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Parsing ambiguous grammars (part 1)

March 4th, 2009

Parsing a language is often much harder than people think, perhaps because they have only seen examples that use a simple language that has been designed to make explanation easy. Most languages in everyday use contain a variety of constructs that make the life of a parser writer difficult. Yes, there are parser generators, tools like bison, that automate the process of turning a grammar into a parser and a language’s grammar is often found in the back of its reference manual. However, these grammars are often written to make the life of the programmer easier, not the life of the parse writer.

People may have spotted technical term like LL(1), LR(1) and LALR(1); what they all have in common is a 1 in brackets, because they all operate by looking one token ahead in the input stream. There is a big advantage to limiting the lookahead to one token, the generated tables are much smaller (back in the days when these tools were first created 64K was considered to be an awful lot of memory and today simple programs in embedded processors, with limited memory, often use simple grammars to parse communication’s traffic). Most existing parser generators operate within this limit and rely on compiler writers to sweat over, and contort, grammars to make them fit.

A simple example is provided by PL/1 (most real life examples tend to be more complicated) which did not have keywords, or to be exact did not restrict the spelling of identifiers that could be used to denote a variable, label or procedure. This meant that in the following code:

IF x THEN y = z; ELSE = w;

when the ELSE was encountered the compiler did not know whether it was the start of the alternative arm of the previously seen if-statement or an assignment statement. The token appearing after the ELSE needed to be examined to settle the question.

In days gone-by the person responsible for parsing PL/1 would have gotten up to some jiggery-pokery, such as having the lexer spot that an ELSE had been encountered and process the next token before reporting back what it had found to the syntax analysis.

A few years ago bison was upgraded to support GLR parsing. Rather than lookahead at more tokens a GLR parser detects that there is more than one way to parse the current input and promptly starts parsing each possibility (it is usually implemented by making copies of the appropriate data structures and updating each copy according to the particular parse being followed). The hope is that eventually all but one of these multiple parsers will reach a point where they cannot successfully parse the input tokens and can be killed off, leaving the one true parse (the case where multiple parses continue to exist was discussed a while ago; actually in another context).

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  1. March 24th, 2009 at 10:05 | #1
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