Recursive descent parser

In computer science, a recursive descent parser is a kind of top-down parser built from a set of mutually recursive procedures (or a non-recursive equivalent) where each such procedure usually implements one of the productions of the grammar. Thus the structure of the resulting program closely mirrors that of the grammar it recognizes.[1]

A predictive parser is a recursive descent parser that does not require backtracking. Predictive parsing is possible only for the class of LL(k) grammars, which are the context-free grammars for which there exists some positive integer k that allows a recursive descent parser to decide which production to use by examining only the next k tokens of input. The LL(k) grammars therefore exclude all ambiguous grammars, as well as all grammars that contain left recursion. Any context-free grammar can be transformed into an equivalent grammar that has no left recursion, but removal of left recursion does not always yield an LL(k) grammar. A predictive parser runs in linear time.

Recursive descent with backtracking is a technique that determines which production to use by trying each production in turn. Recursive descent with backtracking is not limited to LL(k) grammars, but is not guaranteed to terminate unless the grammar is LL(k). Even when they terminate, parsers that use recursive descent with backtracking may require exponential time.

Although predictive parsers are widely used, and are frequently chosen if writing a parser by hand, programmers often prefer to use a table-based parser produced by a parser generator, either for an LL(k) language or using an alternative parser, such as LALR or LR. This is particularly the case if a grammar is not in LL(k) form, as transforming the grammar to LL to make it suitable for predictive parsing is involved. Predictive parsers can also be automatically generated, using tools like ANTLR.

Predictive parsers can be depicted using transition diagrams for each non-terminal symbol where the edges between the initial and the final states are labelled by the symbols (terminals and non-terminals) of the right side of the production rule.[2]

Example parser

The following EBNF-like grammar (for Niklaus Wirth's PL/0 programming language, from Algorithms + Data Structures = Programs) is in LL(1) form:

 program = block "." .
 
 block =
     ["const" ident "=" number {"," ident "=" number} ";"]
     ["var" ident {"," ident} ";"]
     {"procedure" ident ";" block ";"} statement .
 
 statement =
     ident ":=" expression
     | "call" ident
     | "begin" statement {";" statement } "end"
     | "if" condition "then" statement
     | "while" condition "do" statement .
 
 condition =
     "odd" expression
     | expression ("="|"#"|"<"|"<="|">"|">=") expression .
 
 expression = ["+"|"-"] term {("+"|"-") term} .
 
 term = factor {("*"|"/") factor} .
 
 factor =
     ident
     | number
     | "(" expression ")" .

Terminals are expressed in quotes. Each nonterminal is defined by a rule in the grammar, except for ident and number, which are assumed to be implicitly defined.

C implementation

What follows is an implementation of a recursive descent parser for the above language in C. The parser reads in source code, and exits with an error message if the code fails to parse, exiting silently if the code parses correctly.

Notice how closely the predictive parser below mirrors the grammar above. There is a procedure for each nonterminal in the grammar. Parsing descends in a top-down manner, until the final nonterminal has been processed. The program fragment depends on a global variable, sym, which contains the current symbol from the input, and the function nextsym, which updates sym when called.

The implementations of the functions nextsym and error are omitted for simplicity.

typedef enum {ident, number, lparen, rparen, times, slash, plus,
    minus, eql, neq, lss, leq, gtr, geq, callsym, beginsym, semicolon,
    endsym, ifsym, whilesym, becomes, thensym, dosym, constsym, comma,
    varsym, procsym, period, oddsym} Symbol;

Symbol sym;
void nextsym(void);
void error(const char msg[]);

int accept(Symbol s) {
    if (sym == s) {
        nextsym();
        return 1;
    }
    return 0;
}

int expect(Symbol s) {
    if (accept(s))
        return 1;
    error("expect: unexpected symbol");
    return 0;
}

void factor(void) {
    if (accept(ident)) {
        ;
    } else if (accept(number)) {
        ;
    } else if (accept(lparen)) {
        expression();
        expect(rparen);
    } else {
        error("factor: syntax error");
        nextsym();
    }
}

void term(void) {
    factor();
    while (sym == times || sym == slash) {
        nextsym();
        factor();
    }
}

void expression(void) {
    if (sym == plus || sym == minus)
        nextsym();
    term();
    while (sym == plus || sym == minus) {
        nextsym();
        term();
    }
}

void condition(void) {
    if (accept(oddsym)) {
        expression();
    } else {
        expression();
        if (sym == eql || sym == neq || sym == lss || sym == leq || sym == gtr || sym == geq) {
            nextsym();
            expression();
        } else {
            error("condition: invalid operator");
            nextsym();
        }
    }
}

void statement(void) {
    if (accept(ident)) {
        expect(becomes);
        expression();
    } else if (accept(callsym)) {
        expect(ident);
    } else if (accept(beginsym)) {
        do {
            statement();
        } while (accept(semicolon));
        expect(endsym);
    } else if (accept(ifsym)) {
        condition();
        expect(thensym);
        statement();
    } else if (accept(whilesym)) {
        condition();
        expect(dosym);
        statement();
    } else {
        error("statement: syntax error");
        nextsym();
    }
}

void block(void) {
    if (accept(constsym)) {
        do {
            expect(ident);
            expect(eql);
            expect(number);
        } while (accept(comma));
        expect(semicolon);
    }
    if (accept(varsym)) {
        do {
            expect(ident);
        } while (accept(comma));
        expect(semicolon);
    }
    while (accept(procsym)) {
        expect(ident);
        expect(semicolon);
        block();
        expect(semicolon);
    }
    statement();
}

void program(void) {
    nextsym();
    block();
    expect(period);
}

Pascal implementation

What follows is an implementation of a recursive descent parser for the above language in ModernPascal. The parser reads in source code, and exits with an error message if the code fails to parse, exiting silently if the code parses correctly.

Notice how closely the predictive parser below mirrors the grammar above. There is a procedure for each nonterminal in the grammar. Parsing descends in a top-down manner, until the final nonterminal has been processed. The program fragment depends on a global variable, sym, which contains the current symbol from the input, and the function nextsym, which updates sym when called.

The implementations of the functions nextsym and error are omitted for simplicity.

// Modern Pascal implementation (www.ModernPascal.com)
// C example ported to Pascal by Ozz Nixon

{$S-}

type
   SYMBOL = (ident, number, lparen, rparen, times, slash, plus,
    minus, eql, neq, lss, leq, gtr, geq, callsym, beginsym, semicolon,
    endsym, ifsym, whilesym, becomes, thensym, dosym, constsym, comma,
    varsym, procsym, period, oddsym);

var
   sym:SYMBOL;

procedure expression; forward;

procedure nextsym;
begin
// you implement //
end;

procedure error(const msg:String);
begin
// you implement //
end;

function accept(S:Symbol):boolean;
begin
   if sym=s then begin
      nextsym();
      Result:=True;
   end
   else Result:=False;
end;

function expect(S:Symbol):boolean;
begin
   Result:=accept(s);
   if not result then error('Expect: unexpected symbol');
end;

procedure factor;
begin
   if (accept(ident)) then begin
//
   end
   else if (accept(number)) then begin
//
   end
   else if (accept(lparen)) then begin
      expression();
      expect(rparen);
   end
   else begin
      error('factor: syntax error');
      nextsym();
   end;
end;

procedure term;
begin
   factor();
   while (sym=times) or (sym=slash) do begin
      nextsym();
      factor();
   end;
end;

procedure expression;
begin
   if (sym=plus) or (sym=minus) then nextsym();
   term();
   while (sym=plus) or (sym=minus) do begin
      nextsym();
      term();
   end;
end;

procedure condition;
begin
   if (accept(oddsym)) then begin
      expression();
   end
   else begin
      expression();
      if (sym=eql) or (sym=neq) or (sym=lss) or (sym=leq) or (sym=gtr) or (sym=geq) then begin
         nextsym();
         expression();
      end
      else begin
         error('condition: invalid operator');
         nextsym();
      end;
   end;
end;

procedure statement;
begin
   if (accept(ident)) then begin
      expect(becomes);
      expression();
   end
   else if (accept(callsym)) then begin
      expect(ident);
   end
   else if (accept(beginsym)) then begin
      repeat
         statement();
      until not (accept(semicolon));
      expect(endsym);
   end
   else if (accept(ifsym)) then begin
      condition();
      expect(thensym);
      statement();
   end
   else if (accept(whilesym)) then begin
      condition();
      expect(dosym);
      statement();
   end
   else begin
      error('statement: syntax error');
      nextsym();
   end;
end;

procedure block;
begin
   if (accept(constsym)) then begin
      repeat
         expect(ident);
         expect(eql);
         expect(number);
      until not (accept(comma));
      expect(semicolon);
   end;
   if (accept(varsym)) then begin
      repeat
         expect(ident);
      until not (accept(comma));
      expect(semicolon);
   end;
   while (accept(procsym)) do begin
      expect(ident);
      expect(semicolon);
      block();
      expect(semicolon);
   end;
   statement();
end;

begin
   nextsym();
   block();
   expect(period);
end;

See also

References

  1. ↑ Burge, W.H. (1975). Recursive Programming Techniques. ISBN 0-201-14450-6.
  2. ↑ Aho, Alfred V.; Sethi, Ravi; Ullman, Jeffrey (1986). Compilers: Principles, Techniques and Tools (first ed.). Addison Wesley. p. 183.

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

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