MirOS Manual: 15.yacc(PSD)

Yacc: Yet Another Compiler-Compiler                      PS1:15-1

               Yacc: Yet Another Compiler-Compiler

                       Stephen C. Johnson

                     AT&T Bell Laboratories
                  Murray Hill, New Jersey 07974


          Computer program input generally has  some  struc-
     ture;  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.

          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  han-
     dles  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.

          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.

          Yacc is  written  in  portable  C.  The  class  of
     specifications  accepted is a very general one: LALR(1)
     grammars with disambiguating rules.

          In addition to compilers for C, APL, Pascal,  RAT-
     FOR,  etc.,  Yacc  has  also been used for less conven-
     tional languages, including a phototypesetter language,
     several desk calculator languages, a document retrieval
     system, and a Fortran debugging system.

PS1:15-2                      Yacc: Yet Another Compiler-Compiler

0: Introduction

     Yacc provides a general tool for imposing structure  on  the
input  to a computer program. The Yacc user prepares a specifica-
tion of the input process; this  includes  rules  describing  the
input  structure,  code to be invoked when these rules are recog-
nized, and a low-level routine to do the basic input.  Yacc  then
generates a function to control the input process. This function,
called a parser, calls the user-supplied low-level input  routine
(the lexical analyzer) to pick up the basic items (called tokens)
from the input stream. These tokens are  organized  according  to
the  input  structure  rules,  called  grammar rules; when one of
these rules has been recognized, then user code supplied for this
rule,  an  action, is invoked; actions have the ability to return
values and make use of the values of other actions.

     Yacc is written in a portable dialect of C Ritchie Kernighan
Language  Prentice and the actions, and output subroutine, are in
C as well. Moreover, many of the syntactic  conventions  of  Yacc
follow C.

     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

        date  :  month_name  day  ','  year   ;

Here, date, month_name, day, and  year  represent  structures  of
interest  in  the input process; presumably, month_name, day, and
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

        July  4, 1776

might be matched by the above rule.

     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 recog-
nized by the lexical analyzer is called a terminal symbol,  while
the  structure  recognized  by the parser is called a nonterminal
symbol. To avoid confusion,  terminal  symbols  will  usually  be
referred to as tokens.

     There is considerable leeway in deciding whether  to  recog-
nize  structures using the lexical analyzer or grammar rules. For
example, the rules

Yacc: Yet Another Compiler-Compiler                      PS1:15-3

        month_name  :  'J' 'a' 'n'   ;
        month_name  :  'F' 'e' 'b'   ;

                 . . .

        month_name  :  'D' 'e' 'c'   ;

might be used in the above example. The  lexical  analyzer  would
only  need  to recognize individual letters, and 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
month_name was seen; in this case, month_name would be a token.

     Literal characters such as ``,'' must also be passed through
the lexical analyzer, and are also considered tokens.

     Specification files are very flexible. It is realively  easy
to add to the above example the rule

        date  :  month '/' day '/' year   ;


        7 / 4 / 1776

as a synonym for

        July 4, 1776

In most cases, this new rule could be ``slipped in'' to a working
system  with  minimal  effort,  and  little  danger of disrupting
existing input.

     The input being read may not conform to the  specifications.
These input errors are detected as early as is theoretically pos-
sible 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 skip-
ping over the bad data.

     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  recogni-
tion  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 sys-
tems; moreover, the constructions which are difficult for Yacc to

PS1:15-4                      Yacc: Yet Another Compiler-Compiler

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.

     The theory underlying Yacc has been described elsewhere. Aho
Johnson  Surveys LR Parsing Aho Johnson Ullman Ambiguous Grammars
Aho Ullman Principles Compiler Design Yacc has  been  extensively
used  in numerous practical applications, including lint, Johnson
Lint the Portable C Compiler, Johnson  Portable  Compiler  Theory
and  a  system  for  typesetting  mathematics.  Kernighan  Cherry
typesetting system CACM

     The next several sections  describe  the  basic  process  of
preparing  a Yacc specification; Section 1 describes the prepara-
tion of grammar rules, Section 2 the preparation of the user sup-
plied  actions  associated  with  these  rules, and Section 3 the
preparation of lexical analyzers. Section 4 describes the  opera-
tion  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 han-
dling 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 acknowledge-
ments. 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 ver-
sions of Yacc.

1: Basic Specifications

     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  specifica-
tion file consists of three sections: the declarations, (grammar)
rules, and programs. The sections are separated by double percent
``%%''  marks.  (The  percent  ``%''  is  generally  used in Yacc
specifications as an escape character.)

     In other words, a full specification file looks like


Yacc: Yet Another Compiler-Compiler                      PS1:15-5

     The declaration section may be empty. Moreover, if the  pro-
grams section is omitted, the second %% mark may be omitted also;
thus, the smallest legal Yacc specification is


     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.

     The rules section is made up of one or more grammar rules. A
grammar rule has the form:

        A  :  BODY  ;

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.

     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 sym-

     A literal consists of a character enclosed in single  quotes
``'''. As in C, the backslash ``\'' is an escape character within
literals, and all the C escapes are recognized. Thus

        '\n'    newline
        '\r'    return
        '\''    single quote ``'''
        '\\'    backslash ``\''
        '\t'    tab
        '\b'    backspace
        '\f'    form feed
        '\xxx'  ``xxx'' in octal

For a number of technical reasons, the NUL character ('\0' or  0)
should never be used in grammar rules.

     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

        A       :       B  C  D   ;
        A       :       E  F   ;
        A       :       G   ;

can be given to Yacc as

PS1:15-6                      Yacc: Yet Another Compiler-Compiler

        A       :       B  C  D
                |       E  F
                |       G

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.

     If a nonterminal symbol matches the empty string,  this  can
be indicated in the obvious way:

        empty :   ;

     Names representing tokens must be  declared;  this  is  most
simply done by writing

        %token   name1  name2 . . .

in the declarations section. (See Sections 3 , 5, and 6 for  much
more discussion). Every name not defined in the declarations sec-
tion is assumed to represent a nonterminal symbol. Every  nonter-
minal symbol must appear on the left side of at least one rule.

     Of all the nonterminal symbols, one, called the  start  sym-
bol,  has particular importance. The parser is designed to recog-
nize 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:

        %start   symbol

     The end of the input to the parser is signaled by a  special
token, called the endmarker. If the tokens up to, but not includ-
ing, the endmarker form a structure which matches the start  sym-
bol,  the  parser  function  returns to its caller after the end-
marker is seen; it accepts the input. If the endmarker is seen in
any other context, it is an error.

     It is the job  of  the  user-supplied  lexical  analyzer  to
return the endmarker when appropriate; see section 3, below. Usu-
ally the endmarker represents some reasonably obvious I/O status,
such as ``end-of-file'' or ``end-of-record''.

2: Actions

     With each grammar rule, the user may associate actions to be
performed  each time the rule is recognized in the input process.

Yacc: Yet Another Compiler-Compiler                      PS1:15-7

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.

     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,

        A       :       '('  B  ')'
                                {       hello( 1, "abc" );  }


        XXX     :       YYY  ZZZ
                                {       printf("a message\n");
                                        flag = 25;   }

are grammar rules with actions.

     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  con-

     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

                {  $$ = 1;  }

     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

        A       :       B  C  D   ;

for example, then $2 has the value returned  by  C,  and  $3  the
value returned by D.

     As a more concrete example, consider the rule

        expr    :       '('  expr  ')'   ;

The value returned by this rule is usually the value of the  expr
in parentheses. This can be indicated by

        expr    :        '('  expr  ')'         {  $$ = $2 ;  }

     By default, the value of a rule is the value  of  the  first

PS1:15-8                      Yacc: Yet Another Compiler-Compiler

element in it ($1). Thus, grammar rules of the form

        A       :       B    ;

frequently need not have an explicit action.

     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

        A       :       B
                                {  $$ = 1;  }
                                {   x = $2;   y = $3;  }

the effect is to set x to 1, and y to the value returned by C.

     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:

        $ACT    :       /* empty */
                                {  $$ = 1;  }

        A       :       B  $ACT  C
                                {   x = $2;   y = $3;  }

     In many applications, output is not  done  directly  by  the
actions;  rather, a data structure, such as a parse tree, is con-
structed in memory, and transformations are applied to it  before
output  is  generated.  Parse trees are particularly easy to con-
struct, given routines to build and maintain the  tree  structure
desired. For example, suppose there is a C function node, written
so that the call

        node( L, n1, n2 )

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:

        expr    :       expr  '+'  expr
                                {  $$ = node( '+', $1, $3 );  }

Yacc: Yet Another Compiler-Compiler                      PS1:15-9

in the specification.

     The user may define  other  variables  to  be  used  by  the
actions.  Declarations and definitions can appear in the declara-
tions 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,

        %{   int variable = 0;   %}

could be placed in  the  declarations  section,  making  variable
accessible to all of the actions. The Yacc parser uses only names
beginning in ``yy''; the user should avoid such names.

     In these examples, all the values are integers: a discussion
of values of other types will be found in Section 10.

3: Lexical Analysis

     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
yylex.  The  function  returns  an  integer,  the  token  number,
representing the kind of token read. If there is a value  associ-
ated with that token, it should be assigned to the external vari-
able yylval.

     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:

                extern int yylval;
                int c;
                . . .
                c = getchar();
                . . .
                switch( c ) {
                        . . .
                case '0':
                case '1':
                  . . .
                case '9':
                        yylval = c-'0';
                        return( DIGIT );
                        . . .
                . . .

PS1:15-10                     Yacc: Yet Another Compiler-Compiler

     The intent is to return a token number of DIGIT, and a value
equal to the numerical value of the digit. Provided that the lex-
ical 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.

     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 if or while will
almost certainly  cause  severe  difficulties  when  the  lexical
analyzer  is compiled. The token name error is reserved for error
handling, and should not be used naively (see Section 7).

     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.

     To assign a token number to a  token  (including  literals),
the first appearance of the token name or literal in the declara-
tions section  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.

     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.

     A very useful tool for constructing lexical analyzers is the
Lex  program  developed  by  Mike  Lesk.  Lesk  Lex These lexical
analyzers are  designed  to  work  in  close  harmony  with  Yacc
parsers. The specifications for these lexical analyzers use regu-
lar 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.

4: How the Parser Works

     Yacc turns the specification file into a  C  program,  which
parses  the input according to the specification given. The algo-
rithm 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  ambigui-
ties much more comprehensible.

     The parser produced by  Yacc  consists  of  a  finite  state

Yacc: Yet Another Compiler-Compiler                     PS1:15-11

machine  with  a stack. The parser is also capable of reading and
remembering the next input token (called  the  lookahead  token).
The  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.

     The machine has only four actions available  to  it,  called
shift, reduce, accept, and error. A move of the parser is done as

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 yylex
     to obtain the next token.

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.

     The 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:

                IF      shift 34

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  looka-
head token is cleared.

     The 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 usu-
ally it is not; in fact, the default  action  (represented  by  a
``.'') is often a reduce action.

     Reduce actions are associated with individual grammar rules.
Grammar  rules  are  also given small integer numbers, leading to
some confusion. The action

                .       reduce 18

refers to grammar rule 18, while the action

                IF      shift 34

refers to state 34.

PS1:15-12                     Yacc: Yet Another Compiler-Compiler

     Suppose the rule being reduced is

        A       :       x  y  z    ;

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 x,
y, and 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 differ-
ences between the processing of the left hand symbol and an ordi-
nary  shift  of a token, however, so this action is called a 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:

                A       goto 20

causing state 20 to be pushed onto  the  stack,  and  become  the
current state.

     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.

     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 yylval  is  copied  onto  the  value
stack. After the return from the user code, the reduction is car-
ried out. When the goto action is  done,  the  external  variable
yyval  is  copied  onto the value stack. The pseudo-variables $1,
$2, etc., refer to the value stack.

     The other two parser actions are conceptually much  simpler.
The  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 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

Yacc: Yet Another Compiler-Compiler                     PS1:15-13

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  detec-
tion of error) will be covered in Section 7.

     It is time for an example! Consider the specification

        %token  DING  DONG  DELL
        rhyme   :       sound  place
        sound   :       DING  DONG
        place   :       DELL

     When Yacc is invoked with  the  -v  option,  a  file  called
y.output  is  produced,  with a human-readable description of the
parser. The y.output file  corresponding  to  the  above  grammar
(with some statistics stripped off the end) is:

PS1:15-14                     Yacc: Yet Another Compiler-Compiler

        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

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

        DING  DONG  DELL

It is instructive to follow the steps of the  parser  while  pro-
cessing this input.

Yacc: Yet Another Compiler-Compiler                     PS1:15-15

     Initially, the current state is state 0. The parser needs to
refer  to the input in order to decide between the actions avail-
able in state 0, so the first token, DING, is read, becoming  the
lookahead token. The action in state 0 on 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, DONG,
is read, becoming the lookahead token. The action in state  3  on
the  token  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.

                sound  :   DING  DONG

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. Con-
sulting the description of state 0, looking for a goto on sound,

                sound   goto 2

is obtained; thus state 2 is pushed onto the stack, becoming  the
current state.

     In state 2, the next token, 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 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 rhyme
causing the parser to enter state 1. In state  1,  the  input  is
read;  the  endmarker  is  obtained, indicated by ``$end'' in the
y.output file. The action in state 1 when the endmarker  is  seen
is to accept, successfully ending the parse.

     The reader is urged to consider how the  parser  works  when
confronted  with  such  incorrect strings as DING DONG DONG, DING
DONG, 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.

5: Ambiguity and Conflicts

     A set of grammar rules is ambiguous if there is  some  input
string  that can be structured in two or more different ways. For
example, the grammar rule

        expr    :       expr  '-'  expr

is a natural way of expressing the fact that one way  of  forming
an arithmetic expression is to put two other expressions together

PS1:15-16                     Yacc: Yet Another Compiler-Compiler

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

        expr  -  expr  -  expr

the rule allows this input to be structured as either

        (  expr  -  expr  )  -  expr

or as

        expr  -  (  expr  -  expr  )

(The first is called left association, the second right  associa-

     Yacc detects such ambiguities when it is attempting to build
the  parser.  It is instructive to consider the problem that con-
fronts the parser when it is given an input such as

        expr  -  expr  -  expr

When the parser has read the second expr, the input that  it  has

        expr  -  expr

matches the right side of the  grammar  rule  above.  The  parser
could  reduce the input by applying this rule; after applying the
rule; the input is reduced to expr(the left side  of  the  rule).
The parser would then read the final part of the input:

        -  expr

and again reduce. The effect of this is to take the left associa-
tive interpretation.

     Alternatively, when the parser has seen

        expr  -  expr

it could defer the immediate application of the  rule,  and  con-
tinue reading the input until it had seen

        expr  -  expr  -  expr

It could then apply the rule  to  the  rightmost  three  symbols,
reducing them to expr and leaving

        expr  -  expr

Now the rule can be reduced once more; the effect is to take  the
right associative interpretation. Thus, having read

Yacc: Yet Another Compiler-Compiler                     PS1:15-17

        expr  -  expr

the parser can do two legal things, a shift or a  reduction,  and
has  no  way  of  deciding between them. This is called a shift /
reduce conflict. It may also happen that the parser has a  choice
of  two  legal  reductions; this is called a reduce / reduce con-
flict. Note that there are never any ``Shift/shift'' conflicts.

     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 disambiguating

     Yacc invokes two disambiguating rules by default:

1.   In a shift/reduce conflict, the default is to do the shift.

2.   In a reduce/reduce conflict, the default is to reduce by the
     earlier grammar rule (in the input sequence).

     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.

     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.

     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 pres-
ence of conflicts.

     As an example of the power of disambiguating rules, consider
a  fragment  from  a programming language involving an ``if-then-
else'' construction:

        stat    :       IF  '('  cond  ')'  stat
                |       IF  '('  cond  ')'  stat  ELSE  stat

PS1:15-18                     Yacc: Yet Another Compiler-Compiler

In these rules, IF and ELSE are tokens,  cond  is  a  nonterminal
symbol  describing conditional (logical) expressions, and stat is
a nonterminal symbol describing statements. The first  rule  will
be called the simple-if rule, and the second the if-else rule.

     These two rules form an ambiguous construction, since  input
of the form

        IF  (  C1  )  IF  (  C2  )  S1  ELSE  S2

can be structured according to these rules in two ways:

        IF  (  C1  )  {
                IF  (  C2  )  S1
        ELSE  S2


        IF  (  C1  )  {
                IF  (  C2  )  S1
                ELSE  S2

The second interpretation is the one given  in  most  programming
languages having this construct. Each ELSE is associated with the
last preceding ``un-ELSE'd'' IF. In this  example,  consider  the
situation where the parser has seen

        IF  (  C1  )  IF  (  C2  )  S1

and is looking at the ELSE. It  can  immediately  reduce  by  the
simple-if rule to get

        IF  (  C1  )  stat

and then read the remaining input,

        ELSE  S2

and reduce

        IF  (  C1  )  stat  ELSE  S2

by the if-else rule. This leads to the first of the above  group-
ings of the input.

     On the other hand, the ELSE may be  shifted,  S2  read,  and
then the right hand portion of

        IF  (  C1  )  IF  (  C2  )  S1  ELSE  S2

can be reduced by the if-else rule to get

Yacc: Yet Another Compiler-Compiler                     PS1:15-19

        IF  (  C1  )  stat

which can be reduced by the simple-if rule.  This  leads  to  the
second  of  the  above  groupings  of the input, which is usually

     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.

     This shift/reduce conflict arises only when there is a  par-
ticular current input symbol, ELSE, and particular inputs already
seen, such as

        IF  (  C1  )  IF  (  C2  )  S1

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.

     The conflict messages of Yacc are best understood by examin-
ing  the verbose (-v) option output file. For example, the output
corresponding to the above conflict state might be:

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

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

        IF  (  cond  )  stat

and the two grammar rules shown are  active  at  this  time.  The
parser  can  do two possible things. If the input symbol is ELSE,
it is possible to shift into state 45. State  45  will  have,  as
part of its description, the line

        stat  :  IF  (  cond  )  stat  ELSE_stat

PS1:15-20                     Yacc: Yet Another Compiler-Compiler

since the ELSE will have been shifted  in  this  state.  Back  in
state  23,  the  alternative action, described by ``.'', 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 ELSE, the
parser reduces by grammar rule 18:

        stat  :  IF  '('  cond  ')'  stat

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 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  Aho  Johnson Surveys Parsing Aho Johnson
Ullman Deterministic Ambiguous Aho Ullman Principles Design might
be  consulted;  the  services  of  a  local  guru  might  also be

6: Precedence

     There is one common situation where the  rules  given  above
for  resolving conflicts are not sufficient; this is in the pars-
ing of arithmetic expressions. Most of  the  commonly  used  con-
structions  for arithmetic expressions can be naturally described
by the notion of 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

        expr  :  expr  OP  expr


        expr  :  UNARY  expr

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 pars-
ing  conflicts  in  accordance  with these rules, and construct a
parser that realizes the desired precedences and associativities.

     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,

Yacc: Yet Another Compiler-Compiler                     PS1:15-21

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,

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

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 opera-
tors, and the keyword %nonassoc is used  to  describe  operators,
like  the  operator  .LT. in Fortran, that may not associate with
themselves; thus,

        A  .LT.  B  .LT.  C

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

        %right  '='
        %left  '+'  '-'
        %left  '*'  '/'


        expr    :       expr  '='  expr
                |       expr  '+'  expr
                |       expr  '-'  expr
                |       expr  '*'  expr
                |       expr  '/'  expr
                |       NAME

might be used to structure the input

        a  =  b  =  c*d  -  e  -  f*g

as follows:

        a = ( b = ( ((c*d)-e) - (f*g) ) )

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

PS1:15-22                     Yacc: Yet Another Compiler-Compiler

of the grammar rule to become that of the following token name or
literal.  For  example,  to  make  unary minus have the same pre-
cedence as multiplication the rules might resemble:

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


        expr    :       expr  '+'  expr
                |       expr  '-'  expr
                |       expr  '*'  expr
                |       expr  '/'  expr
                |       '-'  expr      %prec  '*'
                |       NAME

     A token declared by %left, %right, and  %nonassoc  need  not
be, but may be, declared by %token as well.

     The precedences and associativities  are  used  by  Yacc  to
resolve  parsing  conflicts;  they  give  rise  to disambiguating
rules. Formally, the rules work as follows:

1.   The precedences and associativities are recorded  for  those
     tokens and literals that have them.

2.   A precedence and associativity is associated with each gram-
     mar rule; it is the precedence and associativity of the last
     token or literal in the body of the rule. If the %prec  con-
     struction  is  used, it overrides this default. Some grammar
     rules may have no precedence  and  associativity  associated
     with them.

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 sec-
     tion are used, and the conflicts are reported.

4.   If there is a shift/reduce conflict, and  both  the  grammar
     rule  and  the  input character have precedence and associa-
     tivity 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

     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  pre-
cedences  may  disguise errors in the input grammar; it is a good

Yacc: Yet Another Compiler-Compiler                     PS1:15-23

idea to be sparing with precedences, and use them  in  an  essen-
tially  ``cookbook''  fashion,  until  some  experience  has been
gained. The y.output file is very useful in deciding whether  the
parser is actually doing what was intended.

7: Error Handling

     Error handling is an extremely difficult area, and  many  of
the problems are semantic ones. When an error is found, for exam-
ple, 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.

     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 algo-
rithms to do this involves discarding a number of tokens from the
input  string,  and attempting to adjust the parser so that input
can continue.

     To allow the user some control over this process, Yacc  pro-
vides  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 looka-
head  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.

     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.

     As an example, a rule of the form

        stat    :       error

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 process-
ing 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.

     Actions may be used with these special  error  rules.  These
actions  might  attempt  to  reinitialize  tables, reclaim symbol

PS1:15-24                     Yacc: Yet Another Compiler-Compiler

table space, etc.

     Error rules such as the above are very general,  but  diffi-
cult to control. Somewhat easier are rules such as

        stat    :       error  ';'

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.

     Another form of error rule arises  in  interactive  applica-
tions, where it may be desirable to permit a line to be reentered
after an error. A possible error rule might be

        input   :       error  '\n'  {  printf( "Reenter last line: " );  }  input
                                {       $$  =  $4;  }

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

        yyerrok ;

in an action resets the parser to its normal mode. The last exam-
ple is better written

        input   :       error  '\n'
                                {       yyerrok;
                                        printf( "Reenter last line: " );   }
                                {       $$  =  $4;  }

     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

        yyclearin ;

in an action will have this  effect.  For  example,  suppose  the
action after error were to call some sophisticated resynchroniza-
tion routine, supplied by the user, that attempted to advance the

Yacc: Yet Another Compiler-Compiler                     PS1:15-25

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

        stat    :       error
                                {       resynch();
                                        yyerrok ;
                                        yyclearin ;   }

     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.

8: The Yacc Environment

     When the user inputs a specification to Yacc, the output  is
a  file  of  C  programs,  called y.tab.c on most systems (due to
local file system conventions, the names may differ from  instal-
lation  to installation). The function produced by Yacc is called
yyparse; it is an integer valued function. When it is called,  it
in  turn repeatedly calls 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) yyparse returns the value 1, or the lexical analyzer
returns the endmarker token and the parser accepts. In this case,
yyparse returns the value 0.

     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 main must be defined, that
eventually  calls  yyparse. In addition, a routine called yyerror
prints a message when a syntax error is detected.

     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 main and yyerror.  The
name  of  this  library  is system dependent; on many systems the
library is accessed by a -ly argument to the loader. To show  the
triviality of these default programs, the source is given below:

                return( yyparse() );


PS1:15-26                     Yacc: Yet Another Compiler-Compiler

        # include <stdio.h>

        yyerror(s) char *s; {
                fprintf( stderr, "%s\n", s );

The argument to 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 mes-
sage when a syntax error is detected. The external integer  vari-
able  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 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.

     The external integer variable 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. Depend-
ing on the operating environment, it may be possible to set  this
variable by using a debugging system.

9: Hints for Preparing Specifications

     This section contains miscellaneous hints on preparing effi-
cient,  easy  to change, and clear specifications. The individual
subsections are more or less independent.

Input Style

     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.

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.''

b.   Put grammar rules and actions on separate lines. This allows
     either to be changed without an automatic need to change the

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.

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.

e.   Indent rule bodies by two tab stops, and  action  bodies  by

Yacc: Yet Another Compiler-Compiler                     PS1:15-27

     three tab stops.

     The example in Appendix A is written following  this  style,
as  are  the examples in the text of this paper (where space per-
mits). 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.

Left Recursion

     The algorithm used by the Yacc parser encourages  so  called
``left recursive'' grammar rules: rules of the form

        name    :       name  rest_of_rule  ;

These rules  frequently  arise  when  writing  specifications  of
sequences and lists:

        list    :       item
                |       list  ','  item


        seq     :       item
                |       seq  item

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.

     With right recursive rules, such as

        seq     :       item
                |       item  seq

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.

     It is worth considering whether a sequence  with  zero  ele-
ments  has  any meaning, and if so, consider writing the sequence
specification with an empty rule:

        seq     :       /* empty */
                |       seq  item

Once again, the first rule would always be reduced exactly  once,
before the first item was read, and then the second rule would be

PS1:15-28                     Yacc: Yet Another Compiler-Compiler

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!

Lexical Tie-ins

     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.

     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:

                int dflag;
          ...  other declarations ...


        prog    :       decls  stats

        decls   :       /* empty */
                                {       dflag = 1;  }
                |       decls  declaration

        stats   :       /* empty */
                                {       dflag = 0;  }
                |       stats  statement

            ...  other rules ...

The flag dflag is now 0 when reading statements, and 1 when read-
ing  declarations, except for the first token in the first state-
ment. 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.

     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.

Reserved Words

     Some programming languages permit the user to use words like
``if'',  which are normally reserved, as label or variable names,

Yacc: Yet Another Compiler-Compiler                     PS1:15-29

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  informa-
tion  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 sub-
section, but it is difficult.

     A number of ways of making this easier are under advisement.
Until  then, it is better that the keywords be reserved; that is,
be forbidden for  use  as  variable  names.  There  are  powerful
stylistic reasons for preferring this, anyway.

10: Advanced Topics

     This section discusses a  number  of  advanced  features  of

Simulating Error and Accept in Actions

     The parsing actions of error and accept can be simulated  in
an  action by use of macros YYACCEPT and YYERROR. YYACCEPT causes
yyparse to return the value  0;  YYERROR  causes  the  parser  to
behave  as  if  the current input symbol had been a syntax error;
yyerror is called, and error recovery takes place. These  mechan-
isms  can be used to simulate parsers with multiple endmarkers or
context-sensitive syntax checking.

Accessing Values in Enclosing Rules.

     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

        sent    :       adj  noun  verb  adj  noun
                                {  look at the sentence . . .  }

        adj     :       THE             {       $$ = THE;  }
                |       YOUNG   {       $$ = YOUNG;  }
                . . .

        noun    :       DOG
                                {       $$ = DOG;  }
                |       CRONE
                                {       if( $0 == YOUNG ){
                                                printf( "what?\n" );
                                        $$ = CRONE;
                . . .

PS1:15-30                     Yacc: Yet Another Compiler-Compiler

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 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.

Support for Arbitrary Value Types

     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 union of the various
types of values desired. The user declares the union, and associ-
ates union member names to each token and nonterminal symbol hav-
ing a value. When the value is referenced through a $$ or $n con-
struction,  Yacc  will automatically insert the appropriate union
name, so that no unwanted conversions will take place.  In  addi-
tion,  type  checking  commands such as Lint Johnson Lint Checker
1273 will be far more silent.

     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.

     To declare the union, the user includes in  the  declaration

        %union  {
                body of union ...

This declares the Yacc value stack, and  the  external  variables
yylval  and  yyval, to have type equal to this union. If Yacc was
invoked with the -d option, the union declaration is copied  onto
the  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:

        typedef union {
                body of union ...
                } YYSTYPE;

The header file must be included in the declarations section,  by
use of %{ and %}.

     Once YYSTYPE is defined, the  union  member  names  must  be

Yacc: Yet Another Compiler-Compiler                     PS1:15-31

associated  with  the various terminal and nonterminal names. The

        < name >

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

        %left  <optype>  '+'  '-'

will cause any reference to values returned by these  two  tokens
to  be tagged with the union member name optype. Another keyword,
%type, is used similarly to associate  union  member  names  with
nonterminals. Thus, one might say

        %type  <nodetype>  expr  stat

     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 a priori type.  Similarly,  refer-
ence  to  left context values (such as $0 - see the previous sub-
section ) 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

        rule    :       aaa  {  $<intval>$  =  3;  } bbb
                                {       fun( $<intval>2, $<other>0 );  }

This syntax has little to recommend it, but the situation  arises

     A sample specification is given in Appendix C.  The  facili-
ties 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 int's, as was true historically.

11: Acknowledgements

     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. Feld-
man, C. Imagna, M. E. Lesk, and A. Snyder will recognize some  of
their  ideas  in the current version of Yacc. C. B. Haley contri-
buted to the error recovery  algorithm.  D.  M.  Ritchie,  B.  W.

PS1:15-32                     Yacc: Yet Another Compiler-Compiler

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.

Yacc: Yet Another Compiler-Compiler                     PS1:15-33


PS1:15-34                     Yacc: Yet Another Compiler-Compiler

Appendix A:  A Simple Example

     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.

     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.

#  include  <stdio.h>
#  include  <ctype.h>

int  regs[26];
int  base;


%start  list


%left  '|'
%left  '&'
%left  '+'  '-'
%left  '*'  '/'  '%'
%left  UMINUS      /*  supplies  precedence  for  unary  minus  */

%%      /*  beginning  of  rules  section  */

list :    /*  empty  */
     |    list  stat  '\n'
     |    list  error  '\n'
               {    yyerrok;  }

stat :    expr
               {    printf( "%d\n", $1 );  }
     |    LETTER  '='  expr
               {    regs[$1]  =  $3;  }

Yacc: Yet Another Compiler-Compiler                     PS1:15-35

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  );

PS1:15-36                     Yacc: Yet Another Compiler-Compiler

Appendix B: Yacc Input Syntax

     This Appendix has a description of the Yacc input syntax, as
a  Yacc  specification.  Context dependencies, etc., are not con-
sidered. 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.

            /*  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      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  {    In  this  action,  eat  up  the  rest  of  the  file    }
      |     /*  empty:  the  second  MARK  is  optional  */

defs  :     /*  empty  */
      |     defs  def

      |     UNION  {  Copy union  definition  to  output  }
      |     LCURL  {  Copy  C  code  to  output  file   }  RCURL
      |     ndefs  rword  tag  nlist

Yacc: Yet Another Compiler-Compiler                     PS1:15-37


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   :     '{'  {  Copy  action,  translate  $$,  etc.  }  '}'

prec  :     /*  empty  */
      |     PREC  IDENTIFIER
      |     PREC  IDENTIFIER  act
      |     prec  ';'

PS1:15-38                     Yacc: Yet Another Compiler-Compiler

Appendix C: An Advanced Example

     This Appendix gives an example of a grammar  using  some  of
the  advanced features discussed in Section 10. The desk calcula-
tor example in Appendix A is modified to provide a desk  calcula-
tor  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  under-
stands intervals, written

                ( x , y )

where x is less than or equal to 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)

     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  double's.  This
structure  is  given a type name, INTERVAL, by using 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.

     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

     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:

                2.5 + ( 3.5 - 4. )


                2.5 + ( 3.5 , 4. )

Notice that the 2.5 is to be used in an interval  valued  expres-
sion  in the second example, but this fact is not known until the
``,'' is read; by this time, 2.5 is finished, and the parser can-
not  go  back  and  change  its mind. More generally, it might be

Yacc: Yet Another Compiler-Compiler                     PS1:15-39

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 opera-
tor: 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 automati-
cally. 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.

     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.

     Finally, a word about the lexical analysis. The only unusual
feature  is  the  treatment  of  floating  point constants. The C
library routine 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.

PS1:15-40                     Yacc: Yet Another Compiler-Compiler


#  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  '\n'
                        {       printf(  "%15.8f\n",  $1  );  }
        |       vexp  '\n'
                        {       printf(  "(%15.8f  ,  %15.8f  )\n",  $1.lo,  $1.hi  );  }
        |       DREG  '='  dexp  '\n'
                        {       dreg[$1]  =  $3;  }

Yacc: Yet Another Compiler-Compiler                     PS1:15-41

        |       VREG  '='  vexp  '\n'
                        {       vreg[$1]  =  $3;  }
        |       error  '\n'
                        {       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\n"  );
        |       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;

PS1:15-42                     Yacc: Yet Another Compiler-Compiler

                                $$  =  vdiv(  $1.lo,  $1.hi,  $3  );  }
        |       dexp  '/'  vexp
                        {       if(  dcheck(  $3  )  )  YYERROR;
                                $$  =  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  */

                        if(  c  ==  'e'  ){
                                if(  exp++  )  return(  'e'  );    /*  will  cause  syntax  error  */

                        /*  end  of  number  */
                        break;                                  }
                *cp  =  '\0';
                if(  (cp-buf)  >=  BSZ  )  printf(  "constant  too  long:  truncated\n"  );
                else  ungetc(  c,  stdin  );    /*  push  back  last  char  read  */
                yylval.dval  =  atof(  buf  );
                return(  CONST  );                              }
        return(  c  );         }

Yacc: Yet Another Compiler-Compiler                     PS1:15-43

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.\n"  );
                return(  1  );                    }           re-
turn(  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  )  );

PS1:15-44                     Yacc: Yet Another Compiler-Compiler

Appendix D: Old Features Supported but not Encouraged

     This Appendix mentions synonyms and features which are  sup-
ported  for  historical continuity, but, for various reasons, are
not encouraged.

1.   Literals may also be delimited by double quotes ``"''.

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.

     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

3.   Most places where % is legal, backslash ``\'' may  be  used.
     In  particular,  \\  is  the  same  as %%, \left the same as
     %left, etc.

4.   There are a number of other synonyms:

             %< 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

5.   Actions may also have the form

             ={ . . . }

     and the curly braces can be dropped if the action is a  sin-
     gle C statement.

6.   C code between %{ and %} used to be permitted at the head of
     the rules section, as well as in the declaration section.

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