Now we show and explain three sample programs written using Bison: a reverse polish notation calculator, an algebraic (infix) notation calculator, and a multi-function calculator. All three have been tested under BSD Unix 4.3; each produces a usable, though limited, interactive desk-top calculator.
These examples are simple, but Bison grammars for real programming languages are written the same way.
The first example is that of a simple double-precision reverse polish notation calculator (a calculator using postfix operators). This example provides a good starting point, since operator precedence is not an issue. The second example will illustrate how operator precedence is handled.
The source code for this calculator is named `rpcalc.y'. The `.y' extension is a convention used for Bison input files.
rpcalcHere are the C and Bison declarations for the reverse polish notation calculator. As in C, comments are placed between `/*...*/'.
/* Reverse polish notation calculator. */
%{
#define YYSTYPE double
#include <math.h>
%}
%token NUM
%% /* Grammar rules and actions follow */
The C declarations section (see section The C Declarations Section) contains two preprocessor directives.
The #define directive defines the macro YYSTYPE, thus
specifying the C data type for semantic values of both tokens and groupings
(see section Data Types of Semantic Values). The Bison parser will use whatever type
YYSTYPE is defined as; if you don't define it, int is the
default. Because we specify double, each token and each expression
has an associated value, which is a floating point number.
The #include directive is used to declare the exponentiation
function pow.
The second section, Bison declarations, provides information to Bison about
the token types (see section The Bison Declarations Section). Each terminal symbol that is
not a single-character literal must be declared here. (Single-character
literals normally don't need to be declared.) In this example, all the
arithmetic operators are designated by single-character literals, so the
only terminal symbol that needs to be declared is NUM, the token
type for numeric constants.
rpcalcHere are the grammar rules for the reverse polish notation calculator.
input: /* empty */
| input line
;
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
;
exp: NUM { $$ = $1; }
| exp exp '+' { $$ = $1 + $2; }
| exp exp '-' { $$ = $1 - $2; }
| exp exp '*' { $$ = $1 * $2; }
| exp exp '/' { $$ = $1 / $2; }
/* Exponentiation */
| exp exp '^' { $$ = pow ($1, $2); }
/* Unary minus */
| exp 'n' { $$ = -$1; }
;
%%
The groupings of the rpcalc "language" defined here are the expression
(given the name exp), the line of input (line), and the
complete input transcript (input). Each of these nonterminal
symbols has several alternate rules, joined by the `|' punctuator
which is read as "or". The following sections explain what these rules
mean.
The semantics of the language is determined by the actions taken when a grouping is recognized. The actions are the C code that appears inside braces. See section Actions.
You must specify these actions in C, but Bison provides the means for
passing semantic values between the rules. In each action, the
pseudo-variable $$ stands for the semantic value for the grouping
that the rule is going to construct. Assigning a value to $$ is the
main job of most actions. The semantic values of the components of the
rule are referred to as $1, $2, and so on.
input
Consider the definition of input:
input: /* empty */
| input line
;
This definition reads as follows: "A complete input is either an empty
string, or a complete input followed by an input line". Notice that
"complete input" is defined in terms of itself. This definition is said
to be left recursive since input appears always as the
leftmost symbol in the sequence. See section Recursive Rules.
The first alternative is empty because there are no symbols between the
colon and the first `|'; this means that input can match an
empty string of input (no tokens). We write the rules this way because it
is legitimate to type Ctrl-d right after you start the calculator.
It's conventional to put an empty alternative first and write the comment
`/* empty */' in it.
The second alternate rule (input line) handles all nontrivial input.
It means, "After reading any number of lines, read one more line if
possible." The left recursion makes this rule into a loop. Since the
first alternative matches empty input, the loop can be executed zero or
more times.
The parser function yyparse continues to process input until a
grammatical error is seen or the lexical analyzer says there are no more
input tokens; we will arrange for the latter to happen at end of file.
line
Now consider the definition of line:
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
;
The first alternative is a token which is a newline character; this means
that rpcalc accepts a blank line (and ignores it, since there is no
action). The second alternative is an expression followed by a newline.
This is the alternative that makes rpcalc useful. The semantic value of
the exp grouping is the value of $1 because the exp in
question is the first symbol in the alternative. The action prints this
value, which is the result of the computation the user asked for.
This action is unusual because it does not assign a value to $$. As
a consequence, the semantic value associated with the line is
uninitialized (its value will be unpredictable). This would be a bug if
that value were ever used, but we don't use it: once rpcalc has printed the
value of the user's input line, that value is no longer needed.
expr
The exp grouping has several rules, one for each kind of expression.
The first rule handles the simplest expressions: those that are just numbers.
The second handles an addition-expression, which looks like two expressions
followed by a plus-sign. The third handles subtraction, and so on.
exp: NUM
| exp exp '+' { $$ = $1 + $2; }
| exp exp '-' { $$ = $1 - $2; }
...
;
We have used `|' to join all the rules for exp, but we could
equally well have written them separately:
exp: NUM ;
exp: exp exp '+' { $$ = $1 + $2; } ;
exp: exp exp '-' { $$ = $1 - $2; } ;
...
Most of the rules have actions that compute the value of the expression in
terms of the value of its parts. For example, in the rule for addition,
$1 refers to the first component exp and $2 refers to
the second one. The third component, '+', has no meaningful
associated semantic value, but if it had one you could refer to it as
$3. When yyparse recognizes a sum expression using this
rule, the sum of the two subexpressions' values is produced as the value of
the entire expression. See section Actions.
You don't have to give an action for every rule. When a rule has no
action, Bison by default copies the value of $1 into $$.
This is what happens in the first rule (the one that uses NUM).
The formatting shown here is the recommended convention, but Bison does not require it. You can add or change whitespace as much as you wish. For example, this:
exp : NUM | exp exp '+' {$$ = $1 + $2; } | ...
means the same thing as this:
exp: NUM
| exp exp '+' { $$ = $1 + $2; }
| ...
The latter, however, is much more readable.
rpcalc Lexical Analyzer
The lexical analyzer's job is low-level parsing: converting characters or
sequences of characters into tokens. The Bison parser gets its tokens by
calling the lexical analyzer. See section The Lexical Analyzer Function yylex.
Only a simple lexical analyzer is needed for the RPN calculator. This
lexical analyzer skips blanks and tabs, then reads in numbers as
double and returns them as NUM tokens. Any other character
that isn't part of a number is a separate token. Note that the token-code
for such a single-character token is the character itself.
The return value of the lexical analyzer function is a numeric code which
represents a token type. The same text used in Bison rules to stand for
this token type is also a C expression for the numeric code for the type.
This works in two ways. If the token type is a character literal, then its
numeric code is the ASCII code for that character; you can use the same
character literal in the lexical analyzer to express the number. If the
token type is an identifier, that identifier is defined by Bison as a C
macro whose definition is the appropriate number. In this example,
therefore, NUM becomes a macro for yylex to use.
The semantic value of the token (if it has one) is stored into the global
variable yylval, which is where the Bison parser will look for it.
(The C data type of yylval is YYSTYPE, which was defined
at the beginning of the grammar; see section Declarations for rpcalc.)
A token type code of zero is returned if the end-of-file is encountered. (Bison recognizes any nonpositive value as indicating the end of the input.)
Here is the code for the lexical analyzer:
/* Lexical analyzer returns a double floating point
number on the stack and the token NUM, or the ASCII
character read if not a number. Skips all blanks
and tabs, returns 0 for EOF. */
#include <ctype.h>
yylex ()
{
int c;
/* skip white space */
while ((c = getchar ()) == ' ' || c == '\t')
;
/* process numbers */
if (c == '.' || isdigit (c))
{
ungetc (c, stdin);
scanf ("%lf", &yylval);
return NUM;
}
/* return end-of-file */
if (c == EOF)
return 0;
/* return single chars */
return c;
}
In keeping with the spirit of this example, the controlling function is
kept to the bare minimum. The only requirement is that it call
yyparse to start the process of parsing.
main ()
{
yyparse ();
}
When yyparse detects a syntax error, it calls the error reporting
function yyerror to print an error message (usually but not always
"parse error"). It is up to the programmer to supply yyerror
(see section Parser C-Language Interface), so here is the definition we will use:
#include <stdio.h>
yyerror (s) /* Called by yyparse on error */
char *s;
{
printf ("%s\n", s);
}
After yyerror returns, the Bison parser may recover from the error
and continue parsing if the grammar contains a suitable error rule
(see section Error Recovery). Otherwise, yyparse returns nonzero. We
have not written any error rules in this example, so any invalid input will
cause the calculator program to exit. This is not clean behavior for a
real calculator, but it is adequate in the first example.
Before running Bison to produce a parser, we need to decide how to arrange
all the source code in one or more source files. For such a simple example,
the easiest thing is to put everything in one file. The definitions of
yylex, yyerror and main go at the end, in the
"additional C code" section of the file (see section The Overall Layout of a Bison Grammar).
For a large project, you would probably have several source files, and use
make to arrange to recompile them.
With all the source in a single file, you use the following command to convert it into a parser file:
bison file_name.y
In this example the file was called `rpcalc.y' (for "Reverse Polish
CALCulator"). Bison produces a file named `file_name.tab.c',
removing the `.y' from the original file name. The file output by
Bison contains the source code for yyparse. The additional
functions in the input file (yylex, yyerror and main)
are copied verbatim to the output.
Here is how to compile and run the parser file:
# List files in current directory.
% ls
rpcalc.tab.c rpcalc.y
# Compile the Bison parser.
# `-lm' tells compiler to search math library for pow.
% cc rpcalc.tab.c -lm -o rpcalc
# List files again.
% ls
rpcalc rpcalc.tab.c rpcalc.y
The file `rpcalc' now contains the executable code. Here is an
example session using rpcalc.
% rpcalc 4 9 + 13 3 7 + 3 4 5 *+- -13 3 7 + 3 4 5 * + - n Note the unary minus, `n' 13 5 6 / 4 n + -3.166666667 3 4 ^ Exponentiation 81 ^D End-of-file indicator %
calcWe now modify rpcalc to handle infix operators instead of postfix. Infix notation involves the concept of operator precedence and the need for parentheses nested to arbitrary depth. Here is the Bison code for `calc.y', an infix desk-top calculator.
/* Infix notation calculator--calc */
%{
#define YYSTYPE double
#include <math.h>
%}
/* BISON Declarations */
%token NUM
%left '-' '+'
%left '*' '/'
%left NEG /* negation--unary minus */
%right '^' /* exponentiation */
/* Grammar follows */
%%
input: /* empty string */
| input line
;
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
;
exp: NUM { $$ = $1; }
| exp '+' exp { $$ = $1 + $3; }
| exp '-' exp { $$ = $1 - $3; }
| exp '*' exp { $$ = $1 * $3; }
| exp '/' exp { $$ = $1 / $3; }
| '-' exp %prec NEG { $$ = -$2; }
| exp '^' exp { $$ = pow ($1, $3); }
| '(' exp ')' { $$ = $2; }
;
%%
The functions yylex, yyerror and main can be the same
as before.
There are two important new features shown in this code.
In the second section (Bison declarations), %left declares token
types and says they are left-associative operators. The declarations
%left and %right (right associativity) take the place of
%token which is used to declare a token type name without
associativity. (These tokens are single-character literals, which
ordinarily don't need to be declared. We declare them here to specify
the associativity.)
Operator precedence is determined by the line ordering of the
declarations; the higher the line number of the declaration (lower on
the page or screen), the higher the precedence. Hence, exponentiation
has the highest precedence, unary minus (NEG) is next, followed
by `*' and `/', and so on. See section Operator Precedence.
The other important new feature is the %prec in the grammar section
for the unary minus operator. The %prec simply instructs Bison that
the rule `| '-' exp' has the same precedence as NEG---in this
case the next-to-highest. See section Context-Dependent Precedence.
Here is a sample run of `calc.y':
% calc 4 + 4.5 - (34/(8*3+-3)) 6.880952381 -56 + 2 -54 3 ^ 2 9
Up to this point, this manual has not addressed the issue of error
recovery---how to continue parsing after the parser detects a syntax
error. All we have handled is error reporting with yyerror. Recall
that by default yyparse returns after calling yyerror. This
means that an erroneous input line causes the calculator program to exit.
Now we show how to rectify this deficiency.
The Bison language itself includes the reserved word error, which
may be included in the grammar rules. In the example below it has
been added to one of the alternatives for line:
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
| error '\n' { yyerrok; }
;
This addition to the grammar allows for simple error recovery in the event
of a parse error. If an expression that cannot be evaluated is read, the
error will be recognized by the third rule for line, and parsing
will continue. (The yyerror function is still called upon to print
its message as well.) The action executes the statement yyerrok, a
macro defined automatically by Bison; its meaning is that error recovery is
complete (see section Error Recovery). Note the difference between
yyerrok and yyerror; neither one is a misprint.
This form of error recovery deals with syntax errors. There are other
kinds of errors; for example, division by zero, which raises an exception
signal that is normally fatal. A real calculator program must handle this
signal and use longjmp to return to main and resume parsing
input lines; it would also have to discard the rest of the current line of
input. We won't discuss this issue further because it is not specific to
Bison programs.
mfcalc
Now that the basics of Bison have been discussed, it is time to move on to
a more advanced problem. The above calculators provided only five
functions, `+', `-', `*', `/' and `^'. It would
be nice to have a calculator that provides other mathematical functions such
as sin, cos, etc.
It is easy to add new operators to the infix calculator as long as they are
only single-character literals. The lexical analyzer yylex passes
back all non-number characters as tokens, so new grammar rules suffice for
adding a new operator. But we want something more flexible: built-in
functions whose syntax has this form:
function_name (argument)
At the same time, we will add memory to the calculator, by allowing you to create named variables, store values in them, and use them later. Here is a sample session with the multi-function calculator:
% mfcalc pi = 3.141592653589 3.1415926536 sin(pi) 0.0000000000 alpha = beta1 = 2.3 2.3000000000 alpha 2.3000000000 ln(alpha) 0.8329091229 exp(ln(beta1)) 2.3000000000 %
Note that multiple assignment and nested function calls are permitted.
mfcalcHere are the C and Bison declarations for the multi-function calculator.
%{
#include <math.h> /* For math functions, cos(), sin(), etc. */
#include "calc.h" /* Contains definition of `symrec' */
%}
%union {
double val; /* For returning numbers. */
symrec *tptr; /* For returning symbol-table pointers */
}
%token <val> NUM /* Simple double precision number */
%token <tptr> VAR FNCT /* Variable and Function */
%type <val> exp
%right '='
%left '-' '+'
%left '*' '/'
%left NEG /* Negation--unary minus */
%right '^' /* Exponentiation */
/* Grammar follows */
%%
The above grammar introduces only two new features of the Bison language. These features allow semantic values to have various data types (see section More Than One Value Type).
The %union declaration specifies the entire list of possible types;
this is instead of defining YYSTYPE. The allowable types are now
double-floats (for exp and NUM) and pointers to entries in
the symbol table. See section The Collection of Value Types.
Since values can now have various types, it is necessary to associate a
type with each grammar symbol whose semantic value is used. These symbols
are NUM, VAR, FNCT, and exp. Their
declarations are augmented with information about their data type (placed
between angle brackets).
The Bison construct %type is used for declaring nonterminal symbols,
just as %token is used for declaring token types. We have not used
%type before because nonterminal symbols are normally declared
implicitly by the rules that define them. But exp must be declared
explicitly so we can specify its value type. See section Nonterminal Symbols.
mfcalc
Here are the grammar rules for the multi-function calculator.
Most of them are copied directly from calc; three rules,
those which mention VAR or FNCT, are new.
input: /* empty */
| input line
;
line:
'\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
| error '\n' { yyerrok; }
;
exp: NUM { $$ = $1; }
| VAR { $$ = $1->value.var; }
| VAR '=' exp { $$ = $3; $1->value.var = $3; }
| FNCT '(' exp ')' { $$ = (*($1->value.fnctptr))($3); }
| exp '+' exp { $$ = $1 + $3; }
| exp '-' exp { $$ = $1 - $3; }
| exp '*' exp { $$ = $1 * $3; }
| exp '/' exp { $$ = $1 / $3; }
| '-' exp %prec NEG { $$ = -$2; }
| exp '^' exp { $$ = pow ($1, $3); }
| '(' exp ')' { $$ = $2; }
;
/* End of grammar */
%%
mfcalc Symbol TableThe multi-function calculator requires a symbol table to keep track of the names and meanings of variables and functions. This doesn't affect the grammar rules (except for the actions) or the Bison declarations, but it requires some additional C functions for support.
The symbol table itself consists of a linked list of records. Its definition, which is kept in the header `calc.h', is as follows. It provides for either functions or variables to be placed in the table.
/* Data type for links in the chain of symbols. */
struct symrec
{
char *name; /* name of symbol */
int type; /* type of symbol: either VAR or FNCT */
union {
double var; /* value of a VAR */
double (*fnctptr)(); /* value of a FNCT */
} value;
struct symrec *next; /* link field */
};
typedef struct symrec symrec;
/* The symbol table: a chain of `struct symrec'. */
extern symrec *sym_table;
symrec *putsym ();
symrec *getsym ();
The new version of main includes a call to init_table, a
function that initializes the symbol table. Here it is, and
init_table as well:
#include <stdio.h>
main ()
{
init_table ();
yyparse ();
}
yyerror (s) /* Called by yyparse on error */
char *s;
{
printf ("%s\n", s);
}
struct init
{
char *fname;
double (*fnct)();
};
struct init arith_fncts[]
= {
"sin", sin,
"cos", cos,
"atan", atan,
"ln", log,
"exp", exp,
"sqrt", sqrt,
0, 0
};
/* The symbol table: a chain of `struct symrec'. */
symrec *sym_table = (symrec *)0;
init_table () /* puts arithmetic functions in table. */
{
int i;
symrec *ptr;
for (i = 0; arith_fncts[i].fname != 0; i++)
{
ptr = putsym (arith_fncts[i].fname, FNCT);
ptr->value.fnctptr = arith_fncts[i].fnct;
}
}
By simply editing the initialization list and adding the necessary include files, you can add additional functions to the calculator.
Two important functions allow look-up and installation of symbols in the
symbol table. The function putsym is passed a name and the type
(VAR or FNCT) of the object to be installed. The object is
linked to the front of the list, and a pointer to the object is returned.
The function getsym is passed the name of the symbol to look up. If
found, a pointer to that symbol is returned; otherwise zero is returned.
symrec *
putsym (sym_name,sym_type)
char *sym_name;
int sym_type;
{
symrec *ptr;
ptr = (symrec *) malloc (sizeof (symrec));
ptr->name = (char *) malloc (strlen (sym_name) + 1);
strcpy (ptr->name,sym_name);
ptr->type = sym_type;
ptr->value.var = 0; /* set value to 0 even if fctn. */
ptr->next = (struct symrec *)sym_table;
sym_table = ptr;
return ptr;
}
symrec *
getsym (sym_name)
char *sym_name;
{
symrec *ptr;
for (ptr = sym_table; ptr != (symrec *) 0;
ptr = (symrec *)ptr->next)
if (strcmp (ptr->name,sym_name) == 0)
return ptr;
return 0;
}
The function yylex must now recognize variables, numeric values, and
the single-character arithmetic operators. Strings of alphanumeric
characters with a leading nondigit are recognized as either variables or
functions depending on what the symbol table says about them.
The string is passed to getsym for look up in the symbol table. If
the name appears in the table, a pointer to its location and its type
(VAR or FNCT) is returned to yyparse. If it is not
already in the table, then it is installed as a VAR using
putsym. Again, a pointer and its type (which must be VAR) is
returned to yyparse.
No change is needed in the handling of numeric values and arithmetic
operators in yylex.
#include <ctype.h>
yylex ()
{
int c;
/* Ignore whitespace, get first nonwhite character. */
while ((c = getchar ()) == ' ' || c == '\t');
if (c == EOF)
return 0;
/* Char starts a number => parse the number. */
if (c == '.' || isdigit (c))
{
ungetc (c, stdin);
scanf ("%lf", &yylval.val);
return NUM;
}
/* Char starts an identifier => read the name. */
if (isalpha (c))
{
symrec *s;
static char *symbuf = 0;
static int length = 0;
int i;
/* Initially make the buffer long enough
for a 40-character symbol name. */
if (length == 0)
length = 40, symbuf = (char *)malloc (length + 1);
i = 0;
do
{
/* If buffer is full, make it bigger. */
if (i == length)
{
length *= 2;
symbuf = (char *)realloc (symbuf, length + 1);
}
/* Add this character to the buffer. */
symbuf[i++] = c;
/* Get another character. */
c = getchar ();
}
while (c != EOF && isalnum (c));
ungetc (c, stdin);
symbuf[i] = '\0';
s = getsym (symbuf);
if (s == 0)
s = putsym (symbuf, VAR);
yylval.tptr = s;
return s->type;
}
/* Any other character is a token by itself. */
return c;
}
This program is both powerful and flexible. You may easily add new
functions, and it is a simple job to modify this code to install predefined
variables such as pi or e as well.
init_table to add these constants to the symbol table.
It will be easiest to give the constants type VAR.
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