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.
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; fre quently, 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 con- tinuation 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, RATFOR, etc., Yacc has also been used for less conventional languages, including a photo-typesetter language, several desk calculator languages, a document retrieval system, and a Fortran debugging system.
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 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 recognized by the lexical analyzer is called a terminal symbol, while the structure recognized by the parser is called a nonterminal. To avoid confusion, terminal symbols will usually be referred to as tokens.
There is considerable leeway in deciding whether to recognize structures using the lexical analyzer or grammar rules. For example, the rules
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 ;
allowing
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 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.
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.
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 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.
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 sec- tions: 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
declarations
%%
rules
%%
programs
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
%%
rules
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 symbols.
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
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 section is assumed to represent a nonterminal symbol. Every nonterminal symbol must appear on the left side of at least one rule.
Of all the nonterminal symbols, one, called the 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:
%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 including, the endmarker form a structure which matches the start symbol, the parser function returns to its caller after the endmarker 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. Usually the endmarker represents some reasonably obvious I/O status, such as ``end-of-file'' or ``end-of-record''.
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.
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" ); }
and
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 context.
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 ')' { $$ = $2 ; }
By default, the value of a rule is the value of the first element in it ($1). Thus, grammar rules of the form
A : B ;
frequently need not have an explicit action.
In the examples above, all the actions came at the end of their rules. Sometimes, it is desirable to get control before a rule is fully parsed. Yacc permits an action to be written in the middle of a rule as well as at the end. This rule is assumed to return a value, accessible through the usual mechanism by the actions to the right of it. In turn, it may access the values returned by the symbols to its left. Thus, in the rule
A : B { $$ = 1; } C { 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 han- dled 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 */ { $$ = 1; } ;
A : B $ACT C { x = $2; y = $3; } ;
In many applications, output is not done directly by the actions; rather, a data structure, such as a parse tree, is constructed in memory, and transformations are applied to it before output is generated. Parse trees are particularly easy to construct, given routines to build and maintain the tree structure desired. For example, suppose there is a C function node, written so that the call
node( L, n1, n2 )
creates a node with label L, and descendants n1 and n2, and returns the index of the newly created node. Then parse tree can be built by supplying actions such as:
expr : expr '+' expr { $$ = node( '+', $1, $3 ); }
in the specification.
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,
%{ 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.
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 associated with that token, it should be assigned to the external variable 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:
yylex() {
extern int yylval;
int c;
. . .
c = getchar();
. . .
switch( c ) {
. . .
case '0':
case '1':
. . .
case '9':
yylval = c-'0';
return( DIGIT );
. . .
}
. . .
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.
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 declarations 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 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.
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.
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 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 follows:
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 lookahead 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 usually 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.
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 differences between the processing of the left hand symbol and an ordinary 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 carried 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 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.
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:
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 processing this input.
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, 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. Consulting 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.
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 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 association).
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
expr - expr - expr
When the parser has read the second expr, the input that it has seen:
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 associative interpretation.
Alternatively, when the parser has seen
expr - expr
it could defer the immediate application of the rule, and continue 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
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 conflict. 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 rule.
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 presence 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 ;
In these rules, IF and ELSE are tokens, cond is a nontermi- nal 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
or
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 groupings 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
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 desired.
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 particular 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 examining 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
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 appropriate.
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 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
and
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 parsing 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, 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 operators, 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 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:
%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 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.
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.
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.
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 y.output file is very useful in deciding whether the parser is actually doing what was intended.
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.
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.
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.
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 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.
Actions may be used with these special error rules. These actions might attempt to reinitialize tables, reclaim symbol table space, etc.
Error rules such as the above are very general, but difficult 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 applications, 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 { $$ = $4; }
There is one potential difficulty with this approach; the parser must correctly process three input tokens before it admits that it has correctly resynchronized after the error. If the reentered line contains an error in the first two tokens, the parser deletes the offending tokens, and gives no message; this is clearly unacceptable. For this reason, there is a mechanism that can be used to force the parser to believe that an error has been fully recovered from. The statement
yyerrok ;
in an action resets the parser to its normal mode. The last example is better written
input : error '\n'
{ yyerrok;
printf( "Reenter last line: " ); }
input
{ $$ = $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 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
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.
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 installation 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:
main(){
return( yyparse() );
}
and
# include <stdio.h>
yyerror(s) char *s; {
fprintf( stderr, "%s\n", s );
}
The argument to yyerror is a string containing an error mes- sage, 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 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. Depending on the operating environment, it may be possible to set this variable by using a debugging system.
This section contains miscellaneous hints on preparing efficient, easy to change, and clear specifications. The individual subsections are more or less independent.
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 other.
c. Put all rules with the same left hand side together. Put the left hand side in only once, and let all fol- lowing 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 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 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.
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 ;
and
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 elements 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 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!
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 reading declarations, 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.
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.
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.
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.
This section discusses a number of advanced features of Yacc.
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 mechanisms can be used to simulate parsers with multiple endmarkers or context-sensitive syntax checking.
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; } ;
. . .
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.
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 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 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 section:
%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 associated with the various terminal and nonterminal names. The construction
< 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, 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
rule : aaa { $<intval>$ = 3; }
bbb { fun( $<intval>2,$<other>0 ); } ;
This syntax has little to recommend it, but the situation arises rarely.
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 int's, as was true historically.
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.
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
%token DIGIT LETTER
%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; } ;
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 ); }
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.
/* 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 { In this action, eat up the rest of the file } | /* empty: the second MARK is optional */ ;
defs : /* empty */ | defs def ;
def : START IDENTIFIER | UNION { Copy union definition to output } | LCURL { Copy C code to output file } 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 : '{' { Copy action, translate $$, etc. } '}' ;
prec : /* empty */ | PREC IDENTIFIER | PREC IDENTIFIER act | prec ';' ;
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 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) value.
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 line.
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. )
and
2.5 + ( 3.5 , 4. )
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.
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.
%{
# 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; }
| 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" );
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 = '\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 ); }
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 ); }
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 ) ); }
This Appendix mentions synonyms and features which are supported 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 analyzer.
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 single 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.