which refer to the values returned by the
components of the right side of a rule, reading from left to right.
Thus, if the rule is
.DS
A : B C D ;
.DE
for example, then $2 has the value returned by C, and $3 the value returned by D.
.PP
As a more concrete example, consider the rule
.DS
expr : \'(\' expr \')\' ;
.DE
The value returned by this rule is usually the value of the
.I expr
in parentheses.
This can be indicated by
.DS
expr : \'(\' expr \')\' { $$ = $2 ; }
.DE
.PP
By default, the value of a rule is the value of the first element in it ($1).
Thus, grammar rules of the form
.DS
A : B ;
.DE
frequently need not have an explicit action.
.PP
In the examples above, all the actions came at the end of their rules.
Sometimes, it is desirable to get control before a rule is fully parsed.
Yacc permits an action to be written in the middle of a rule as well
as at the end.
This rule is assumed to return a value, accessible
through the usual \$ mechanism by the actions to
the right of it.
In turn, it may access the values
returned by the symbols to its left.
Thus, in the rule
.DS
A : B
{ $$ = 1; }
C
{ x = $2; y = $3; }
;
.DE
the effect is to set
.I x
to 1, and
.I y
to the value returned by C.
.PP
Actions that do not terminate a rule are actually
handled by Yacc by manufacturing a new nonterminal
symbol name, and a new rule matching this
name to the empty string.
The interior action is the action triggered off by recognizing
this added rule.
Yacc actually treats the above example as if
it had been written:
.DS
$ACT : /* empty */
{ $$ = 1; }
;
A : B $ACT C
{ x = $2; y = $3; }
;
.DE
.PP
In many applications, output is not done directly by the actions;
rather, a data structure, such as a parse tree, is constructed in memory,
and transformations are applied to it before output is generated.
Parse trees are particularly easy to
construct, given routines to build and maintain the tree
structure desired.
For example, suppose there is a C function
.I node ,
written so that the call
.DS
node( L, n1, n2 )
.DE
creates a node with label L, and descendants n1 and n2, and returns the index of
the newly created node.
Then parse tree can be built by supplying actions such as:
.DS
expr : expr \'+\' expr
{ $$ = node( \'+\', $1, $3 ); }
.DE
in the specification.
.PP
The user may define other variables to be used by the actions.
Declarations and definitions can appear in
the declarations section,
enclosed in the marks ``%{'' and ``%}''.
These declarations and definitions have global scope,
so they are known to the action statements and the lexical analyzer.
For example,
.DS
%{ int variable = 0; %}
.DE
could be placed in the declarations section,
making
.I variable
accessible to all of the actions.
The Yacc parser uses only names beginning in ``yy'';
the user should avoid such names.
.PP
In these examples, all the values are integers: a discussion of
values of other types will be found in Section 10.
.SH
3: Lexical Analysis
.PP
The user must supply a lexical analyzer to read the input stream and communicate tokens
(with values, if desired) to the parser.
The lexical analyzer is an integer-valued function called
.I yylex .
The function returns an integer, the
.I "token number" ,
representing the kind of token read.
If there is a value associated with that token, it should be assigned
to the external variable
.I yylval .
.PP
The parser and the lexical analyzer must agree on these token numbers in order for
communication between them to take place.
The numbers may be chosen by Yacc, or chosen by the user.
In either case, the ``# define'' mechanism of C is used to allow the lexical analyzer
to return these numbers symbolically.
For example, suppose that the token name DIGIT has been defined in the declarations section of the
Yacc specification file.
The relevant portion of the lexical analyzer might look like:
.DS
yylex(){
extern int yylval;
int c;
. . .
c = getchar();
. . .
switch( c ) {
. . .
case \'0\':
case \'1\':
. . .
case \'9\':
yylval = c\-\'0\';
return( DIGIT );
. . .
}
. . .
.DE
.PP
The intent is to return a token number of DIGIT, and a value equal to the numerical value of the
digit.
Provided that the lexical analyzer code is placed in the programs section of the specification file,
the identifier DIGIT will be defined as the token number associated
with the token DIGIT.
.PP
This mechanism leads to clear,
easily modified lexical analyzers; the only pitfall is the need
to avoid using any token names in the grammar that are reserved
or significant in C or the parser; for example, the use of
token names
.I if
or
.I while
will almost certainly cause severe
difficulties when the lexical analyzer is compiled.
The token name
.I error
is reserved for error handling, and should not be used naively
(see Section 7).
.PP
As mentioned above, the token numbers may be chosen by Yacc or by the user.
In the default situation, the numbers are chosen by Yacc.
The default token number for a literal
character is the numerical value of the character in the local character set.
Other names are assigned token numbers
starting at 257.
.PP
To assign a token number to a token (including literals),
the first appearance of the token name or literal
.I
in the declarations section
.R
can be immediately followed by
a nonnegative integer.
This integer is taken to be the token number of the name or literal.
Names and literals not defined by this mechanism retain their default definition.
It is important that all token numbers be distinct.
.PP
For historical reasons, the endmarker must have token
number 0 or negative.
This token number cannot be redefined by the user; thus, all
lexical analyzers should be prepared to return 0 or negative as a token number
upon reaching the end of their input.
.PP
A very useful tool for constructing lexical analyzers is
the
.I Lex
program developed by Mike Lesk\*(<.\*([.8\*(.]\*(>.
These lexical analyzers are designed to work in close
harmony with Yacc parsers.
The specifications for these lexical analyzers
use regular expressions instead of grammar rules.
Lex can be easily used to produce quite complicated lexical analyzers,
but there remain some languages (such as FORTRAN) which do not
fit any theoretical framework, and whose lexical analyzers
must be crafted by hand.
.SH
4: How the Parser Works
.PP
Yacc turns the specification file into a C program, which
parses the input according to the specification given.
The algorithm used to go from the
specification to the parser is complex, and will not be discussed
here (see
the references for more information).
The parser itself, however, is relatively simple,
and understanding how it works, while
not strictly necessary, will nevertheless make
treatment of error recovery and ambiguities much more
comprehensible.
.PP
The parser produced by Yacc consists
of a finite state machine with a stack.
The parser is also capable of reading and remembering the next
input token (called the
.I lookahead
token).
The
.I "current state"
is always the one on the top of the stack.
The states of the finite state machine are given
small integer labels; initially, the machine is in state 0,
the stack contains only state 0, and no lookahead token has been read.
.PP
The machine has only four actions available to it, called
.I shift ,
.I reduce ,
.I accept ,
and
.I error .
A move of the parser is done as follows:
.IP 1.
Based on its current state, the parser decides
whether it needs a lookahead token to decide
what action should be done; if it needs one, and does
not have one, it calls
.I yylex
to obtain the next token.
.IP 2.
Using the current state, and the lookahead token
if needed, the parser decides on its next action, and
carries it out.
This may result in states being pushed onto the stack, or popped off of
the stack, and in the lookahead token being processed
or left alone.
.PP
The
.I shift
action is the most common action the parser takes.
Whenever a shift action is taken, there is always
a lookahead token.
For example, in state 56 there may be
an action:
.DS
IF shift 34
.DE
which says, in state 56, if the lookahead token is IF,
the current state (56) is pushed down on the stack,
and state 34 becomes the current state (on the
top of the stack).
The lookahead token is cleared.
.PP
The
.I reduce
action keeps the stack from growing without
bounds.
Reduce actions are appropriate when the parser has seen
the right hand side of a grammar rule,
and is prepared to announce that it has seen
an instance of the rule, replacing the right hand side
by the left hand side.
It may be necessary to consult the lookahead token
to decide whether to reduce, but
usually it is not; in fact, the default
action (represented by a ``.'') is often a reduce action.
.PP
Reduce actions are associated with individual grammar rules.
Grammar rules are also given small integer
numbers, leading to some confusion.
The action
.DS
\fB.\fR reduce 18
.DE
refers to
.I "grammar rule"
18, while the action
.DS
IF shift 34
.DE
refers to
.I state
34.
.PP
Suppose the rule being reduced is
.DS
A \fB:\fR x y z ;
.DE
The reduce action depends on the
left hand symbol (A in this case), and the number of
symbols on the right hand side (three in this case).
To reduce, first pop off the top three states
from the stack
(In general, the number of states popped equals the number of symbols on the
right side of the rule).
In effect, these states were the ones
put on the stack while recognizing
.I x ,
.I y ,
and
.I z ,
and no longer serve any useful purpose.
After popping these states, a state is uncovered
which was the state the parser was in before beginning to
process the rule.
Using this uncovered state, and the symbol
on the left side of the rule, perform what is in
effect a shift of A.
A new state is obtained, pushed onto the stack, and parsing continues.
There are significant differences between the processing of
the left hand symbol and an ordinary shift of a token,
however, so this action is called a
.I goto
action.
In particular, the lookahead token is cleared by a shift, and
is not affected by a goto.
In any case, the uncovered state contains an entry such as:
.DS
A goto 20
.DE
causing state 20 to be pushed
onto the stack, and become the current state.
.PP
In effect, the reduce action ``turns back the clock'' in the parse,
popping the states off the stack to go back to the
state where the right hand side of the rule was first seen.
The parser then behaves as if it had seen the left side at that time.
If the right hand side of the rule is empty,
no states are popped off of the stack: the uncovered state
is in fact the current state.
.PP
The reduce action is also important in the treatment of user-supplied
actions and values.
When a rule is reduced, the code supplied with the rule is executed
before the stack is adjusted.
In addition to the stack holding the states, another stack,
running in parallel with it, holds the values returned
from the lexical analyzer and the actions.
When a shift takes place, the external variable
.I yylval
is copied onto the value stack.
After the return from the user code, the reduction is carried out.
When the
.I goto
action is done, the external variable
.I yyval
is copied onto the value stack.
The pseudo-variables $1, $2, etc., refer to the value stack.
.PP
The other two parser actions are conceptually much simpler.
The
.I accept
action indicates that the entire input has been seen and
that it matches the specification.
This action appears only when the lookahead token is
the endmarker, and indicates that the parser has successfully
done its job.
The
.I error
action, on the other hand, represents a place where the parser
can no longer continue parsing according to the specification.
The input tokens it has seen, together with the lookahead token,
cannot be followed by anything that would result
in a legal input.
The parser reports an error, and attempts to recover the situation and
resume parsing: the error recovery (as opposed to the detection of error)
will be covered in Section 7.
.PP
It is time for an example!
Consider the specification
.DS
%token DING DONG DELL
%%
rhyme : sound place
;
sound : DING DONG
;
place : DELL
;
.DE
.PP
When Yacc is invoked with the
.B \-v
option, a file called
.I y.output
is produced, with a human-readable description of the parser.
The
.I y.output
file corresponding to the above grammar (with some statistics
stripped off the end) is:
.DS
state 0
$accept : \_rhyme $end
DING shift 3
. error
rhyme goto 1
sound goto 2
state 1
$accept : rhyme\_$end
$end accept
. error
state 2
rhyme : sound\_place
DELL shift 5
. error
place goto 4
state 3
sound : DING\_DONG
DONG shift 6
. error
state 4
rhyme : sound place\_ (1)
. reduce 1
state 5
place : DELL\_ (3)
. reduce 3
state 6
sound : DING DONG\_ (2)
. reduce 2
.DE
Notice that, in addition to the actions for each state, there is a
description of the parsing rules being processed in each
state. The \_ character is used to indicate
what has been seen, and what is yet to come, in each rule.
Suppose the input is
.DS
DING DONG DELL
.DE
It is instructive to follow the steps of the parser while
processing this input.
.PP
Initially, the current state is state 0.
The parser needs to refer to the input in order to decide
between the actions available in state 0, so
the first token,
.I DING ,
is read, becoming the lookahead token.
The action in state 0 on
.I DING
is
is ``shift 3'', so state 3 is pushed onto the stack,
and the lookahead token is cleared.
State 3 becomes the current state.
The next token,
.I DONG ,
is read, becoming the lookahead token.
The action in state 3 on the token
.I DONG
is ``shift 6'',
so state 6 is pushed onto the stack, and the lookahead is cleared.
The stack now contains 0, 3, and 6.
In state 6, without even consulting the lookahead,
the parser reduces by rule 2.
.DS
sound : DING DONG
.DE
This rule has two symbols on the right hand side, so
two states, 6 and 3, are popped off of the stack, uncovering state 0.
Consulting the description of state 0, looking for a goto on
.I sound ,
.DS
sound goto 2
.DE
is obtained; thus state 2 is pushed onto the stack,
becoming the current state.
.PP
In state 2, the next token,
.I DELL ,
must be read.
The action is ``shift 5'', so state 5 is pushed onto the stack, which now has
0, 2, and 5 on it, and the lookahead token is cleared.
In state 5, the only action is to reduce by rule 3.
This has one symbol on the right hand side, so one state, 5,
is popped off, and state 2 is uncovered.
The goto in state 2 on
.I place ,
the left side of rule 3,
is state 4.
Now, the stack contains 0, 2, and 4.
In state 4, the only action is to reduce by rule 1.
There are two symbols on the right, so the top two states are popped off,
uncovering state 0 again.
In state 0, there is a goto on
.I rhyme
causing the parser to enter state 1.
In state 1, the input is read; the endmarker is obtained,
indicated by ``$end'' in the
.I y.output
file.
The action in state 1 when the endmarker is seen is to accept,
successfully ending the parse.
.PP
The reader is urged to consider how the parser works
when confronted with such incorrect strings as
.I "DING DONG DONG" ,
.I "DING DONG" ,
.I "DING DONG DELL DELL" ,
etc.
A few minutes spend with this and other simple examples will
probably be repaid when problems arise in more complicated contexts.
.SH
5: Ambiguity and Conflicts
.PP
A set of grammar rules is
.I ambiguous
if there is some input string that can be structured in two or more different ways.
For example, the grammar rule
.DS
expr : expr \'\-\' expr
.DE
is a natural way of expressing the fact that one way of forming an arithmetic expression
is to put two other expressions together with a minus sign between them.
Unfortunately, this grammar rule does not
completely specify the way that all complex inputs
should be structured.
For example, if the input is
.DS
expr \- expr \- expr
.DE
the rule allows this input to be structured as either
.DS
( expr \- expr ) \- expr
.DE
or as
.DS
expr \- ( expr \- expr )
.DE
(The first is called
.I "left association" ,
the second
.I "right association" ).
.PP
Yacc detects such ambiguities when it is attempting to build the parser.
It is instructive to consider the problem that confronts the parser when it is
given an input such as
.DS
expr \- expr \- expr
.DE
When the parser has read the second expr, the input that it has seen:
.DS
expr \- expr
.DE
matches the right side of the grammar rule above.
The parser could
.I reduce
the input by applying this rule;
after applying the rule;
the input is reduced to
.I expr (the
left side of the rule).
The parser would then read the final part of the input:
.DS
\- expr
.DE
and again reduce.
The effect of this is to take the left associative interpretation.
.PP
Alternatively, when the parser has seen
.DS
expr \- expr
.DE
it could defer the immediate application of the rule, and continue reading
the input until it had seen
.DS
expr \- expr \- expr
.DE
It could then apply the rule to the rightmost three symbols, reducing them to
.I expr
and leaving
.DS
expr \- expr
.DE
Now the rule can be reduced once more; the effect is to
take the right associative interpretation.
Thus, having read
.DS
expr \- expr
.DE
the parser can do two legal things, a shift or a reduction, and has no way of
deciding between them.
This is called a
.I "shift / reduce conflict" .
It may also happen that the parser has a choice of two legal reductions;
this is called a
.I "reduce / reduce conflict" .
Note that there are never any ``Shift/shift'' conflicts.
.PP
When there are shift/reduce or reduce/reduce conflicts, Yacc still produces a parser.
It does this by selecting one of the valid steps wherever it has a choice.
A rule describing which choice to make in a given situation is called
a
.I "disambiguating rule" .
.PP
Yacc invokes two disambiguating rules by default:
.IP 1.
In a shift/reduce conflict, the default is to do the shift.
.IP 2.
In a reduce/reduce conflict, the default is to reduce by the
.I earlier
grammar rule (in the input sequence).
.PP
Rule 1 implies that reductions are deferred whenever there is a choice,
in favor of shifts.
Rule 2 gives the user rather crude control over the behavior of the parser
in this situation, but reduce/reduce conflicts should be avoided whenever possible.
.PP
Conflicts may arise because of mistakes in input or logic, or because the grammar rules, while consistent,
require a more complex parser than Yacc can construct.
The use of actions within rules can also cause conflicts, if the action must
be done before the parser can be sure which rule is being recognized.
In these cases, the application of disambiguating rules is inappropriate,
and leads to an incorrect parser.
For this reason, Yacc
always reports the number of shift/reduce and reduce/reduce conflicts resolved by Rule 1 and Rule 2.
.PP
In general, whenever it is possible to apply disambiguating rules to produce a correct parser, it is also
possible to rewrite the grammar rules so that the same inputs are read but there are no
conflicts.
For this reason, most previous parser generators
have considered conflicts to be fatal errors.
Our experience has suggested that this rewriting is somewhat unnatural,
and produces slower parsers; thus, Yacc will produce parsers even in the presence of conflicts.
.PP
As an example of the power of disambiguating rules, consider a fragment from a programming
language involving an ``if-then-else'' construction:
.DS
stat : IF \'(\' cond \')\' stat
| IF \'(\' cond \')\' stat ELSE stat
;
.DE
In these rules,
.I IF
and
.I ELSE
are tokens,
.I cond
is a nonterminal symbol describing
conditional (logical) expressions, and
.I stat
is a nonterminal symbol describing statements.
The first rule will be called the
.ul
simple-if
rule, and the
second the
.ul
if-else
rule.
.PP
These two rules form an ambiguous construction, since input of the form
.DS
IF ( C1 ) IF ( C2 ) S1 ELSE S2
.DE
can be structured according to these rules in two ways:
.DS
IF ( C1 ) {
IF ( C2 ) S1
}
ELSE S2
.DE
or
.DS
IF ( C1 ) {
IF ( C2 ) S1
ELSE S2
}
.DE
The second interpretation is the one given in most programming languages
having this construct.
Each
.I ELSE
is associated with the last preceding
``un-\fIELSE'\fRd''
.I IF .
In this example, consider the situation where the parser has seen
.DS
IF ( C1 ) IF ( C2 ) S1
.DE
and is looking at the
.I ELSE .
It can immediately
reduce
by the simple-if rule to get
.DS
IF ( C1 ) stat
.DE
and then read the remaining input,
.DS
ELSE S2
.DE
and reduce
.DS
IF ( C1 ) stat ELSE S2
.DE
by the if-else rule.
This leads to the first of the above groupings of the input.
.PP
On the other hand, the
.I ELSE
may be shifted,
.I S2
read, and then the right hand portion of
.DS
IF ( C1 ) IF ( C2 ) S1 ELSE S2
.DE
can be reduced by the if-else rule to get
.DS
IF ( C1 ) stat
.DE
which can be reduced by the simple-if rule.
This leads to the second of the above groupings of the input, which
is usually desired.
.PP
Once again the parser can do two valid things \- there is a shift/reduce conflict.
The application of disambiguating rule 1 tells the parser to shift in this case,
which leads to the desired grouping.
.PP
This shift/reduce conflict arises only when there is a particular current input symbol,
.I ELSE ,
and particular inputs already seen, such as
.DS
IF ( C1 ) IF ( C2 ) S1
.DE
In general, there may be many conflicts, and each one
will be associated with an input symbol and
a set of previously read inputs.
The previously read inputs are characterized by the
state
of the parser.
.PP
The conflict messages of Yacc are best understood
by examining the verbose (\fB\-v\fR) option output file.
For example, the output corresponding to the above
conflict state might be:
.DS L
23: shift/reduce conflict (shift 45, reduce 18) on ELSE
state 23
stat : IF ( cond ) stat\_ (18)
stat : IF ( cond ) stat\_ELSE stat
ELSE shift 45
. reduce 18
.DE
The first line describes the conflict, giving the state and the input symbol.
The ordinary state description follows, giving
the grammar rules active in the state, and the parser actions.
Recall that the underline marks the
portion of the grammar rules which has been seen.
Thus in the example, in state 23 the parser has seen input corresponding
to
.DS
IF ( cond ) stat
.DE
and the two grammar rules shown are active at this time.
The parser can do two possible things.
If the input symbol is
.I ELSE ,
it is possible to shift into state
45.
State 45 will have, as part of its description, the line
.DS
stat : IF ( cond ) stat ELSE\_stat
.DE
since the
.I ELSE
will have been shifted in this state.
Back in state 23, the alternative action, described by ``\fB.\fR'',
is to be done if the input symbol is not mentioned explicitly in the above actions; thus,
in this case, if the input symbol is not
.I ELSE ,
the parser reduces by grammar rule 18:
.DS
stat : IF \'(\' cond \')\' stat
.DE
Once again, notice that the numbers following ``shift'' commands refer to other states,
while the numbers following ``reduce'' commands refer to grammar
rule numbers.
In the
.I y.output
file, the rule numbers are printed after those rules which can be reduced.
In most one states, there will be at most reduce action possible in the
state, and this will be the default command.
The user who encounters unexpected shift/reduce conflicts will probably want to
look at the verbose output to decide whether the default actions are appropriate.
In really tough cases, the user might need to know more about
the behavior and construction of the parser than can be covered here.
In this case, one of the theoretical references\*([.2,\|3,\|4\*(.]
might be consulted; the services of a local guru might also be appropriate.
.SH
6: Precedence
.PP
There is one common situation
where the rules given above for resolving conflicts are not sufficient;
this is in the parsing of arithmetic expressions.
Most of the commonly used constructions for arithmetic expressions can be naturally
described by the notion of
.I precedence
levels for operators, together with information about left
or right associativity.
It turns out that ambiguous grammars with appropriate disambiguating rules
can be used to create parsers that are faster and easier to
write than parsers constructed from unambiguous grammars.
The basic notion is to write grammar rules
of the form
.DS
expr : expr OP expr
.DE
and
.DS
expr : UNARY expr
.DE
for all binary and unary operators desired.
This creates a very ambiguous grammar, with many parsing conflicts.
As disambiguating rules, the user specifies the precedence, or binding
strength, of all the operators, and the associativity
of the binary operators.
This information is sufficient to allow Yacc to resolve the parsing conflicts
in accordance with these rules, and construct a parser that realizes the desired
precedences and associativities.
.PP
The precedences and associativities are attached to tokens in the declarations section.
This is done by a series of lines beginning with a Yacc keyword: %left, %right,
or %nonassoc, followed by a list of tokens.
All of the tokens on the same line are assumed to have the same precedence level
and associativity; the lines are listed in
order of increasing precedence or binding strength.
Thus,
.DS
%left \'+\' \'\-\'
%left \'*\' \'/\'
.DE
describes the precedence and associativity of the four arithmetic operators.
Plus and minus are left associative, and have lower precedence than
star and slash, which are also left associative.
The keyword %right is used to describe right associative operators,
and the keyword %nonassoc is used to describe operators, like
the operator .LT. in Fortran, that may not associate with themselves; thus,
.DS
A .LT. B .LT. C
.DE
is illegal in Fortran, and such an operator would be described with the keyword
%nonassoc in Yacc.
As an example of the behavior of these declarations, the description
.DS
%right \'=\'
%left \'+\' \'\-\'
%left \'*\' \'/\'
%%
expr : expr \'=\' expr
| expr \'+\' expr
| expr \'\-\' expr
| expr \'*\' expr
| expr \'/\' expr
| NAME
;
.DE
might be used to structure the input
.DS
a = b = c*d \- e \- f*g
.DE
as follows:
.DS
a = ( b = ( ((c*d)\-e) \- (f*g) ) )
.DE
When this mechanism is used,
unary operators must, in general, be given a precedence.
Sometimes a unary operator and a binary operator
have the same symbolic representation, but different precedences.
An example is unary and binary \'\-\'; unary minus may be given the same
strength as multiplication, or even higher, while binary minus has a lower strength than
multiplication.
The keyword, %prec, changes the precedence level associated with a particular grammar rule.
%prec appears immediately after the body of the grammar rule, before the action or closing semicolon,
and is followed by a token name or literal.
It
causes the precedence of the grammar rule to become that of the following token name or literal.
For example, to make unary minus have the same precedence as multiplication the rules might resemble:
.DS
%left \'+\' \'\-\'
%left \'*\' \'/\'
%%
expr : expr \'+\' expr
| expr \'\-\' expr
| expr \'*\' expr
| expr \'/\' expr
| \'\-\' expr %prec \'*\'
| NAME
;
.DE
.PP
A token declared
by %left, %right, and %nonassoc need not be, but may be, declared by %token as well.
.PP
The precedences and associativities are used by Yacc to
resolve parsing conflicts; they give rise to disambiguating rules.
Formally, the rules work as follows:
.IP 1.
The precedences and associativities are recorded for those tokens and literals
that have them.
.IP 2.
A precedence and associativity is associated with each grammar rule; it is the precedence
and associativity of the last token or literal in the body of the rule.
If the %prec construction is used, it overrides this default.
Some grammar rules may have no precedence and associativity associated with them.
.IP 3.
When there is a reduce/reduce conflict, or there is a shift/reduce conflict
and either the input symbol or the grammar rule has no precedence and associativity,
then the two disambiguating rules given at the beginning of the section are used,
and the conflicts are reported.
.IP 4.
If there is a shift/reduce conflict, and both the grammar rule and the input character
have precedence and associativity associated with them, then the conflict is resolved
in favor of the action (shift or reduce) associated with the higher precedence.
If the precedences are the same, then the associativity is used; left
associative implies reduce, right associative implies shift, and nonassociating
implies error.
.PP
Conflicts resolved by precedence are not counted in the number of shift/reduce and reduce/reduce
conflicts reported by Yacc.
This means that mistakes in the specification of precedences may
disguise errors in the input grammar; it is a good idea to be sparing
with precedences, and use them in an essentially ``cookbook'' fashion,
until some experience has been gained.
The
.I y.output
file
is very useful in deciding whether the parser is actually doing
what was intended.
.SH
7: Error Handling
.PP
Error handling is an extremely difficult area, and many of the problems are semantic ones.
When an error is found, for example, it may be necessary to reclaim parse tree storage,
delete or alter symbol table entries, and, typically, set switches to avoid generating any further output.
.PP
It is seldom acceptable to stop all processing when an error is found; it is more useful to continue
scanning the input to find further syntax errors.
This leads to the problem of getting the parser ``restarted'' after an error.
A general class of algorithms to do this involves discarding a number of tokens
from the input string, and attempting to adjust the parser so that input can continue.
.PP
To allow the user some control over this process,
Yacc provides a simple, but reasonably general, feature.
The token name ``error'' is reserved for error handling.
This name can be used in grammar rules;
in effect, it suggests places where errors are expected, and recovery might take place.
The parser pops its stack until it enters a state where the token ``error'' is legal.
It then behaves as if the token ``error'' were the current lookahead token,
and performs the action encountered.
The lookahead token is then reset to the token that caused the error.
If no special error rules have been specified, the processing halts when an error is detected.
.PP
In order to prevent a cascade of error messages, the parser, after
detecting an error, remains in error state until three tokens have been successfully
read and shifted.
If an error is detected when the parser is already in error state,
no message is given, and the input token is quietly deleted.
.PP
As an example, a rule of the form
.DS
stat : error
.DE
would, in effect, mean that on a syntax error the parser would attempt to skip over the statement
in which the error was seen.
More precisely, the parser will
scan ahead, looking for three tokens that might legally follow
a statement, and start processing at the first of these; if
the beginnings of statements are not sufficiently distinctive, it may make a
false start in the middle of a statement, and end up reporting a
second error where there is in fact no error.
.PP
Actions may be used with these special error rules.
These actions might attempt to reinitialize tables, reclaim symbol table space, etc.
.PP
Error rules such as the above are very general, but difficult to control.
Somewhat easier are rules such as
.DS
stat : error \';\'
.DE
Here, when there is an error, the parser attempts to skip over the statement, but
will do so by skipping to the next \';\'.
All tokens after the error and before the next \';\' cannot be shifted, and are discarded.
When the \';\' is seen, this rule will be reduced, and any ``cleanup''
action associated with it performed.
.PP
Another form of error rule arises in interactive applications, where
it may be desirable to permit a line to be reentered after an error.
A possible error rule might be
.DS
input : error \'\en\' { printf( "Reenter last line: " ); } input
{ $$ = $4; }
.DE
There is one potential difficulty with this approach;
the parser must correctly process three input tokens before it
admits that it has correctly resynchronized after the error.
If the reentered line contains an error
in the first two tokens, the parser deletes the offending tokens,
and gives no message; this is clearly unacceptable.
For this reason, there is a mechanism that
can be used to force the parser
to believe that an error has been fully recovered from.
The statement
.DS
yyerrok ;
.DE
in an action
resets the parser to its normal mode.
The last example is better written
.DS
input : error \'\en\'
{ yyerrok;
printf( "Reenter last line: " ); }
input
{ $$ = $4; }
;
.DE
.PP
As mentioned above, the token seen immediately
after the ``error'' symbol is the input token at which the
error was discovered.
Sometimes, this is inappropriate; for example, an
error recovery action might
take upon itself the job of finding the correct place to resume input.
In this case,
the previous lookahead token must be cleared.
The statement
.DS
yyclearin ;
.DE
in an action will have this effect.
For example, suppose the action after error
were to call some sophisticated resynchronization routine,
supplied by the user, that attempted to advance the input to the
beginning of the next valid statement.
After this routine was called, the next token returned by yylex would presumably
be the first token in a legal statement;
the old, illegal token must be discarded, and the error state reset.
This could be done by a rule like
.DS
stat : error
{ resynch();
yyerrok ;
yyclearin ; }
;
.DE
.PP
These mechanisms are admittedly crude, but do allow for a simple, fairly effective recovery of the parser
from many errors;
moreover, the user can get control to deal with
the error actions required by other portions of the program.
.SH
8: The Yacc Environment
.PP
When the user inputs a specification
to Yacc, the output is a file of C programs, called
.I y.tab.c
on most
systems
(due to local file system conventions, the names may differ from
installation to installation).
The function produced by Yacc is called
.I yyparse \|;
it is an integer valued function.
When it is called, it in turn repeatedly calls
.I yylex ,
the lexical analyzer
supplied by the user (see Section 3)
to obtain input tokens.
Eventually, either an error is detected, in which case
(if no error recovery is possible)
.I yyparse
returns the value 1,
or the lexical analyzer returns the endmarker token
and the parser accepts.
In this case,
.I yyparse
returns the value 0.
.PP
The user must provide a certain amount of environment for this
parser in order to obtain a working program.
For example, as with every C program, a program called
.I main
must be defined, that eventually calls
.I yyparse .
In addition, a routine called
.I yyerror
prints a message
when a syntax error is detected.
.PP
These two routines must be supplied in one form or another by the
user.
To ease the initial effort of using Yacc, a library has been
provided with default versions of
.I main
and
.I yyerror .
The name of this library is system dependent;
on many systems the library is accessed by a
.B \-ly
argument to the loader.
To show the triviality of these default programs, the source is
given below:
.DS
main(){
return( yyparse() );
}
.DE
and
.DS
# include <stdio.h>
yyerror(s) char *s; {
fprintf( stderr, "%s\en", s );
}
.DE
The argument to
.I yyerror
is a string containing an error message, usually
the string ``syntax error''.
The average application will want to do better than this.
Ordinarily, the program should keep track of the input line number, and print it
along with the message when a syntax error is detected.
The external integer variable
.I yychar
contains the lookahead token number at the time the error was detected;
this may be of some interest in giving better diagnostics.
Since the
.I main
program is probably supplied by the user (to read arguments, etc.)
the Yacc library is useful only in small
projects, or in the earliest stages of larger ones.
.PP
The external integer variable
.I yydebug
is normally set to 0.
If it is set to a nonzero value, the parser will output a
verbose description of its actions, including
a discussion of which input symbols have been read, and
what the parser actions are.
Depending on the operating environment,
it may be possible to set this variable by using a debugging system.
.SH
9: Hints for Preparing Specifications
.PP
This section contains miscellaneous hints on preparing efficient, easy to change,
and clear specifications.
The individual subsections are more or less
independent.
.SH
Input Style
.PP
It is difficult to
provide rules with substantial actions
and still have a readable specification file.
The following style hints owe much to Brian Kernighan.
.IP a.
Use all capital letters for token names, all lower case letters for
nonterminal names.
This rule comes under the heading of ``knowing who to blame when
things go wrong.''
.IP b.
Put grammar rules and actions on separate lines.
This allows either to be changed without
an automatic need to change the other.
.IP c.
Put all rules with the same left hand side together.
Put the left hand side in only once, and let all
following rules begin with a vertical bar.
.IP d.
Put a semicolon only after the last rule with a given left hand side,
and put the semicolon on a separate line.
This allows new rules to be easily added.
.IP e.
Indent rule bodies by two tab stops, and action bodies by three
tab stops.
.PP
The example in Appendix A is written following this style, as are
the examples in the text of this paper (where space permits).
The user must make up his own mind about these stylistic questions;
the central problem, however, is to make the rules visible through
the morass of action code.
.SH
Left Recursion
.PP
The algorithm used by the Yacc parser encourages so called ``left recursive''
grammar rules: rules of the form
.DS
name : name rest_of_rule ;
.DE
These rules frequently arise when
writing specifications of sequences and lists:
.DS
list : item
| list \',\' item
;
.DE
and
.DS
seq : item
| seq item
;
.DE
In each of these cases, the first rule
will be reduced for the first item only, and the second rule
will be reduced for the second and all succeeding items.
.PP
With right recursive rules, such as
.DS
seq : item
| item seq
;
.DE
the parser would be a bit bigger, and the items would be seen, and reduced,
from right to left.
More seriously, an internal stack in the parser
would be in danger of overflowing if a very long sequence were read.
Thus, the user should use left recursion wherever reasonable.
.PP
It is worth considering whether a sequence with zero
elements has any meaning, and if so, consider writing
the sequence specification with an empty rule:
.DS
seq : /* empty */
| seq item
;
.DE
Once again, the first rule would always be reduced exactly once, before the
first item was read,
and then the second rule would be reduced once for each item read.
Permitting empty sequences
often leads to increased generality.
However, conflicts might arise if Yacc is asked to decide
which empty sequence it has seen, when it hasn't seen enough to
know!
.SH
Lexical Tie-ins
.PP
Some lexical decisions depend on context.
For example, the lexical analyzer might want to
delete blanks normally, but not within quoted strings.
Or names might be entered into a symbol table in declarations,
but not in expressions.
.PP
One way of handling this situation is
to create a global flag that is
examined by the lexical analyzer, and set by actions.
For example, suppose a program
consists of 0 or more declarations, followed by 0 or more statements.
Consider:
.DS
%{
int dflag;
%}
... other declarations ...
%%
prog : decls stats
;
decls : /* empty */
{ dflag = 1; }
| decls declaration
;
stats : /* empty */
{ dflag = 0; }
| stats statement
;
... other rules ...
.DE
The flag
.I dflag
is now 0 when reading statements, and 1 when reading declarations,
.ul
except for the first token in the first statement.
This token must be seen by the parser before it can tell that
the declaration section has ended and the statements have
begun.
In many cases, this single token exception does not
affect the lexical scan.
.PP
This kind of ``backdoor'' approach can be elaborated
to a noxious degree.
Nevertheless, it represents a way of doing some things
that are difficult, if not impossible, to
do otherwise.
.SH
Reserved Words
.PP
Some programming languages
permit the user to
use words like ``if'', which are normally reserved,
as label or variable names, provided that such use does not
conflict with the legal use of these names in the programming language.
This is extremely hard to do in the framework of Yacc;
it is difficult to pass information to the lexical analyzer
telling it ``this instance of `if' is a keyword, and that instance is a variable''.
The user can make a stab at it, using the
mechanism described in the last subsection,
but it is difficult.
.PP
A number of ways of making this easier are under advisement.
Until then, it is better that the keywords be
.I reserved \|;
that is, be forbidden for use as variable names.
There are powerful stylistic reasons for preferring this, anyway.
.SH
10: Advanced Topics
.PP
This section discusses a number of advanced features
of Yacc.
.SH
Simulating Error and Accept in Actions
.PP
The parsing actions of error and accept can be simulated
in an action by use of macros YYACCEPT and YYERROR.
YYACCEPT causes
.I yyparse
to return the value 0;
YYERROR causes
the parser to behave as if the current input symbol
had been a syntax error;
.I yyerror
is called, and error recovery takes place.
These mechanisms can be used to simulate parsers
with multiple endmarkers or context-sensitive syntax checking.
.SH
Accessing Values in Enclosing Rules.
.PP
An action may refer to values
returned by actions to the left of the current rule.
The mechanism is simply the same as with ordinary actions,
a dollar sign followed by a digit, but in this case the
digit may be 0 or negative.
Consider
.DS
sent : adj noun verb adj noun
{ \fIlook at the sentence\fR . . . }
;
adj : THE { $$ = THE; }
| YOUNG { $$ = YOUNG; }
. . .
;
noun : DOG
{ $$ = DOG; }
| CRONE
{ if( $0 == YOUNG ){
printf( "what?\en" );
}
$$ = CRONE;
}
;
. . .
.DE
In the action following the word CRONE, a check is made that the
preceding token shifted was not YOUNG.
Obviously, this is only possible when a great deal is known about
what might precede the symbol
.I noun
in the input.
There is also a distinctly unstructured flavor about this.
Nevertheless, at times this mechanism will save a great
deal of trouble, especially when a few combinations are to
be excluded from an otherwise regular structure.
.SH
Support for Arbitrary Value Types
.PP
By default, the values returned by actions and the lexical analyzer are integers.
Yacc can also support
values of other types, including structures.
In addition, Yacc keeps track of the types, and inserts
appropriate union member names so that the resulting parser will
be strictly type checked.
The Yacc value stack (see Section 4)
is declared to be a
.I union
of the various types of values desired.
The user declares the union, and associates union member names
to each token and nonterminal symbol having a value.
When the value is referenced through a $$ or $n construction,
Yacc will automatically insert the appropriate union name, so that
no unwanted conversions will take place.
In addition, type checking commands such as
.I Lint\|\*([.5\*(.]
will be far more silent.
.PP
There are three mechanisms used to provide for this typing.
First, there is a way of defining the union; this must be
done by the user since other programs, notably the lexical analyzer,
must know about the union member names.
Second, there is a way of associating a union member name with tokens
and nonterminals.
Finally, there is a mechanism for describing the type of those
few values where Yacc can not easily determine the type.
.PP
To declare the union, the user includes in the declaration section:
.DS
%union {
body of union ...
}
.DE
This declares the Yacc value stack,
and the external variables
.I yylval
and
.I yyval ,
to have type equal to this union.
If Yacc was invoked with the
.B \-d
option, the union declaration
is copied onto the
.I y.tab.h
file.
Alternatively,
the union may be declared in a header file, and a typedef
used to define the variable YYSTYPE to represent
this union.
Thus, the header file might also have said:
.DS
typedef union {
body of union ...
} YYSTYPE;
.DE
The header file must be included in the declarations
section, by use of %{ and %}.
.PP
Once YYSTYPE is defined,
the union member names must be associated
with the various terminal and nonterminal names.
The construction
.DS
< name >
.DE
is used to indicate a union member name.
If this follows
one of the
keywords %token,
%left, %right, and %nonassoc,
the union member name is associated with the tokens listed.
Thus, saying
.DS
%left <optype> \'+\' \'\-\'
.DE
will cause any reference to values returned by these two tokens to be
tagged with
the union member name
.I optype .
Another keyword, %type, is
used similarly to associate
union member names with nonterminals.
Thus, one might say
.DS
%type <nodetype> expr stat
.DE
.PP
There remain a couple of cases where these mechanisms are insufficient.
If there is an action within a rule, the value returned
by this action has no
.I "a priori"
type.
Similarly, reference to left context values (such as $0 \- see the
previous subsection ) leaves Yacc with no easy way of knowing the type.
In this case, a type can be imposed on the reference by inserting
a union member name, between < and >, immediately after
the first $.
An example of this usage is
.DS
rule : aaa { $<intval>$ = 3; } bbb
{ fun( $<intval>2, $<other>0 ); }
;
.DE
This syntax has little to recommend it, but the situation arises rarely.
.PP
A sample specification is given in Appendix C.
The facilities in this subsection are not triggered until they are used:
in particular, the use of %type will turn on these mechanisms.
When they are used, there is a fairly strict level of checking.
For example, use of $n or $$ to refer to something with no defined type
is diagnosed.
If these facilities are not triggered, the Yacc value stack is used to
hold
.I int' s,
as was true historically.
.SH
11: Acknowledgements
.PP
Yacc owes much to a
most stimulating collection of users, who have goaded
me beyond my inclination, and frequently beyond my
ability, in their endless search for ``one more feature''.
Their irritating unwillingness to learn how to
do things my way has usually led to my doing things their way;
most of the time, they have been right.
B. W. Kernighan, P. J. Plauger, S. I. Feldman, C. Imagna,
M. E. Lesk,
and A. Snyder will recognize some of their ideas in the current version
of Yacc.
C. B. Haley contributed to the error recovery algorithm.
D. M. Ritchie, B. W. Kernighan, and M. O. Harris helped translate this document into English.
Al Aho also deserves special credit for bringing
the mountain to Mohammed, and other favors.
'\" .SG "MH-1273-SCJ-unix"
.bp
.]<
.ds [F 1
.]-
.ds [T The C Programming Language
.ds [A B. W. Kernighan
.as [A " and D. M. Ritchie
.ds [I Prentice-Hall
.ds [C Englewood Cliffs, New Jersey
.ds [D 1978
.nr [T 0
.nr [A 0
.nr [O 0
.][ 2 book
.ds [F 2
.]-
.ds [T LR Parsing
.ds [A A. V. Aho
.as [A " and S. C. Johnson
.ds [J Comp. Surveys
.ds [V 6
.ds [N 2
.ds [P 99-124
.nr [P 1
.ds [D June 1974
.nr [T 0
.nr [A 0
.nr [O 0
.][ 1 journal-article
.ds [F 3
.]-
.ds [T Deterministic Parsing of Ambiguous Grammars
.ds [A A. V. Aho
.as [A ", S. C. Johnson
.as [A ", and J. D. Ullman
.ds [J Comm. Assoc. Comp. Mach.
.ds [K acm cacm
.ds [V 18
.ds [N 8
.ds [P 441-452
.nr [P 1
.ds [D August 1975
.nr [T 0
.nr [A 0
.nr [O 0
.][ 1 journal-article
.ds [F 4
.]-
.ds [A A. V. Aho
.as [A " and J. D. Ullman
.ds [T Principles of Compiler Design
.ds [I Addison-Wesley
.ds [C Reading, Mass.
.ds [D 1977
.nr [T 0
.nr [A 0
.nr [O 0
.][ 2 book
.ds [F 5
.]-
.ds [r 65
.ds [R Comp. Sci. Tech. Rep. No. 65
.ds [K CSTR
.ds [A S. C. Johnson
.ds [T Lint, a C Program Checker
.ds [D December 1977
.nr [T 0
.nr [A 0
.nr [O 0
.][ 4 tech-report
.ds [F 6
.]-
.ds [T A Portable Compiler: Theory and Practice
.ds [A S. C. Johnson
.ds [J Proc. 5th ACM Symp. on Principles of Programming Languages
.ds [P 97-104
.nr [P 1
.ds [D January 1978
.nr [T 0
.nr [A 0
.nr [O 0
.][ 1 journal-article
.ds [F 7
.]-
.ds [r 17
.ds [K cstr
.ds [R Comp. Sci. Tech. Rep. No. 17
.ds [I Bell Laboratories
.ds [C Murray Hill, New Jersey
.ds [A B. W. Kernighan
.as [A ", L. L. Cherry
.as [A ", and C. Scrocca
.ds [T A System for Typesetting Mathematics
.ds [d July 1974, revised July 1976, August 1978
.ds [J Comm. Assoc. Comp. Mach.
.ds [K acm cacm
.ds [V 18
.ds [P 151-157
.nr [P 1
.ds [D March 1975
.nr [T 0
.nr [A 0
.nr [O 0
.][ 1 journal-article
.ds [F 8
.]-
.ds [r 39
.ds [K CSTR
.ds [R Comp. Sci. Tech. Rep. No. 39
.ds [I Bell Laboratories
.ds [C Murray Hill, New Jersey
.ds [A M. E. Lesk
.ds [T Lex \(em A Lexical Analyzer Generator
.ds [D October 1975
.nr [T 0
.nr [A 0
.nr [O 0
.][ 4 tech-report
.]>
.bp
.SH
Appendix A: A Simple Example
.PP
This example gives the complete Yacc specification for a small desk calculator;
the desk calculator has 26 registers, labeled ``a'' through ``z'', and accepts
arithmetic expressions made up of the operators +, \-, *, /,
% (mod operator), & (bitwise and), | (bitwise or), and assignment.
If an expression at the top level is an assignment, the value is not
printed; otherwise it is.
As in C, an integer that begins with 0 (zero) is assumed to be octal;
otherwise, it is assumed to be decimal.
.PP
As an example of a Yacc specification, the desk calculator
does a reasonable job of showing how precedences and ambiguities
are used, and demonstrating simple error recovery.
The major oversimplifications are that the
lexical analysis phase is much simpler than for most applications, and the
output is produced immediately, line by line.
Note the way that decimal and octal integers are read in by the grammar rules;
This job is probably better done by the lexical analyzer.
.sp
.nf
.ta .5i 1i 1.5i 2i 2.5i
%{
# include <stdio.h>
# include <ctype.h>
int regs[26];
int base;
%}
%start list
%token DIGIT LETTER
%left \'|\'
%left \'&\'
%left \'+\' \'\-\'
%left \'*\' \'/\' \'%\'
%left UMINUS /* supplies precedence for unary minus */
%% /* beginning of rules section */
list : /* empty */
| list stat \'\en\'
| list error \'\en\'
{ yyerrok; }
;
stat : expr
{ printf( "%d\en", $1 ); }
| LETTER \'=\' expr
{ regs[$1] = $3; }
;
expr : \'(\' expr \')\'
{ $$ = $2; }
| expr \'+\' expr
{ $$ = $1 + $3; }
| expr \'\-\' expr
{ $$ = $1 \- $3; }
| expr \'*\' expr
{ $$ = $1 * $3; }
| expr \'/\' expr
{ $$ = $1 / $3; }
| expr \'%\' expr
{ $$ = $1 % $3; }
| expr \'&\' expr
{ $$ = $1 & $3; }
| expr \'|\' expr
{ $$ = $1 | $3; }
| \'\-\' expr %prec UMINUS
{ $$ = \- $2; }
| LETTER
{ $$ = regs[$1]; }
| number
;
number : DIGIT
{ $$ = $1; base = ($1==0) ? 8 : 10; }
| number DIGIT
{ $$ = base * $1 + $2; }
;
%% /* start of programs */
yylex() { /* lexical analysis routine */
/* returns LETTER for a lower case letter, yylval = 0 through 25 */
/* return DIGIT for a digit, yylval = 0 through 9 */
/* all other characters are returned immediately */
int c;
while( (c=getchar()) == \' \' ) { /* skip blanks */ }
/* c is now nonblank */
if( islower( c ) ) {
yylval = c \- \'a\';
return ( LETTER );
}
if( isdigit( c ) ) {
yylval = c \- \'0\';
return( DIGIT );
}
return( c );
}
.fi
.bp
.SH
Appendix B: Yacc Input Syntax
.PP
This Appendix has a description of the Yacc input syntax, as a Yacc specification.
Context dependencies, etc., are not considered.
Ironically, the Yacc input specification language
is most naturally specified as an LR(2) grammar; the sticky
part comes when an identifier is seen in a rule, immediately
following an action.
If this identifier is followed by a colon, it is the start of the
next rule; otherwise
it is a continuation of the current rule, which just happens to have
an action embedded in it.
As implemented, the lexical analyzer looks
ahead after seeing an identifier, and
decide whether the next token (skipping blanks, newlines, comments, etc.)
is a colon.
If so, it returns the token C_IDENTIFIER.
Otherwise, it returns IDENTIFIER.
Literals (quoted strings) are also returned as IDENTIFIERS,
but never as part of C_IDENTIFIERs.
.sp
.nf
.ta .6i 1.2i 1.8i 2.4i 3i 3.6i
/* grammar for the input to Yacc */
/* basic entities */
%token IDENTIFIER /* includes identifiers and literals */
%token C_IDENTIFIER /* identifier (but not literal) followed by colon */
%token NUMBER /* [0-9]+ */
/* reserved words: %type => TYPE, %left => LEFT, etc. */
%token LEFT RIGHT NONASSOC TOKEN PREC TYPE START UNION
%token MARK /* the %% mark */
%token LCURL /* the %{ mark */
%token RCURL /* the %} mark */
/* ascii character literals stand for themselves */
%start spec
%%
spec : defs MARK rules tail
;
tail : MARK { \fIIn this action, eat up the rest of the file\fR }
| /* empty: the second MARK is optional */
;
defs : /* empty */
| defs def
;
def : START IDENTIFIER
| UNION { \fICopy union definition to output\fR }
| LCURL { \fICopy C code to output file\fR } RCURL
| ndefs rword tag nlist
;
rword : TOKEN
| LEFT
| RIGHT
| NONASSOC
| TYPE
;
tag : /* empty: union tag is optional */
| \'<\' IDENTIFIER \'>\'
;
nlist : nmno
| nlist nmno
| nlist \',\' nmno
;
nmno : IDENTIFIER /* NOTE: literal illegal with %type */
| IDENTIFIER NUMBER /* NOTE: illegal with %type */
;
/* rules section */
rules : C_IDENTIFIER rbody prec
| rules rule
;
rule : C_IDENTIFIER rbody prec
| '|' rbody prec
;
rbody : /* empty */
| rbody IDENTIFIER
| rbody act
;
act : \'{\' { \fICopy action, translate $$, etc.\fR } \'}\'
;
prec : /* empty */
| PREC IDENTIFIER
| PREC IDENTIFIER act
| prec \';\'
;
.fi
.bp
.SH
Appendix C: An Advanced Example
.PP
This Appendix gives an example of a grammar using some
of the advanced features discussed in Section 10.
The desk calculator example in Appendix A is
modified to provide a desk calculator that
does floating point interval arithmetic.
The calculator understands floating point
constants, the arithmetic operations +, \-, *, /,
unary \-, and = (assignment), and has 26 floating
point variables, ``a'' through ``z''.
Moreover, it also understands
.I intervals ,
written
.DS
( x , y )
.DE
where
.I x
is less than or equal to
.I y .
There are 26 interval valued variables ``A'' through ``Z''
that may also be used.
The usage is similar to that in Appendix A; assignments
return no value, and print nothing, while expressions print
the (floating or interval) value.
.PP
This example explores a number of interesting features
of Yacc and C.
Intervals are represented by a structure, consisting of the
left and right endpoint values, stored as
.I double 's.
This structure is given a type name, INTERVAL, by using
.I typedef .
The Yacc value stack can also contain floating point scalars, and
integers (used to index into the arrays holding the variable values).
Notice that this entire strategy depends strongly on being able to
assign structures and unions in C.
In fact, many of the actions call functions that return structures
as well.
.PP
It is also worth noting the use of YYERROR to handle error conditions:
division by an interval containing 0, and an interval presented in
the wrong order.
In effect, the error recovery mechanism of Yacc is used to throw away the
rest of the offending line.
.PP
In addition to the mixing of types on the value stack,
this grammar also demonstrates an interesting use of syntax to
keep track of the type (e.g. scalar or interval) of intermediate
expressions.
Note that a scalar can be automatically promoted to an interval if
the context demands an interval value.
This causes a large number of conflicts when the grammar is run through
Yacc: 18 Shift/Reduce and 26 Reduce/Reduce.
The problem can be seen by looking at the two input lines:
.DS
2.5 + ( 3.5 \- 4. )
.DE
and
.DS
2.5 + ( 3.5 , 4. )
.DE
Notice that the 2.5 is to be used in an interval valued expression
in the second example, but this fact is not known until
the ``,'' is read; by this time, 2.5 is finished, and the parser cannot go back
and change its mind.
More generally, it might be necessary to look ahead an arbitrary number of
tokens to decide whether to convert a scalar to an interval.
This problem is evaded by having two rules for each binary interval
valued operator: one when the left operand is a scalar, and one when
the left operand is an interval.
In the second case, the right operand must be an interval,
so the conversion will be applied automatically.
Despite this evasion, there are still many cases where the
conversion may be applied or not, leading to the above
conflicts.
They are resolved by listing the rules that yield scalars first
in the specification file; in this way, the conflicts will
be resolved in the direction of keeping scalar
valued expressions scalar valued until they are forced to become
intervals.
.PP
This way of handling multiple types is very instructive, but not very general.
If there were many kinds of expression types, instead of just two,
the number of rules needed would increase dramatically, and the conflicts
even more dramatically.
Thus, while this example is instructive, it is better practice in a
more normal programming language environment to
keep the type information as part of the value, and not as part
of the grammar.
.PP
Finally, a word about the lexical analysis.
The only unusual feature is the treatment of floating point constants.
The C library routine
.I atof
is used to do the actual conversion from a character string
to a double precision value.
If the lexical analyzer detects an error,
it responds by returning a token that
is illegal in the grammar, provoking a syntax error
in the parser, and thence error recovery.
.DS L
%{
# include <stdio.h>
# include <ctype.h>
typedef struct interval {
double lo, hi;
} INTERVAL;
INTERVAL vmul(), vdiv();
double atof();
double dreg[ 26 ];
INTERVAL vreg[ 26 ];
%}
%start lines
%union {
int ival;
double dval;
INTERVAL vval;
}
%token <ival> DREG VREG /* indices into dreg, vreg arrays */
%token <dval> CONST /* floating point constant */
%type <dval> dexp /* expression */
%type <vval> vexp /* interval expression */
/* precedence information about the operators */
%left \'+\' \'\-\'
%left \'*\' \'/\'
%left UMINUS /* precedence for unary minus */
%%
lines : /* empty */
| lines line
;
line : dexp \'\en\'
{ printf( "%15.8f\en", $1 ); }
| vexp \'\en\'
{ printf( "(%15.8f , %15.8f )\en", $1.lo, $1.hi ); }
| DREG \'=\' dexp \'\en\'
{ dreg[$1] = $3; }
| VREG \'=\' vexp \'\en\'
{ vreg[$1] = $3; }
| error \'\en\'
{ yyerrok; }
;
dexp : CONST
| DREG
{ $$ = dreg[$1]; }
| dexp \'+\' dexp
{ $$ = $1 + $3; }
| dexp \'\-\' dexp
{ $$ = $1 \- $3; }
| dexp \'*\' dexp
{ $$ = $1 * $3; }
| dexp \'/\' dexp
{ $$ = $1 / $3; }
| \'\-\' dexp %prec UMINUS
{ $$ = \- $2; }
| \'(\' dexp \')\'
{ $$ = $2; }
;
vexp : dexp
{ $$.hi = $$.lo = $1; }
| \'(\' dexp \',\' dexp \')\'
{
$$.lo = $2;
$$.hi = $4;
if( $$.lo > $$.hi ){
printf( "interval out of order\en" );
YYERROR;
}
}
| VREG
{ $$ = vreg[$1]; }
| vexp \'+\' vexp
{ $$.hi = $1.hi + $3.hi;
$$.lo = $1.lo + $3.lo; }
| dexp \'+\' vexp
{ $$.hi = $1 + $3.hi;
$$.lo = $1 + $3.lo; }
| vexp \'\-\' vexp
{ $$.hi = $1.hi \- $3.lo;
$$.lo = $1.lo \- $3.hi; }
| dexp \'\-\' vexp
{ $$.hi = $1 \- $3.lo;
$$.lo = $1 \- $3.hi; }
| vexp \'*\' vexp
{ $$ = vmul( $1.lo, $1.hi, $3 ); }
| dexp \'*\' vexp
{ $$ = vmul( $1, $1, $3 ); }
| vexp \'/\' vexp
{ if( dcheck( $3 ) ) YYERROR;
$$ = vdiv( $1.lo, $1.hi, $3 ); }
| dexp \'/\' vexp
{ if( dcheck( $3 ) ) YYERROR;
$$ = vdiv( $1, $1, $3 ); }
| \'\-\' vexp %prec UMINUS
{ $$.hi = \-$2.lo; $$.lo = \-$2.hi; }
| \'(\' vexp \')\'
{ $$ = $2; }
;
%%
# define BSZ 50 /* buffer size for floating point numbers */
/* lexical analysis */
yylex(){
register c;
while( (c=getchar()) == \' \' ){ /* skip over blanks */ }
if( isupper( c ) ){
yylval.ival = c \- \'A\';
return( VREG );
}
if( islower( c ) ){
yylval.ival = c \- \'a\';
return( DREG );
}
if( isdigit( c ) || c==\'.\' ){
/* gobble up digits, points, exponents */
char buf[BSZ+1], *cp = buf;
int dot = 0, exp = 0;
for( ; (cp\-buf)<BSZ ; ++cp,c=getchar() ){
*cp = c;
if( isdigit( c ) ) continue;
if( c == \'.\' ){
if( dot++ || exp ) return( \'.\' ); /* will cause syntax error */
continue;
}
if( c == \'e\' ){
if( exp++ ) return( \'e\' ); /* will cause syntax error */
continue;
}
/* end of number */
break;
}
*cp = \'\e0\';
if( (cp\-buf) >= BSZ ) printf( "constant too long: truncated\en" );
else ungetc( c, stdin ); /* push back last char read */
yylval.dval = atof( buf );
return( CONST );
}
return( c );
}
INTERVAL hilo( a, b, c, d ) double a, b, c, d; {
/* returns the smallest interval containing a, b, c, and d */
/* used by *, / routines */
INTERVAL v;
if( a>b ) { v.hi = a; v.lo = b; }
else { v.hi = b; v.lo = a; }
if( c>d ) {
if( c>v.hi ) v.hi = c;
if( d<v.lo ) v.lo = d;
}
else {
if( d>v.hi ) v.hi = d;
if( c<v.lo ) v.lo = c;
}
return( v );
}
INTERVAL vmul( a, b, v ) double a, b; INTERVAL v; {
return( hilo( a*v.hi, a*v.lo, b*v.hi, b*v.lo ) );
}
dcheck( v ) INTERVAL v; {
if( v.hi >= 0. && v.lo <= 0. ){
printf( "divisor interval contains 0.\en" );
return( 1 );
}
return( 0 );
}
INTERVAL vdiv( a, b, v ) double a, b; INTERVAL v; {
return( hilo( a/v.hi, a/v.lo, b/v.hi, b/v.lo ) );
}
.DE
.bp
.SH
Appendix D: Old Features Supported but not Encouraged
.PP
This Appendix mentions synonyms and features which are supported for historical
continuity, but, for various reasons, are not encouraged.
.IP 1.
Literals may also be delimited by double quotes ``"''.
.IP 2.
Literals may be more than one character long.
If all the characters are alphabetic, numeric, or \_, the type number of the literal is defined,
just as if the literal did not have the quotes around it.
Otherwise, it is difficult to find the value for such literals.
.IP
The use of multi-character literals is likely to mislead those unfamiliar with
Yacc, since it suggests that Yacc is doing a job which must be actually done by the lexical analyzer.
.IP 3.
Most places where % is legal, backslash ``\e'' may be used.
In particular, \e\e is the same as %%, \eleft the same as %left, etc.
.IP 4.
There are a number of other synonyms:
.DS
%< is the same as %left
%> is the same as %right
%binary and %2 are the same as %nonassoc
%0 and %term are the same as %token
%= is the same as %prec
.DE
.IP 5.
Actions may also have the form
.DS
={ . . . }
.DE
and the curly braces can be dropped if the action is a
single C statement.
.IP 6.
C code between %{ and %} used to be permitted at the
head of the rules section, as well as in the
declaration section.
.sp
.I "May 1979"