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Wed, 06 Jan 2016


What are the reasonable computer languages?

"You see things; and you say 'Why?' But I dream things that never were; and I say 'Why not?'" -- George Bernard Shaw

In the 1960's and 1970's computer languages were evolving rapidly. It was not clear which way they were headed. Would most programming be done with general-purpose languages? Or would programmers create a language for every task domain? Or even for every project? And, if lots of languages were going to be created, what kinds of languages would be needed?

It was in that context that Čulik and Cohen, in a 1973 paper, outlined what they thought programmers would want and should have. In keeping with the spirit of the time, it was quite a lot:

Today, we think we know that Čulik and Cohen's vision was naive, because we think we know that parsing technology cannot support it. We think we know that parsing is much harder than they thought.

The eyeball grammars

As a thought problem, consider the "eyeball" class of grammars. The "eyeball" class of grammars contains all the grammars that a human can parse at a glance. If a grammar is in the eyeball class, but a computer cannot parse it, it presents an interesting choice. Either,

There are some people out there (I am one of them) who don't believe that everything the mind can do reduces to a machine computation. But even those people will tend to go for the choice in this case: There must be some practical computer parsing algorithm which can do at least as well at parsing as a human can do by "eyeball". In other words, the class of "reasonable grammars" should contain the eyeball class.

Čulik and Cohen's candidate for the class of "reasonable grammars" were the grammars that a deterministic parse engine could parse if it had a lookahead that was infinite, but restricted to distinguishing between regular expressions. They called these the LR-regular, or LRR, grammars. And the LRR grammars do in fact seem to be a good first approximation to the eyeball class. They do not allow lookahead that contains things that you have to count, like palindromes. And, while I'd be hard put to eyeball every possible string for every possible regular expression, intuitively the concept of scanning for a regular expression does seem close to capturing the idea of glancing through a text looking for a telltale pattern.

So what happened?

Alas, the algorithm in the Čulik and Cohen paper turned out to be impractical. But in 1991, Joop Leo discovered a way to adopt Earley's algorithm to parse the LRR grammars in linear time, without doing the lookahead. And Leo's algorithm does have a practical implementation: Marpa.

References, comments, etc.

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: 10:24 | direct link to this entry

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