History of the Marpa algorithm
- Jay Earley invents the algorithm that now bears his name.
- Joop Leo describes a way to modify Earley's algorithm so that it runs in O(n) time for all LR-regular grammars. LR-regular is a vast class of grammars, including all the LR(k) grammars, all grammars parseable with recursive descent, and regular expressions. LR-regular can safely be thought of as including all grammars in practical use today, and then some.
- Aycock and Horspool describe a way to do LR(0) precomputation for Earley's algorithm. Their method makes Earley's faster in most practical situations, but not all. In particular, right-recursion remains quadratic in the Aycock and Horspool algorithm. Worst case is no better than Earley's. Leo is unaware of Aycock and Horspool's work and Aycock and Horspool seem unaware of Leo.
- Marpa combines the Leo and Aycock-Horspool algorithms, in the process making significant changes to both of them. The result preserves the best features of both. Marpa also tackles the many remaining implementation issues.
Aho and Ullman 1972The Theory of Parsing, Translation and Compiling, Volume I: Parsing by Alfred Aho and Jeffrey Ullman (Prentice-Hall: Englewood Cliffs, New Jersey, 1972). I think this was the standard source for Earley's algorithm for decades. It certainly was my standard source. The account of Earley's algorithm is on pages 320-330.
Aycock and Horspool 2002Marpa is based on ideas from John Aycock and R. Nigel Horspool's ``Practical Earley Parsing'', The Computer Journal, Vol. 45, No. 6, 2002, pp. 620-630. The idea of doing LR(0) precomputation for Earley's general parsing algorithm, and Marpa's approach to handling nullable symbols and rules, both came from this article.
The Aycock and Horspool paper summarizes Earley's very nicely and is available on the web: <http://www.cs.uvic.ca/~nigelh/Publications/PracticalEarleyParsing.pdf>. Unlike ``Earley 1970'', Aycock and Horspool 2002 is not easy reading. I have been following this particular topic on and off for years and nonetheless found this paper very heavy going.
Dominus 2005Although my approach to parsing is not influenced by Mark Jason Dominus's Higher Order Perl, Mark's treatment of parsing is an excellent introduction to parsing, especially in a Perl context. His focus on just about every other technique except general BNF parsing is pretty much standard, and will help a beginner understand how unconventional Marpa's approach is.
Mark's book opened my eyes to many new ideas. Both Mark's Perl and his English are examples of good writing, and the book is dense with insights. Mark's discussion on memoization in Chapter 3 is the best I've seen. I wish I'd bought his book earlier in my coding.
Mark's book is available on-line. You can download chapter-by-chapter or the whole thing at once, and you can take your pick of his original sources or PDF, at <http://hop.perl.plover.com/book/>. A PDF of the parsing chapter is at <http://hop.perl.plover.com/book/pdf/08Parsing.pdf>.
Earley 1970Of Jay Earley's papers on his general parsing algorithm, the most readily available is ``An efficient context-free parsing algorithm'', Communications of the Association for Computing Machinery, 13:2:94-102, 1970.
Ordinarily, I'd not bother pointing out 35-year old nits in a brilliant and historically important article. But more than a few people treat this article as not just the first word in Earley parsing, but the last as well. Many implementations of Earley's algorithm come, directly and unaltered, from his paper. These implementers and their users need to be aware of two issues.
First, the recognition engine itself, as described, has a serious bug. There's an easy fix, but one that greatly slows down an algorithm whose main problem, in its original form, was speed. This issue is well laid out by Aycock and Horspool in their article.
Second, according to Tomita there is a mistake in the parse tree representation. See page 153 of ``Grune and Jacobs 1990'', page 210 of ``Grune and Jacobs 2008'', and the bibliography entry for Earley 1970 in ``Grune and Jacobs 2008''. In the printed edition of the 2008 bibliography, the entry is on page 578, and on the web (<ftp://ftp.cs.vu.nl/pub/dick/PTAPG_2nd_Edition/CompleteList.pdf>), it's on pp. 583-584. My methods for producing parse results from Earley sets do not come from Earley 1970, so I am taking Tomita's word on this one.
Grune and Jacobs 1990Parsing Techniques: A Practical Guide, by Dick Grune and Ceriel Jacobs, (Ellis Horwood Limited: Chichester, West Sussex, England, 1990). This book is available on the Web: <http://www.cs.vu.nl/~dick/PTAPG.html>
Grune and Jacobs 2008Parsing Techniques: A Practical Guide, by Dick Grune and Ceriel Jacobs, 2nd Edition. (Springer: New York NY, 2008). This is the most authoritative and comprehensive introduction to parsing I know of. In theory it requires no mathematics, only a programming background, but even so it is moderately difficult reading.
This is ``Grune and Jacobs 1990'' updated. The bibliography for this book is available in enlarged form on the web: <ftp://ftp.cs.vu.nl/pub/dick/PTAPG_2nd_Edition/CompleteList.pdf>.
Kegler 2013My writeup of the theory behind Marpa, with proofs of correctness and of my complexity claims is available online: <https://docs.google.com/file/d/0B9_mR_M2zOc4Ni1zSW5IYzk3TGc/edit?usp=sharing>.
Leo 1991Marpa's handling of right-recursion uses the ideas in Joop M.I.M. Leo's ``A General Context-Free Parsing Algorithm Running in Linear Time on Every LR(k) Grammar Without Using Lookahead'', Theoretical Computer Science, Vol. 82, No. 1, 1991, pp 165-176. This is a difficult paper. Unfortunately, there is no copy of it on-line.
WikipediaWikipedia's article on Backus-Naur form is <http://en.wikipedia.org/wiki/Backus-Naur_form>. It's a great place to start if you don't know the basics of grammars and parsing. As Wikipedia points out, BNF might better be called Panini-Backus Form. The grammarian Panini gave a precise description of Sanskrit more than 23 centuries earlier in India using a similar notation.
Copyright and License
Copyright 2014 Jeffrey Kegler This file is part of Marpa::R2. Marpa::R2 is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. Marpa::R2 is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with Marpa::R2. If not, see http://www.gnu.org/licenses/.
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