bison_5.htm

Lex和Yacc的Manual

2.3000000000
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</PRE>

<P>
Note that multiple assignment and nested function calls are permitted.

</P>



<H3><A NAME="SEC30" HREF="index.html#SEC30">Declarations for <CODE>mfcalc</CODE></A></H3>

<P>
Here are the C and Bison declarations for the multi-function calculator.

</P>

<PRE>
%{
#include &#60;math.h&#62;  /* 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 &#60;val&#62;  NUM        /* Simple double precision number   */
%token &#60;tptr&#62; VAR FNCT   /* Variable and Function            */
%type  &#60;val&#62;  exp

%right '='
%left '-' '+'
%left '*' '/'
%left NEG     /* Negation--unary minus */
%right '^'    /* Exponentiation        */

/* Grammar follows */

%%
</PRE>

<P>
The above grammar introduces only two new features of the Bison language.
These features allow semantic values to have various data types
(see section <A HREF="bison_6.html#SEC45">More Than One Value Type</A>).

</P>
<P>
The <CODE>%union</CODE> declaration specifies the entire list of possible types;
this is instead of defining <CODE>YYSTYPE</CODE>.  The allowable types are now
double-floats (for <CODE>exp</CODE> and <CODE>NUM</CODE>) and pointers to entries in
the symbol table.  See section <A HREF="bison_6.html#SEC52">The Collection of Value Types</A>.

</P>
<P>
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 <CODE>NUM</CODE>, <CODE>VAR</CODE>, <CODE>FNCT</CODE>, and <CODE>exp</CODE>.  Their
declarations are augmented with information about their data type (placed
between angle brackets).

</P>
<P>
The Bison construct <CODE>%type</CODE> is used for declaring nonterminal symbols,
just as <CODE>%token</CODE> is used for declaring token types.  We have not used
<CODE>%type</CODE> before because nonterminal symbols are normally declared
implicitly by the rules that define them.  But <CODE>exp</CODE> must be declared
explicitly so we can specify its value type.  See section <A HREF="bison_6.html#SEC53">Nonterminal Symbols</A>.

</P>


<H3><A NAME="SEC31" HREF="index.html#SEC31">Grammar Rules for <CODE>mfcalc</CODE></A></H3>

<P>
Here are the grammar rules for the multi-function calculator.
Most of them are copied directly from <CODE>calc</CODE>; three rules,
those which mention <CODE>VAR</CODE> or <CODE>FNCT</CODE>, are new.

</P>

<PRE>
input:   /* empty */
        | input line
;

line:
          '\n'
        | exp '\n'   { printf ("\t%.10g\n", $1); }
        | error '\n' { yyerrok;                  }
;

exp:      NUM                { $$ = $1;                         }
        | VAR                { $$ = $1-&#62;value.var;              }
        | VAR '=' exp        { $$ = $3; $1-&#62;value.var = $3;     }
        | FNCT '(' exp ')'   { $$ = (*($1-&#62;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 */
%%
</PRE>



<H3><A NAME="SEC32" HREF="index.html#SEC32">The <CODE>mfcalc</CODE> Symbol Table</A></H3>
<P>
<A NAME="IDX48"></A>

</P>
<P>
The 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.

</P>
<P>
The symbol table itself consists of a linked list of records.  Its
definition, which is kept in the header <TT>`calc.h'</TT>, is as follows.  It
provides for either functions or variables to be placed in the table.

</P>

<PRE>
/* 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 ();
</PRE>

<P>
The new version of <CODE>main</CODE> includes a call to <CODE>init_table</CODE>, a
function that initializes the symbol table.  Here it is, and
<CODE>init_table</CODE> as well:

</P>

<PRE>
#include &#60;stdio.h&#62;

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-&#62;value.fnctptr = arith_fncts[i].fnct;
    }
}
</PRE>

<P>
By simply editing the initialization list and adding the necessary include
files, you can add additional functions to the calculator.

</P>
<P>
Two important functions allow look-up and installation of symbols in the
symbol table.  The function <CODE>putsym</CODE> is passed a name and the type
(<CODE>VAR</CODE> or <CODE>FNCT</CODE>) 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 <CODE>getsym</CODE> is passed the name of the symbol to look up.  If
found, a pointer to that symbol is returned; otherwise zero is returned.

</P>

<PRE>
symrec *
putsym (sym_name,sym_type)
     char *sym_name;
     int sym_type;
{
  symrec *ptr;
  ptr = (symrec *) malloc (sizeof (symrec));
  ptr-&#62;name = (char *) malloc (strlen (sym_name) + 1);
  strcpy (ptr-&#62;name,sym_name);
  ptr-&#62;type = sym_type;
  ptr-&#62;value.var = 0; /* set value to 0 even if fctn.  */
  ptr-&#62;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-&#62;next)
    if (strcmp (ptr-&#62;name,sym_name) == 0)
      return ptr;
  return 0;
}
</PRE>

<P>
The function <CODE>yylex</CODE> 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.

</P>
<P>
The string is passed to <CODE>getsym</CODE> for look up in the symbol table.  If
the name appears in the table, a pointer to its location and its type
(<CODE>VAR</CODE> or <CODE>FNCT</CODE>) is returned to <CODE>yyparse</CODE>.  If it is not
already in the table, then it is installed as a <CODE>VAR</CODE> using
<CODE>putsym</CODE>.  Again, a pointer and its type (which must be <CODE>VAR</CODE>) is
returned to <CODE>yyparse</CODE>.
</P>
<P>
No change is needed in the handling of numeric values and arithmetic
operators in <CODE>yylex</CODE>.

</P>

<PRE>
#include &#60;ctype.h&#62;
yylex ()
{
  int c;

  /* Ignore whitespace, get first nonwhite character.  */
  while ((c = getchar ()) == ' ' || c == '\t');

  if (c == EOF)
    return 0;

  /* Char starts a number =&#62; parse the number.         */
  if (c == '.' || isdigit (c))
    {
      ungetc (c, stdin);
      scanf ("%lf", &#38;yylval.val);
      return NUM;
    }

  /* Char starts an identifier =&#62; 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 &#38;&#38; isalnum (c));

      ungetc (c, stdin);
      symbuf[i] = '\0';

      s = getsym (symbuf);
      if (s == 0)
        s = putsym (symbuf, VAR);
      yylval.tptr = s;
      return s-&#62;type;
    }

  /* Any other character is a token by itself.        */
  return c;
}
</PRE>

<P>
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 <CODE>pi</CODE> or <CODE>e</CODE> as well.

</P>


<H2><A NAME="SEC33" HREF="index.html#SEC33">Exercises</A></H2>
<P>
<A NAME="IDX49"></A>

</P>

<OL>
<LI>

Add some new functions from <TT>`math.h'</TT> to the initialization list.

<LI>

Add another array that contains constants and their values.  Then
modify <CODE>init_table</CODE> to add these constants to the symbol table.
It will be easiest to give the constants type <CODE>VAR</CODE>.

<LI>

Make the program report an error if the user refers to an
uninitialized variable in any way except to store a value in it.
</OL>

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