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Sun, 20 Dec 2015

Top-down parsing is guessing

Top-down parsing is guessing. Literally. Bottom-up parsing is looking.

The way you'll often hear that phrased is that top-down parsing is looking, starting at the top, and bottom-up parsing is looking, starting at the bottom. But that is misleading, because the input is at the bottom -- at the top there is nothing to look at. A usable top-down parser must have a bottom-up component, even if that component is just lookahead.

A more generous, but still accurate, way to describe the top-down component of parsers is "prediction". And prediction is, indeed, a very useful component of a parser, when used in combination with other techniques.

Of course, if a parser does nothing but predict, it can predict only one input. Top-down parsing must always be combined with a bottom-up component. This bottom-up component may be as modest as lookahead, but it must be there or else top-down parsing is really not parsing at all.

So why is top-down parsing used so much?

Top-down parsing may be unusable in its pure form, but from one point of view that is irrelevant. Top-down parsing's biggest advantage is that it is highly flexible -- there's no reason to stick to its "pure" form.

A top-down parser can be written as a series of subroutine calls -- a technique called recursive descent. Recursive descent allows you to hook in custom-written bottom-up logic at every top-down choice point, and it is a technique which is completely understandable to programmers with little or no training in parsing theory. When dealing with recursive descent parsers, it is more useful to be a seasoned, far-thinking programmer than it is to be a mathematician. This makes recursive descent very appealing to seasoned, far-thinking programmers, and they are the audience that counts.

Switching techniques

You can even use the flexibility of top-down to switch away from top-down parsing. For example, you could claim that a top-down parser could do anything my own parser (Marpa) could do, because a recursive descent parser can call a Marpa parser.

A less dramatic switchoff, and one that still leaves the parser with a good claim to be basically top-down, is very common. Arithmetic expressions are essential for a computer language. But they are also among the many things top-down parsing cannot handle, even with ordinary lookahead. Even so, most computer languages these days are parsed top-down -- by recursive descent. These recursive descent parsers deal with expressions by temporarily handing control over to an bottom-up operator precedence parser. Neither of these parsers is extremely smart about the hand-over and hand-back -- it is up to the programmer to make sure the two play together nicely. But used with caution, this approach works.

Top-down parsing and language-oriented programming

But what about taking top-down methods into the future of language-oriented programming, extensible languages, and grammars which write grammars? Here we are forced to confront the reality -- that the effectiveness of top-down parsing comes entirely from the foreign elements that are added to it. Starting from a basis of top-down parsing is literally starting with nothing. As I have shown in more detail elsewhere, top-down techniques simply do not have enough horsepower to deal with grammar-driven programming.

Perl 6 grammars are top-down -- PEG with lots of extensions. These extensions include backtracking, backtracking control, a new style of tie-breaking and lots of opportunity for the programmer to intervene and customize everything. But behind it all is a top-down parse engine.

One aspect of Perl 6 grammars might be seen as breaking out of the top-down trap. That trick of switching over to a bottom-up operator precedence parser for expressions, which I mentioned above, is built into Perl 6 and semi-automated. (I say semi-automated because making sure the two parsers "play nice" with each other is not automated -- that's still up to the programmer.)

As far as I know, this semi-automation of expression handling is new with Perl 6 grammars, and it may prove handy for duplicating what is done in recursive descent parsers. But it adds no new technique to those already in use. And features like

all of which are available and in current use in Marpa, are impossible for the technology behind Perl 6 grammars.

I am a fan of the Perl 6 effort. Obviously, I have doubts about one specific set of hopes for Perl 6 grammars. But these hopes have not been central to the Perl 6 effort, and I will be an eager student of the Perl 6 team's work over the coming months.


To learn more about Marpa, there's the official web site maintained by Ron Savage. I also have a Marpa web site. Comments on this post can be made in Marpa's Google group, or on our IRC channel: #marpa at freenode.net.

posted at: 15:21 | direct link to this entry

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