Lexical analysis

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Lexical analysis is the processing of an input sequence of characters (such as the source code of a computer program) to produce, as output, a sequence of symbols called "lexical tokens", or just "tokens". For example, lexers for many programming languages convert the character sequence 123 abc into two tokens: 123 and abc (whitespace is not a token in most languages). The purpose of producing these tokens is usually to forward them as input to another program, such as a parser.

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[edit] Implementation details

For many languages lexical analysis can only be performed in a single pass (ie, no backtracking) by reading a character at a time from the input. This means it is relatively straightforward to automate the generation of programs to perform it and a number of these have been written (eg, flex). However, most commercial compilers use hand written lexers because it is possible to integrate much better error handling into them.

A lexical analyzer, or lexer for short, can be thought of having two stages, namely a scanner and an evaluator. (These are often integrated, for efficiency reasons, so they operate in parallel.)

The first stage, the scanner, is usually based on a finite state machine. It has encoded within it information on the possible sequences of characters that can be contained within any of the tokens it handles (individual instances of these character sequences are known as lexemes). For instance, an integer token may contain any sequence of numerical digit characters. In many cases the first non-whitespace character can be used to deduce the kind of token that follows, the input characters are then processed one at a time until reaching a character that is not in the set of characters acceptable for that token (this is known as the maximal munch rule). In some languages the lexeme creation rules are more complicated and may involve backtracking over previously read characters.

A lexeme, however, is only a string of characters known to be of a certain kind (eg, a string literal, a sequence of letters). In order to construct a token, the lexical analyzer needs a second stage, the evaluator, which goes over the characters of the lexeme to produce a value. The lexeme's type combined with its value is what properly constitutes a token, which can be given to a parser. (Some tokens such as parentheses do not really have values, and so the evaluator function for these can return nothing. The evaluators for integers, identifiers, and strings can be considerably more complex. Sometimes evaluators can suppress a lexeme entirely, concealing it from the parser, which is useful for whitespace and comments.)

For example, in the source code of a computer program the string

net_worth_future = (assets - liabilities);

might be converted (with whitespace suppressed) into the lexical token stream:

NAME "net_worth_future" 
EQUALS 
OPEN_PARENTHESIS 
NAME "assets" 
MINUS 
NAME "liabilities" 
CLOSE_PARENTHESIS 
SEMICOLON

Though it is possible and sometimes necessary to write a lexer by hand, lexers are often generated by automated tools. These tools generally accept regular expressions that describe the tokens allowed in the input stream. Each regular expression is associated with a production in the lexical grammar of the programming language that evaluates the lexemes matching the regular expression. These tools may generate source code that can be compiled and executed or construct a state table for a finite state machine (which is plugged into template code for compilation and execution).

Regular expressions compactly represent patterns that the characters in lexemes might follow. For example, for an English-based language, a NAME token might be any English alphabetical character or an underscore, followed by any number of instances of any ASCII alphanumeric character or an underscore. This could be represented compactly by the string [a-zA-Z_][a-zA-Z_0-9]*. This means "any character a-z, A-Z or _, followed by 0 or more of a-z, A-Z, _ or 0-9".

Regular expressions and the finite state machines they generate are not powerful enough to handle recursive patterns, such as "n opening parentheses, followed by a statement, followed by n closing parentheses." They are not capable of keeping count, and verifying that n is the same on both sides — unless you have a finite set of permissible values for n. It takes a full-fledged parser to recognize such patterns in their full generality. A parser can push parentheses on a stack and then try to pop them off and see if the stack is empty at the end.

The Lex programming tool and its compiler is designed to generate code for fast lexical analysers based on a formal description of the lexical syntax. It is not generally considered sufficient for applications with a complicated set of lexical rules and severe performance requirements; for instance, the GNU Compiler Collection uses hand-written lexers.

[edit] Example lexical analyzer

This is an example of a scanner (written in the C programming language) for the instructional programming language PL/0.

The symbols recognized are:

'+', '-', '*', '/', '=', '(', ')', ',', ';', '.', ':=', '<', '<=', '<>', '>', '>='

numbers: 0-9 {0-9}
identifiers: a-zA-Z {a-zA-Z0-9}
keywords:

"begin", "call", "const", "do", "end", "if", "odd", "procedure", "then", "var", "while"

External variables used:

  • FILE *source -- the source file
  • int cur_line, cur_col, err_line, err_col -- for error reporting
  • int num -- last number read stored here, for the parser
  • char id[] -- last identifier read stored here, for the parser
  • Hashtab *keywords -- list of keywords

External routines called:

  • error(const char msg[]) -- report an error
  • Hashtab *create_htab(int estimate) -- create a lookup table
  • int enter_htab(Hashtab *ht, char name[], void *data) -- add an entry to a lookup table
  • Entry *find_htab(Hashtab *ht, char *s) -- find an entry in a lookup table
  • void *get_htab_data(Entry *entry) -- returns data from a lookup table
  • FILE *fopen(char fn[], char mode[]) -- opens a file for reading
  • fgetc(FILE *stream) -- read the next character from a stream
  • ungetc(int ch, FILE *stream) -- put-back a character onto a stream
  • isdigit(int ch), isalpha(int ch), isalnum(int ch) -- character classification

External types:

  • Symbol -- an enumerated type of all the symbols in the PL/0 language.
  • Hashtab -- represents a lookup table
  • Entry -- represents an entry in the lookup table

Scanning is started by calling init_scan, passing the name of the source file. If the source file is successfully opened, the parser calls getsym repeatedly to return successive symbols from the source file.

The heart of the scanner, getsym, should be straightforward. First, whitespace is skipped. Then the retrieved character is classified. If the character represents a multiple-character symbol, additional processing must be done. Numbers are converted to internal form, and identifiers are checked to see if they represent a keyword.

int read_ch(void) {
  int ch = fgetc(source);
  cur_col++;
  if (ch == '\n') {
    cur_line++;
    cur_col = 0;
  }
  return ch;
}

void put_back(int ch) {
  ungetc(ch, source);
  cur_col--;
  if (ch == '\n') cur_line--;
}

Symbol getsym(void) {
  int ch;

  while ((ch = read_ch()) != EOF && ch <= ' ')
    ;
  err_line = cur_line;
  err_col  = cur_col;
  switch (ch) {
    case EOF: return eof;
    case '+': return plus;
    case '-': return minus;
    case '*': return times;
    case '/': return slash;
    case '=': return eql;
    case '(': return lparen;
    case ')': return rparen;
    case ',': return comma;
    case ';': return semicolon;
    case '.': return period;
    case ':':
      ch = read_ch();
      return (ch == '=') ? becomes : nul;
    case '<':
      ch = read_ch();
      if (ch == '>') return neq;
      if (ch == '=') return leq;
      put_back(ch);
      return lss;
    case '>':
      ch = read_ch();
      if (ch == '=') return geq;
      put_back(ch);
      return gtr;
    default:
      if (isdigit(ch)) {
        num = 0;
        do {  /* no checking for overflow! */
          num = 10 * num + ch - '0';
          ch = read_ch();
        } while ( ch != EOF && isdigit(ch));
        put_back(ch);
        return number;
      }
      if (isalpha(ch)) {
        Entry *entry;
        id_len = 0;
        do {
          if (id_len < MAX_ID) {
            id[id_len] = (char)ch;
            id_len++;
          }
          ch = read_ch();
        } while ( ch != EOF && isalnum(ch));
        id[id_len] = '\0';
        put_back(ch);
        entry = find_htab(keywords, id);
        return entry ? (Symbol)get_htab_data(entry) : ident;
      }

      error("getsym: invalid character '%c'", ch);
      return nul;
  }
}

int init_scan(const char fn[]) {
  if ((source = fopen(fn, "r")) == NULL) return 0;
  cur_line = 1;
  cur_col = 0;
  keywords = create_htab(11);
  enter_htab(keywords, "begin", beginsym);
  enter_htab(keywords, "call", callsym);
  enter_htab(keywords, "const", constsym);
  enter_htab(keywords, "do", dosym);
  enter_htab(keywords, "end", endsym);
  enter_htab(keywords, "if", ifsym);
  enter_htab(keywords, "odd", oddsym);
  enter_htab(keywords, "procedure", procsym);
  enter_htab(keywords, "then", thensym);
  enter_htab(keywords, "var", varsym);
  enter_htab(keywords, "while", whilesym);
  return 1;
}

Now, contrast the above code with the code needed for a FLEX generated scanner for the same language:


%{
#include "y.tab.h"
%}

digit         [0-9]
letter        [a-zA-Z]

%%
"+"                  { return PLUS;       }
"-"                  { return MINUS;      }
"*"                  { return TIMES;      }
"/"                  { return SLASH;      }
"("                  { return LPAREN;     }
")"                  { return RPAREN;     }
";"                  { return SEMICOLON;  }
","                  { return COMMA;      }
"."                  { return PERIOD;     }
":="                 { return BECOMES;    }
"="                  { return EQL;        }
"<>"                 { return NEQ;        }
"<"                  { return LSS;        }
">"                  { return GTR;        }
"<="                 { return LEQ;        }
">="                 { return GEQ;        }
"begin"              { return BEGINSYM;   }
"call"               { return CALLSYM;    }
"const"              { return CONSTSYM;   }
"do"                 { return DOSYM;      }
"end"                { return ENDSYM;     }
"if"                 { return IFSYM;      }
"odd"                { return ODDSYM;     }
"procedure"          { return PROCSYM;    }
"then"               { return THENSYM;    }
"var"                { return VARSYM;     }
"while"              { return WHILESYM;   }
{letter}({letter}|{digit})* {
                       yylval.id = (char *)strdup(yytext);
                       return IDENT;      }
{digit}+             { yylval.num = atoi(yytext);
                       return NUMBER;     }
[ \t\n\r]            /* skip whitespace */
.                    { printf("Unknown character [%c]\n",yytext[0]);
                       return UNKNOWN;    }
%%

int yywrap(void){return 1;}

About 50 lines of code for FLEX versus about 100 lines of hand-written code.

Generally, scanners are not that hard to write. If done correctly, a hand-written scanner should be faster and offer more flexibility as compared to using a scanner generator. But the simple utility of using a scanner generator should not be discounted, especially in the developmental phase, when a language specification might change daily. In that case, much time may be saved by using a scanner generator.

[edit] See also

[edit] External links

[edit] References

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