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LINUX GAZETTE
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Yacc - Parser Generator - Part 2
By Hiran Ramankutty



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1. Calculator - Next Version

The next version of the calculator to be described below is substantially much more complex with major changes in the inclusion of if-then-else and while constructs. In addition a syntax tree is constructed during parsing. We can traverse or walk down the tree to get the output. Designing of the tree walk routine can be done in two ways:

To make things more concrete, here is a sample program.

x = 0;
while(x < 3) {
	print x;
	x = x + 1;
}

The output of the interpretive version will be:

1
2
3

while that of the compiler version will be:

	push 0
	push x
LC0:
	push x
	push 3
	complt
	jz LC1
	push x
	print
	push x
	push 1
	add
	pop x
	jmp LC0
LC1:
	ret

The include file contains declarations for the syntax tree and symbol table. The symbol table, sym allows for single character variable names. A node in the syntax tree may hold a constant, an identifier or an internal node with an operator. All three variants are encapsulated in a union nodetype and the structure we have can be determined by nodetype.type.

The lex input file contains patterns for VARIABLE and INTEGER tokens. In addition, tokens are identified for two-character operators such as EQ and NE. Single character operators are simply returned as themselves.

The yacc input file defines YYSTYPE, the type of yylval, as

%union {
	int ivalue;		/* integer value */
	char sIndex;		/* symbol table index */
	nodeType *nPtr;		/* node pointer */
};

This causes the following to be generated in y.tab.h:

typedef union {
	int iValue;		/* integer value;
	char sIndex;            /* symbol table index */
	nodeType *nPtr;         /* node pointer */
}YYSTYPE;

extern YYSTYPE yylval;

Constants, variables and nodes can be represented by yylval in the parser's value stack. Notice the type definitions

%token <iValue>	INTEGER
%token <nPtr>	expr

This binds expr to nPtr, and INTEGER to iValue in the YYSTYPE union. This is essential so that yacc can generate the correct code. For example, the rule

expr: INTEGER { $$ = con($1); }

should generate the following code.

yylval.nPtr = con(yyvsp[0].iValue);

Note that yyvsp is the value stack pointer and yyvsp[0] addresses the top of the value stack, or the value associated with INTEGER.

The unary minus operator is given higher priority than binary operators as follows:

%left GE LE EQ NE '<' '>'
%left '+' '-'
%left '*' '/'
%nonassoc UMINUS

The %nonassoc indicates no associativity is implied. It is frequently used in conjunction with %prec to specify precedence as a rule.

The bottom-up technique is used to construct the syntax tree. Leaf nodes are allocated as integers and variables are reduced. When operators are encountered, a node is allocated and pointers to previously allocated nodes are entered as operands. As statements are reduced, ex is called to do a depth-first walk of the syntax tree. Since the tree was constructed bottom-up, a depth first walk visits nodes in the order that they were originally allocated. This results in operators being applied in the order that they were encountered during parsing.

2. Include File

typedef enum { typeCon, typeId, typeOpr } nodeEnum; 
 
/* constants */ 
typedef struct { 
    nodeEnum type;              /* type of node */ 
    int value;                  /* value of constant */ 
} conNodeType; 
 
/* identifiers */ 
typedef struct { 
    nodeEnum type;              /* type of node */ 
    int i;                      /* subscript to ident array */ 
} idNodeType; 
 
/* operators */ 
typedef struct { 
    nodeEnum type;              /* type of node */ 
    int oper;                   /* operator */ 
    int nops;                   /* number of operands */ 
    union nodeTypeTag *op[1];   /* operands (expandable) */ 
} oprNodeType; 
 
typedef union nodeTypeTag { 
    nodeEnum type;              /* type of node */ 
    conNodeType con;            /* constants */ 
    idNodeType id;              /* identifiers */ 
    oprNodeType opr;            /* operators */ 
} nodeType; 
 
extern int sym[26];

3. Lex Input

%{ 
#include <stdlib.h> 
#include "calc3.h" 
#include "y.tab.h" 
void yyerror(char *); 
%} 
 
%% 
 
[a-z]       {  
                yylval.sIndex = *yytext - 'a'; 
                return VARIABLE; 
            } 
 
[0-9]+      { 
                yylval.iValue = atoi(yytext); 
                return INTEGER; 
            } 
 
[-()<>=+*/;{}.] { 
                return *yytext; 
             } 
 
">="         return GE; 
"<="         return LE; 
"=="            return EQ; 
"!="            return NE; 
"while"         return WHILE; 
"if"            return IF; 
"else"          return ELSE; 
"print"         return PRINT; 
 
[ \t\n]+        ;       /* ignore whitespace */ 
 
.               yyerror("Unknown character"); 
%% 
int yywrap(void) { 
    return 1; 
}

4. Yacc Input

%{ 
#include <stdio.h> 
#include <stdlib.h> 
#include <stdarg.h> 
#include "calc3.h" 
 
/* prototypes */ 
nodeType *opr(int oper, int nops, ...); 
nodeType *id(int i); 
nodeType *con(int value); 
void freeNode(nodeType *p); 
int ex(nodeType *p); 
int yylex(void); 
void yyerror(char *s); 
int sym[26];                    /* symbol table */ 
%} 
 
%union { 
    int iValue;                 /* integer value */ 
    char sIndex;                /* symbol table index */ 
    nodeType *nPtr;             /* node pointer */ 
}; 
 
%token <iValue> INTEGER 
%token <sIndex> VARIABLE 
%token WHILE IF PRINT 
%nonassoc IFX 
%nonassoc ELSE 
 
%left GE LE EQ NE '>' '<' 
%left '+' '-' 
%left '*' '/' 
%nonassoc UMINUS 
 
%type <nPtr> stmt expr stmt_list 
 
%% 
 

program: 
        function                { exit(0); } 
        ; 
 
function: 
          function stmt         { ex($2); freeNode($2); } 
        | /* NULL */ 
        ; 
 
stmt: 
          ';'                   { $$ = opr(';', 2, NULL, NULL); } 
        | expr ';'              { $$ = $1; } 
        | PRINT expr ';'        { $$ = opr(PRINT, 1, $2); } 
        | VARIABLE '=' expr ';' { $$ = opr('=', 2, id($1), $3); } 
        | WHILE '(' expr ')' stmt         
                { $$ = opr(WHILE, 2, $3, $5); } 
        | IF '(' expr ')' stmt %prec IFX  
                { $$ = opr(IF, 2, $3, $5); } 
        | IF '(' expr ')' stmt ELSE stmt  
                { $$ = opr(IF, 3, $3, $5, $7); } 
        | '{' stmt_list '}'     { $$ = $2; } 
        ; 
 
stmt_list: 
          stmt                  { $$ = $1; } 
        | stmt_list stmt        { $$ = opr(';', 2, $1, $2); } 
        ; 
 
expr: 
          INTEGER               { $$ = con($1); } 
        | VARIABLE              { $$ = id($1); } 
        | '-' expr %prec UMINUS { $$ = opr(UMINUS, 1, $2); } 
        | expr '+' expr         { $$ = opr('+', 2, $1, $3); } 
        | expr '-' expr         { $$ = opr('-', 2, $1, $3); } 
        | expr '*' expr         { $$ = opr('*', 2, $1, $3); } 
        | expr '/' expr         { $$ = opr('/', 2, $1, $3); } 
        | expr '<' expr      { $$ = opr('<', 2, $1, $3); } 
        | expr '>' expr      { $$ = opr('>', 2, $1, $3); } 
        | expr GE expr          { $$ = opr(GE, 2, $1, $3); } 
        | expr LE expr          { $$ = opr(LE, 2, $1, $3); } 
        | expr NE expr          { $$ = opr(NE, 2, $1, $3); } 
        | expr EQ expr          { $$ = opr(EQ, 2, $1, $3); } 
        | '(' expr ')'          { $$ = $2; } 
        ; 
 
%% 
 

nodeType *con(int value) { 
    nodeType *p; 
 
    /* allocate node */ 
    if ((p = malloc(sizeof(conNodeType))) == NULL) 
        yyerror("out of memory"); 
 
    /* copy information */ 
    p->type = typeCon; 
    p->con.value = value; 
 
    return p; 
} 
 
nodeType *id(int i) { 
    nodeType *p; 
 
    /* allocate node */ 
    if ((p = malloc(sizeof(idNodeType))) == NULL) 
        yyerror("out of memory"); 
 
    /* copy information */ 
    p->type = typeId; 
    p->id.i = i; 
 
    return p; 
} 
 
nodeType *opr(int oper, int nops, ...) { 
    va_list ap; 
    nodeType *p; 
    size_t size; 
    int i; 
 
    /* allocate node */ 
    size = sizeof(oprNodeType) + (nops - 1) * sizeof(nodeType*); 
    if ((p = malloc(size)) == NULL) 
        yyerror("out of memory"); 
 
    /* copy information */ 
    p->type = typeOpr; 
    p->opr.oper = oper; 
    p->opr.nops = nops; 
    va_start(ap, nops); 
    for (i = 0; i < nops; i++) 
        p->opr.op[i] = va_arg(ap, nodeType*); 
    va_end(ap); 
    return p; 
} 
 

void freeNode(nodeType *p) { 
    int i; 
 
    if (!p) return; 
    if (p->type == typeOpr) { 
        for (i = 0; i < p->opr.nops; i++) 
            freeNode(p->opr.op[i]); 
    } 
    free (p); 
} 
 
void yyerror(char *s) { 
    fprintf(stdout, "%s\n", s); 
} 
 
int main(void) { 
    yyparse(); 
    return 0; 
}

5. Interpreter

#include <stdio.h> 
#include "calc3.h" 
#include "y.tab.h" 
 
int ex(nodeType *p) { 
    if (!p) return 0; 
    switch(p->type) { 
    case typeCon:    return p->con.value; 
    case typeId:     return sym[p->id.i]; 
    case typeOpr: 
        switch(p->opr.oper) { 
        case WHILE:  while(ex(p->opr.op[0]))  
                         ex(p->opr.op[1]);  
                     return 0; 
        case IF:     if (ex(p->opr.op[0])) 
                         ex(p->opr.op[1]); 
                     else if (p->opr.nops > 2) 
                         ex(p->opr.op[2]); 
                     return 0; 
        case PRINT:  printf("%d\n", ex(p->opr.op[0]));  
                     return 0; 
        case ';':    ex(p->opr.op[0]);  
                     return ex(p->opr.op[1]); 
        case '=':    return sym[p->opr.op[0]->id.i] =  
                         ex(p->opr.op[1]); 
        case UMINUS: return -ex(p->opr.op[0]); 
        case '+':    return ex(p->opr.op[0]) + ex(p->opr.op[1]); 
        case '-':    return ex(p->opr.op[0]) - ex(p->opr.op[1]); 
        case '*':    return ex(p->opr.op[0]) * ex(p->opr.op[1]); 
        case '/':    return ex(p->opr.op[0]) / ex(p->opr.op[1]); 
        case '<':    return ex(p->opr.op[0]) < ex(p->opr.op[1]); 
        case '>':    return ex(p->opr.op[0]) > ex(p->opr.op[1]); 
        case GE:     return ex(p->opr.op[0]) >= ex(p->opr.op[1]); 
        case LE:     return ex(p->opr.op[0]) <= ex(p->opr.op[1]); 
        case NE:     return ex(p->opr.op[0]) != ex(p->opr.op[1]); 
        case EQ:     return ex(p->opr.op[0]) == ex(p->opr.op[1]); 
        } 
    } 
}
6. Compiler
#include <stdio.h> 
#include "calc3.h" 
#include "y.tab.h" 
 
static int lbl; 
 
int ex(nodeType *p) { 
    int lbl1, lbl2; 
 
    if (!p) return 0; 
    switch(p->type) { 
    case typeCon:        
        printf("\tpush\t%d\n", p->con.value);  
        break; 
    case typeId:         
        printf("\tpush\t%c\n", p->id.i + 'a');  
        break; 
    case typeOpr: 
        switch(p->opr.oper) { 
        case WHILE: 
            printf("L%03d:\n", lbl1 = lbl++); 
            ex(p->opr.op[0]); 
            printf("\tjz\tL%03d\n", lbl2 = lbl++); 
            ex(p->opr.op[1]); 
            printf("\tjmp\tL%03d\n", lbl1); 
            printf("L%03d:\n", lbl2); 
            break; 
        case IF: 
            ex(p->opr.op[0]); 
            if (p->opr.nops > 2) { 
                /* if else */ 
                printf("\tjz\tL%03d\n", lbl1 = lbl++); 
                ex(p->opr.op[1]); 
                printf("\tjmp\tL%03d\n", lbl2 = lbl++); 
                printf("L%03d:\n", lbl1); 
                ex(p->opr.op[2]); 
                printf("L%03d:\n", lbl2); 
            } else { 
                /* if */ 
                printf("\tjz\tL%03d\n", lbl1 = lbl++); 
                ex(p->opr.op[1]); 
                printf("L%03d:\n", lbl1); 
            } 
            break; 
         

        case PRINT:      
            ex(p->opr.op[0]); 
            printf("\tprint\n"); 
            break; 
        case '=':        
            ex(p->opr.op[1]); 
            printf("\tpop\t%c\n", p->opr.op[0]->id.i + 'a'); 
            break; 
        case UMINUS:     
            ex(p->opr.op[0]); 
            printf("\tneg\n"); 
            break; 
        default: 
            ex(p->opr.op[0]); 
            ex(p->opr.op[1]); 
            switch(p->opr.oper) { 
            case '+':   printf("\tadd\n"); break; 
            case '-':   printf("\tsub\n"); break;  
            case '*':   printf("\tmul\n"); break; 
            case '/':   printf("\tdiv\n"); break; 
            case '<':   printf("\tcompLT\n"); break; 
            case '>':   printf("\tcompGT\n"); break; 
            case GE:    printf("\tcompGE\n"); break; 
            case LE:    printf("\tcompLE\n"); break; 
            case NE:    printf("\tcompNE\n"); break; 
            case EQ:    printf("\tcompEQ\n"); break; 
            } 
        } 
    } 
} 

7. If-Else Ambiguity

The shift-reduce conflict (as explained in Part 1) that frequently occurs involves the if-else construct. Assume we have the following rules:

stmt:
	IF expr stmt
	|	IF expr stmt ELSE stmt
	...

and the following state:

IF expr stmt IF expr stmt . ELSE stmt

During parsing what do we do when we come across ELSE.Do we shift the ELSE, or reduce the IF expr stmt at the top of the stack. If we shift, then we have

IF expr stmt IF expr stmt . ELSE stmt
IF expr stmt IF expr stmt ELSE . stmt
IF expr stmt IF expr stmt ELSE stmt .
IF expr stmt stmt .

where the second ELSE is paired with the second IF. If we reduce, we have

IF expr stmt IF expr stmt . ELSE stmt
IF expr stmt stmt . ELSE stmt
IF expr stmt . ELSE stmt
IF expr stmt ELSE . stmt
IF expr stmt ELSE stmt .

where the ELSE is paired with the first IF. Modern programming languages pair an ELSE with the most recent unpaired IF, and so the former behaviour is expected. This works well with yacc. The default action of shifting is taken whenever a shift-reduce conflict arises. Bur along with it, yacc issues a warning message. To remove the message, give IF-ELSE a higher precedence than the simple IF statement:

%nonassoc IFX
%nonassoc ELSE

stmt:
	IF expr stmt %prec IFX
	|	IF expr stmt ELSE stmt

8. Conclusion

The 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.

Yacc usually generates warnings. But errors may also arise. A message like "syntax error" would leave you wandering where the error occurred and what the error is. Error handling is much more difficult and I am not dealing with it right now.

 

[BIO] I have just given my final year B.Tech examinations in Computer Science and Engineering and a native of Kerala, India.


Copyright © 2003, Hiran Ramankutty. Copying license http://www.linuxgazette.com/copying.html
Published in Issue 93 of Linux Gazette, August 2003

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