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3. Compiler Tools

Two tools, Flex and Bison, are provided for the compiler development. If you are having a general idea regarding them you can skip the next two sections, since I have got nothing new to say.

3.1 Flex

Flex is a fast lexical analyzer generator. As explained, the first phase of building a compiler is lexical analysis. Flex is an efficient tool for performing the pattern matching on text. In the absence of Flex we will have to write our own routines for obtaining tokens from the input text.

But with flex we can provide the regular expression to be matched and the action to be taken when a perfect match is found. Our file will have an extension .l, which shows that it is a valid lex file. The output of the flex is a file called lex.yy.c. It has a routine yylex() defined in it. The file, lex.yy.c can be compiled and linked with the '-lfl' library to produce the executable.

One or two examples will make the things clearer. Create a small file, say lex.l with the following contents.

%%

"good"  { printf("bad"); }

%%

Produce the executable with the commands


lex lex.l  
cc lex.yy.c -lfl 

Run the executable. We find that for each occurrence of the string "good", a replacement with the string "bad" is made. For any other input, the input is just echoed. We here have our first lesson - the default action is to just copy the input to the output.

The general structure of the flex file is


definitions 
%% 
rules 
%% 
user code 

The definitions may contain a 'name definition'. For example,


DIGIT [0-9] 

It defines "DIGIT" to be a regular expression, which matches a single digit. The main purpose of name definition is to simplify the scanner specification.

Next is the 'rules' section of the flex file. The general form is

pattern action

where the pattern may be a regular expression. The action should reside on the same line of pattern. The patterns and actions are described below.

In the 'rules' section it is permissible to use variable declarations enclosed in %{ }. It should appear before the first rule. They are local to the scanning routine.

Let us look at an example.


%{
#define WHILE 1
#define IF 2
%}

%%
while           {return WHILE; }
if              {return IF; }
%%

main()
{
        int val;
        while (val = yylex())
                printf("%d",val);
        printf("final =%d\n", val);
}

In the above program for the occurrence of "while" and "if", the corresponding integer value is printed. At the end, for an EOF, the program terminates by returning zero.

Patterns

Here I have only mentioned about the general patterns, which will be required in our compiler construction. For a complete list you are encouraged to refer the manual page.



`x'             match the character x.
`.'             any character except the newline.
`[xyz]'         either an `x' or a `y' or a `z'.
`[a-z]'         either an `a' or a `b' ... or a `z'.
`[^A-Z]'        any character except an uppercase letter.
`r*'            zero or more r's.
`r+'            one or more r's.
`r?'            zero or one r's.
`{name}'        the expansion of the "name" description.
                (As explained above).
`\x'            if x is an `a', `b', `f', `n', `r', `t' or `v'
                then the ANSI C representation of \x. Otherwise
                a literal `x'.
`\0'            the NULL character.
`(r)'           match an r.
                parentheses to override precedence.
`rs'            concatenation of r and s.
`r|s'           either an r or an s

The regular expressions mentioned above are arranged in the decreasing order of precedence. The topmost one has the highest precedence. In case of any confusion you can make use of parentheses to explicitly show what you mean.

Generally, the first question that will be coming in our mind will be - What happens when multiple matches are found. In that case the scanner chooses the one with the maximum length. That is, if we have a file,


%%

"ab"            {printf("first"); }
"abc"           {printf("second"); }

%%

and we are providing the input "abcd" then the two possibilities are "firstcd" and "secondd". The scanner prefers only the second.

But consider the case when the lengths are same. Then the rule given first in the file will get preference over the other.

Once the match is clearly defined then the corresponding action provided can be executed. The text corresponding to the match is available in 'yytext' and its length in 'yyleng', both global values. It is better to avoid local names starting with 'yy' because of its extensive use by the scanner and parser. Its avoidance also contributes to better readability.


%%

[0-9]+  {printf("The value of first yytext is %s\n",yytext);}
[a-z]+  {printf("The value of sec yytext is %s\n",yytext);}

%%

Actions

We find that for each pattern given in the lex file it has an associated action. The action can be any arbitrary C code. It is possible to use the constructs like 'return' to return a value to the caller of yylex. In our compiler we need only simple actions, which can be understood by anyone having some knowledge with the C language.

The above mentioned details are more than enough for our compiler. For the beginners it is highly recommended to try out the various examples and check the different variations of the regular expressions. Before proceeding to the next section you should have a basic idea regarding the Flex.

3.2 Bison

Once we get used with the lexical analyzer, we are ready to meet its best companion - the parser generator, Bison. Given a description for an LALR(1) context-free grammar, it is the duty of Bison to generate a C program to parse that grammar. As explained, the second stage of compiler construction is parsing. We are supplied with the tokens from the lex. We have to define a grammar for a language and see whether the given input is a valid one.

Before proceeding let us look what a context free grammar is and what we mean by terminals and nonterminals.

A context free grammar is a finite set of nonterminals, each of which represents a language. The language represented by the nonterminals is defined recursively in terms of each other and with the help of primitive symbols called terminals.

Thus in simple words terminals are those which can't be further subdivided whereas nonterminals are formed from the grouping of smaller constructs. It is possible to subdivide the nonterminals.

As an example, consider the grammar

Note: I haven't used the bison syntax in this example.


A -> Ab 
A -> b 

It denotes all the strings having only one or more b's. Here A is a nonterminal because it can be divided further using the given productions. But b is a terminal symbol because it is not possible to further divide it.

Suppose we are given a string "bbb". We have to check whether it is accepted by the above productions. Assume the start symbol is 'A'.

A -> Ab      {rule -1}
  -> Abb     {rule -1}
  -> bbb     {rule -2} and thus accepted.

In Bison, generally the terminal symbols are represented in uppercase Ex := NUM (say, for a number) or by using character literal as in the case of '+'. As we expect, the nonterminals are represented by using lowercase letter. Ex := exp. (We'll obey this rule when we switch to Bison examples. ).

Flex and Bison work with perfect mutual understanding. A Bison grammar rule may say that "an expression is made of a number followed by a plus sign followed again by a number". The flex whenever sees a number informs the bison that it has found a number. That is it informs the presence of a token to the parser.

The grammar rule is only concerned whether the given input obeys the rules. Suppose we are given a terminal symbol NUM. The grammar rules no longer bother whether we are having a value 1 as NUM or whether the value is 100. For the grammar all the numbers are just the terminal symbols NUM. But we may be certainly interested in the value of NUM. Here comes the importance of 'Semantic Values' and 'Semantic Actions'.

Associated with each grammar rule the parser allows us to define certain actions. For the above example,

A -> b { printf("We have found a `b'\n"); }

In most cases the actions may not be simple as the above one. Suppose we are implementing a small calculator, the semantic action may be to perform an addition operation.

The terminals and nonterminals present in the grammar can have an associated value. The value is extracted using the symbol '$n' where n is an integer. A rule can have a semantic value. ( Actually it is the value of the nonterminal represented by that rule). It is defined by using the symbol '$$'.

For example,


exp: exp '+' exp        {$$ = $1 + $3;}
which stands for exp -> exp '+' exp. The contents of{ } denote the semantic action. The semantic actions are generally made of C statements.

In the above example, consider the right hand side of the production. The first exp is denoted by '$1'. The terminal symbol '+' is represented by '$2' and the last exp is denoted by '$3'. We find here that it is possible for a terminal symbol like '+' to have no associated semantic value. The value associated with the grammar is '$$' which is the sum of the first and third token.

Suppose we are also having a rule,


exp: NUM        {$$ = $1;}

Let the given input be '1 + 2'. Then the tokens 1 and 2 will match the NUM. The semantic value of the rule exp: exp '+' exp would be 3 due to the corresponding semantic action.

Bison Grammar File

The general form of a bison parser file is


%{
C DECLARATIONS
%}

BISON DECLARATIONS

%%
GRAMMAR RULES
%%

ADDITIONAL C CODE

The C declarations generally contain the #include's and other declarations. The bison declarations handle the terminals and nonterminals. The productions explained in the above section form the Grammar rules. Additional C code contains the rest of the programs used (if needed).

The ideas will be clearer with an example. Consider a small grammar capable of taking lines of expressions and returning their values.

The lexical file, lex.l is given. No explanations are given for the file. In case of any doubt refer the Flex section.


%{
#include"parse.tab.h"
#include<stdio.h>
%}
%%
[0-9]+                  {yylval=atoi(yytext);return NUM;}
"+"                     {return '+';}
"*"                     {return '*';}
"-"                     {return '-';}
"\n"                    {return '\n';}
"/"                     {return '/';}
%%

The parser file, parse.y is also given.


%{
#include<stdio.h>
%}

%token NUM
%left '+' '-'
%left '*' '/'

%start line 

%%

line:   
       /* empty */ 
     |line exp '\n' {printf("%d\n",$2);}
     | error '\n';

exp:      exp '+' exp {$$ = $1 + $3;}
        | exp '*' exp {$$ = $1 * $3;}
        | exp '-' exp {$$ = $1 - $3;}
        | exp '/' exp { if ($3 == 0)
                                $$ = 0;
                        else
                                $$ = $1/$3;}
        | NUM          {$$ = $1;};
%%

yyerror()
{
        printf("Error detected in parsing\n");
}

main()
{
        yyparse();
}

Let us explore the program line by line. Also let us look how the program works with the lexical file.

The C declaration part is simple. Here we are using only stdio.h. If required other header files can also be included. The second part of the bison file consists of the bison declarations. Every terminals that are used in the file have to be declared here. Implicit terminals such as a character literal needn't be mentioned. Here we are only dealing with a single terminal called NUM. Others are character literals such as '\n', '+' etc.

%token NUM 

completes the declaration.

In the expression we will be handling a number of operators such as '+', '-', '*' and '/'. The different operators are having different precedence. (For example, '/' will be having more precedence than the '+'. '+' and '-' have the same precedence). Also the operators will be having different associativity. All the operators in our code are left associative. This information is passed to the parser with the following declarations

%left  ->  for left associative.
%right ->  for right associative.

The order in which the declarations are made defines the precedence. Higher the line number, higher will be the precedence. If we are declaring "%left '/'" under "%left '+'", the '/' will have higher precedence. As expected declarations on same line denote equal precedence.

"%start" gives information to the parser about the start symbol. If not defined the first production is taken as the starting one.

Now let us move on to the Grammar rules. The first rule states that a line can be empty. No semantic actions are associated with that. The second rule

line:   line exp '\n' {printf("%d\n",$2); }

is the important one. It says that a line can be an expression followed by a newline. The left recursion used in the rule is just a technique used to parse multiple lines. You can avoid it if you are interested in parsing only a single line. The semantic action associated with the above rule is to print the value of the expression.

The rule - line : error '\n' will be explained later.

The rules for expression are simple. It just suggests that an expression can be an expression followed by any given operator and an expression. The rule exp: NUM provides a way to move out of the recursive rules. The semantic actions are just to perform the various operations.

The last section of the bison file defines the other C declarations. We have included only two functions. The main function just invokes the parser; and yyerror routine prints the error message. The function yyerror is invoked whenever the parser meets a parse error. The rule

line: error '\n'

is included to detect the error and consider the error as just another rule. If we are not including the production, the parser will terminate as soon as it meets an error. The nonterminal 'error' is implicitly declared in the parser and we can use them without any declaration.

Let us now look at the working of the parser and scanner. Suppose we provide the input "1+2". The scanner returns the token NUM whenever it finds a number. Also the value is stored in the global variable 'yylval' of the scanner. The parser checks whether the input is a valid one (according to the rules provided) and if it is, the corresponding actions are performed with the semantic values supplied.

But the problem is that the terminal NUM was declared only in the parser file. It has to be used in the lexical file. The problem is avoided by using the command


bison -d parse.y 

It causes the creation of the file parse.tab.h, which includes all the required declarations. We can include it in the lexer.

Test and understand the working of the scanner and parser. Create the files given above and produce the executable with the following commands

lex lex.l
bison -d parse.y
cc parse.tab.c lex.yy.c -lfl

The above mentioned example is a simple one capable of recognizing only simple lines of expressions. But what we are going to deal is a compiler creation for a small programming language. Although the basic ideas are same, we have to acquire more understanding about the parser to work with a programming language. Keeping this in mind let us look at another example.

We create a new language with the following constructs - variable declarations, assignments and print statements. The lexical file is more or less same as the old one. But the parser file is different. The two files are given - lex.l and parse.y.

lex.l

%{
#include"parse.tab.h"
#include<stdio.h>
#include<string.h>
%}
%%

[0-9]+                  {yylval.val=atoi(yytext);return NUM;}
"print"                 {return PRINT;}
"declare"               {return DECL;}
[a-z]([0-9]|[a-z])*     {yylval.str= strdup(yytext);return NAME;}
"+"                     {return '+';}
"*"                     {return '*';}
"-"                     {return '-';}
"\n"                    {return '\n';}
"/"                     {return '/';}
"="                     {return '=';}

%%
parse.y

%{
#include<stdio.h>
#include<string.h>
#include<stdlib.h>

        struct node{
                char *name;
                int value;
        };
        static struct node* sym_table[100];
%}
%union{
        char *str;
        int val;
}

%token <val> NUM
%token <str> NAME
%token PRINT    
%token DECL
%left '+' '-'
%left '*' '/'

%type <val> exp

%start input 

%%
input: /* empty */
        | input line ;

line:   
       exp '\n'          {}
     | DECL NAME '\n'    {return_value($2);}    
     | NAME '=' exp '\n' {assign_value($1,$3);}
     | PRINT NAME '\n'   {printf("%d\n",return_value($2));}
     | error ;

exp:      exp '+' exp {$$ = $1 + $3;}
        | exp '*' exp {$$ = $1 * $3;}
        | exp '-' exp {$$ = $1 - $3;}
        | exp '/' exp { if ($3 == 0)
                                $$ = 0;
                        else
                                $$ = $1/$3;}
        | NUM         {$$ = $1;}
        | NAME        {$$ = return_value($1);}; 
%%

yyerror()
{
        printf("Error detected in parsing\n");
}

int assign_value(char *s,int symvalue)
{
        char *symname;
        int len,i;
        len=strlen(s) + 1;
        symname=malloc(sizeof(char *) * len);
        strcpy(symname,s);
        for(i=0;sym_table[i];i++)
                if(!strcmp(symname,sym_table[i]->name)){
                        sym_table[i]->value=symvalue;
                        return symvalue;
                }
        sym_table[i]=malloc(sizeof(struct node));
        sym_table[i]->name=symname;
        sym_table[i]->value=symvalue;
        return symvalue;
}

int return_value(char *s)
{
        char *symname;
        int len,i;
        len=strlen(s) + 1;
        symname=malloc(sizeof(char *) * len);
        strcpy(symname,s);
        for(i=0;sym_table[i];i++)
                if(!strcmp(symname,sym_table[i]->name))
                        return sym_table[i]->value;
        sym_table[i]=malloc(sizeof(struct node));
        sym_table[i]->name=symname;
        sym_table[i]->value=0;
        return 0;
}

main()
{
        yyparse();
}
        

In the parser file we find a new declaration %union. It is used to define the entire list of possible types. In the first example we had to work with only integers. But here the values can have more than one type. This information is passed through %union declaration. Since more than one type exists, the type information has to be specified for all the terminals and nonterminals whose semantic values are used in the grammar rules. It is shown in angle brackets. In the example we are making use of semantic values of NAME and NUM but not of PRINT and DECL. Similar changes are also made in the lexical file for 'yylval'.

%type <val> exp

is used to define the nonterminal and to specify the type.

The rest of the file is easy to understand. Whenever we see a new identifier we insert it into the symbol table. For new identifiers the initial value is made to be zero. Assignment statements cause the specified value to be stored in the symbol table. Two functions - assign_value and return_value are used for the symbol table manipulations.


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