Jeffrey Kegler's blog about Marpa, his new parsing algorithm, and other topics of interest
Marpa resources
The Ocean of Awareness blog: home page, chronological index, and annotated index.
Jeffrey Kegler's blog about Marpa, his new parsing algorithm, and other topics of interest
The Ocean of Awareness blog: home page, chronological index, and annotated index.
The fourth century BCE: In India, Pannini creates a sophisticated description of the Sanskrit language, exact and complete, and including pronunciation. Sanskrit could be recreated using nothing but Pannini's grammar. Pannini's grammar is probably the first formal system of any kind, predating Euclid. Even today, nothing like it exists for any other natural language of comparable size or corpus. Pannini is the object of serious study today. But in the 1940's and 1950's Pannini is almost unknown in the West. His work has no direct effect on the other events in this timeline.
1943: Emil Post defines and studies a formal rewriting system using productions. With this, the process of reinventing Pannini in the West begins.
1948: Claude Shannon publishes the foundation paper of information theory. Andrey Markov's finite state processes are used heavily.
1952: Grace Hopper writes a linker-loader and describes it as a "compiler". She seems to be the first person to use this term for a computer program. Hopper uses the term "compiler" in its original sense: "something or someone that brings other things together".
1954: At IBM, a team under John Backus begins working on the language which will be called FORTRAN. The term "compiler" is still being used in Hopper's looser sense, instead of its modern one. In particular, there is no implication that the output of a "compiler" is ready for execution by a computer. The output of one 1954 "compiler", for example, produces relative addresses, which need to be translated by hand before a machine can execute them.
1955: Noam Chomsky is awarded a Ph.D. in linguistics and accepts a teaching post at MIT. MIT does not have a linguistics department and Chomsky, in his linguistics course, is free to teach his own approach, highly original and very mathematical.
1956: Chomsky publishes the paper which is usually considered the foundation of Western formal language theory. The paper advocates a natural language approach that involves
These layers resemble, and will inspire, the lexical, syntactic and AST transformation phases of modern parsers. For finite state processes, Chomsky acknowledges Markov. The other layers seem to be Chomsky's own formulations -- Chomsky does not cite Post's work.
1957: Steven Kleene discovers regular expressions, a very handy notation for Markov's processes. Regular expressions turn out to describe exactly the mathematical objects being studied as finite state automata, as well as some of the objects being studied as neural nets.
1957: Noam Chomsky publishes Syntactic Structures, one of the most influential books of all time. The orthodoxy in 1957 is structural linguistics which argues, with Sherlock Holmes, that "it is a capital mistake to theorize in advance of the facts". Structuralists start with the utterances in a language, and build upward.
But Chomsky claims that without a theory there are no facts: there is only noise. The Chomskyan approach is to start with a grammar, and use the corpus of the language to check its accuracy. Chomsky's approach will soon come to dominate linguistics.
1957: Backus's team makes the first FORTRAN compiler available to IBM customers. FORTRAN is the first high-level language that will find widespread implementation. As of this writing, it is the oldest language that survives in practical use. FORTRAN is a line-by-line language and its parsing is primitive.
1958: John McCarthy's LISP appears. LISP goes beyond the line-by-line syntax -- it is recursively structured. But the LISP interpreter does not find the recursive structure: the programmer must explicitly indicate the structure herself, using parentheses.
1959: Backus invents a new notation to describe the IAL language (aka ALGOL). Backus's notation is influenced by his study of Post -- he seems not to have read Chomsky until later.
1960: Peter Naur improves the Backus notation and uses it to describe ALGOL 60. The improved notation will become known as Backus-Naur Form (BNF).
1960: The ALGOL 60 report specifies, for the first time, a block structured language. ALGOL 60 is recursively structured but the structure is implicit -- newlines are not semantically significant, and parentheses indicate syntax only in a few specific cases. The ALGOL compiler will have to find the structure. It is a case of 1960's optimism at its best. As the ALGOL committee is well aware, a parsing algorithm capable of handling ALGOL 60 does not yet exist. But the risk they are taking will soon pay off.
1960: A.E. Gleenie publishes his description of a compiler-compiler. Glennie's "universal compiler" is more of a methodology than an implementation -- the compilers must be written by hand. Glennie credits both Chomsky and Backus, and observes that the two notations are "related". He also mentions Post's productions. Glennie may have been the first to use BNF as a description of a procedure instead of as the description of a Chomsky grammar. Glennie points out that the distinction is "important".
Chomskyan BNF and procedural BNF: BNF, when used as a Chomsky grammar, describes a set of strings, and does not describe how to parse strings according to the grammar. BNF notation, if used to describe a procedure, is a set of instructions, to be tried in some order, and used to process a string. Procedural BNF describes a procedure first, and a language only indirectly.
Both procedural and Chomskyan BNF describe languages, but usually not the same language. That is,
The pre-Chomskyan approach, using procedural BNF, is far more natural to someone trained as a computer programmer. The parsing problem appears to the programmer in the form of strings to be parsed, exactly the starting point of procedural BNF and pre-Chomsky parsing.
Even when the Chomskyan approach is pointed out, it does not at first seem very attractive. With the pre-Chomskyan approach, the examples of the language more or less naturally lead to a parser. In the Chomskyan approach the programmer has to search for an algorithm to parse strings according to his grammar -- and the search for good algorithms to parse Chomskyan grammars has proved surprisingly long and difficult. Handling semantics is more natural with a Chomksyan approach. But, using captures, semantics can be added to a pre-Chomskyan parser and, with practice, this seems natural enough.
Despite the naturalness of the pre-Chomskyan approach to parsing, we will find that the first fully-described automated parsers are Chomskyan. This is a testimony to Chomsky's influence at the time. We will also see that Chomskyan parsers have been dominant ever since.
1961: In January, Ned Irons publishes a paper describing his ALGOL 60 parser. It is the first paper to fully describe any parser. The Irons algorithm is Chomskyan and top-down with a "left corner" element. The Irons algorithm is general, meaning that it can parse anything written in BNF. It is syntax-driven (aka declarative), meaning that the parser is actually created from the BNF -- the parser does not need to be hand-written.
1961: Peter Lucas publishes the first description of a purely top-down parser. This can be considered to be recursive descent, though in Lucas's paper the algorithm has a syntax-driven implementation, useable only for a restricted class of grammars. Today we think of recursive descent as a methodology for writing parsers by hand. Hand-coded approaches became more popular in the 1960's due to three factors:
1963: L. Schmidt, Howard Metcalf, and Val Schorre present papers on syntax-directed compilers at a Denver conference.
1964: Schorre publishes a paper on the Meta II "compiler writing language", summarizing the papers of the 1963 conference. Schorre cites both Backus and Chomsky as sources for Meta II's notation. Schorre notes that his parser is "entirely different" from that of Irons 1961 -- in fact it is pre-Chomskyan. Meta II is a template, rather than something that readers can use, but in principle it can be turned into a fully automated compiler-compiler.
1965: Don Knuth invents LR parsing. The LR algorithm is deterministic, Chomskyan and bottom-up, but it is not thought to be practical. Knuth is primarily interested in the mathematics.
1968: Jay Earley invents the algorithm named after him. Like the Irons algorithm, Earley's algorithm is Chomskyan, syntax-driven and fully general. Unlike the Irons algorithm, it does not backtrack. Earley's algorithm is both top-down and bottom-up at once -- it uses dynamic programming and keeps track of the parse in tables. Earley's approach makes a lot of sense and looks very promising indeed, but there are three serious issues:
1969: Frank DeRemer describes a new variant of Knuth's LR parsing. DeRemer's LALR algorithm requires only a stack and a state table of quite manageable size. LALR looks practical.
1969: Ken Thompson writes the "ed" editor as one of the first components of UNIX. At this point, regular expressions are an esoteric mathematical formalism. Through the "ed" editor and its descendants, regular expressions will become an everyday part of the working programmer's toolkit.
Recognizers: In comparing algorithms, it can be important to keep in mind whether they are recognizers or parsers. A recognizer is a program which takes a string and produces a "yes" or "no" according to whether a string is in part of a language. Regular expressions are typically used as recognizers. A parser is a program which takes a string and produces a tree reflecting its structure according to a grammar. The algorithm for a compiler clearly must be a parser, not a recognizer. Recognizers can be, to some extent, used as parsers by introducing captures.
1972: Alfred Aho and Jeffrey Ullman publish a two volume textbook summarizing the theory of parsing. This book is still important. It is also distressingly up-to-date -- progress in parsing theory slowed dramatically after 1972. Aho and Ullman describe a straightforward fix to the zero-length rule bug in Earley's original algorithm. Unfortunately, this fix involves adding even more bookkeeping to Earley's.
1972: Under the names TDPL and GTDPL, Aho and Ullman investigate the non-Chomksyan parsers in the Schorre lineage. They note that "it can be quite difficult to determine what language is defined by a TDPL parser". That is, GTDPL parsers do whatever they do, and that whatever is something the programmer in general will not be able to describe. The best a programmer can usually do is to create a test suite and fiddle with the GTDPL description until it passes. Correctness cannot be established in any stronger sense. GTDPL is an extreme form of the old joke that "the code is the documentation" -- with GTDPL nothing documents the language of the parser, not even the code.
GTDPL's obscurity buys nothing in the way of additional parsing power. Like all non-Chomskyan parsers, GTDPL is basically a extremely powerful recognizer. Pressed into service as a parser, it is comparatively weak. As a parser, GTDPL is essentially equivalent to Lucas's 1961 syntax-driven algorithm, which was in turn a restricted form of recursive descent.
At or around this time, rumor has it that the main line of development for GTDPL parsers is classified secret by the US government. GTDPL parsers have the property that even small changes in GTDPL parsers can be very labor-intensive. For some government contractors, GTDPL parsing provides steady work for years to come. Public interest in GTDPL fades.
1975: Bell Labs converts its C compiler from hand-written recursive descent to DeRemer's LALR algorithm.
1977: The first "Dragon book" comes out. This soon-to-be classic textbook is nicknamed after the drawing on the front cover, in which a knight takes on a dragon. Emblazoned on the knight's lance are the letters "LALR". From here on out, to speak lightly of LALR will be to besmirch the escutcheon of parsing theory.
1979: Bell Laboratories releases Version 7 UNIX. V7 includes what is, by far, the most comprehensive, useable and easily available compiler writing toolkit yet developed.
1979: Part of the V7 toolkit is Yet Another Compiler Compiler (YACC). YACC is LALR-powered. Despite its name, YACC is the first compiler-compiler in the modern sense. For some useful languages, the process of going from Chomskyan specification to executable is fully automated. Most practical languages, including the C language and YACC's own input language, still require manual hackery. Nonetheless, after two decades of research, it seems that the parsing problem is solved.
1987: Larry Wall introduces Perl 1. Perl embraces complexity like no previous language. Larry uses YACC and LALR very aggressively -- to my knowledge more aggressively than anyone before or since.
1991: Joop Leo discovers a way of speeding up right recursions in Earley's algorithm. Leo's algorithm is linear for just about every unambiguous grammar of practical interest, and many ambiguous ones as well. In 1991 hardware is six orders of magnitude faster than 1968 hardware, so that the issue of bookkeeping overhead had receded in importance. This is a major discovery. When it comes to speed, the game has changed in favor of the Earley algorithm.
But Earley parsing is almost forgotten. Twenty years will pass before anyone writes a practical implementation of Leo's algorithm.
1990's: Earley's is forgotten. So everyone in LALR-land is content, right? Wrong. Far from it, in fact. Users of LALR are making unpleasant discoveries. While LALR automatically generates their parsers, debugging them is so hard they could just as easily write the parser by hand. Once debugged, their LALR parsers are fast for correct inputs. But almost all they tell the users about incorrect inputs is that they are incorrect. In Larry's words, LALR is "fast but stupid".
2000: Larry Wall decides on a radical reimplementation of Perl -- Perl 6. Larry does not even consider using LALR again.
2002: John Aycock and R. Nigel Horspool publish their attempt at a fast, practical Earley's parser. Missing from it is Joop Leo's improvement -- they seem not to be aware of it. Their own speedup is limited in what it achieves and the complications it introduces can be counter-productive at evaluation time. But buried in their paper is a solution to the zero-length rule bug. And this time the solution requires no additional bookkeeping.
2004: Bryan Ford publishes his paper on PEG. Implementers by now are avoiding YACC, and it seems as if there might soon be no syntax-driven algorithms in practical use. Ford fills this gap by repackaging the nearly-forgotten GTDPL. Ford adds packratting, so that PEG is always linear, and provides PEG with an attractive new syntax. But nothing has been done to change the problematic behaviors of GTDPL.
2006: GNU announces that the GCC compiler's parser has been rewritten. For three decades, the industry's flagship C compilers have used LALR as their parser -- proof of the claim that LALR and serious parsing are equivalent. Now, GNU replaces LALR with the technology that it replaced a quarter century earlier: recursive descent.
Today: After five decades of parsing theory, the state of the art seems to be back where it started. We can imagine someone taking Ned Iron's original 1961 algorithm from the first paper ever published describing a parser, and republishing it today. True, he would have to translate its code from the mix of assembler and ALGOL into something more fashionable, say Haskell. But with that change, it might look like a breath of fresh air.
The recollections of my teachers cover most of this timeline. My own begin around 1970. Very early on, as a graduate student, I became unhappy with the way the field was developing. Earley's algorithm looked interesting, and it was something I returned to on and off.
The original vision of the 1960's was a parser that was
By 2010 this vision seemed to have gone the same way as many other 1960's dreams. The rhetoric stayed upbeat, but parsing practice had become a series of increasingly desperate compromises.
But, while nobody was looking for them, the solutions to the problems encountered in the 1960's had appeared in the literature. Aycock and Horspool had solved the zero-length rule bug. Joop Leo had found the speedup for right recursion. And the issue of bookkeeping overhead had pretty much evaporated on its own. Machine operations are now a billion times faster than in 1968, and are probably no longer relevant in any case -- cache misses are now the bottleneck.
The programmers of the 1960's would have been prepared to trust a fully declarative Chomskyan parser. With the experience with LALR in their collective consciousness, modern programmers might be more guarded. As Lincoln said, "Once a cat's been burned, he won't even sit on a cold stove." But I found it straightforward to rearrange the Earley parse engine to allow efficient event-driven handovers between procedural and syntax-driven logic. And Earley tables provide the procedural logic with full knowledge of the state of the parse so far, so that Earley's algorithm is a better platform for hand-written procedural logic than recursive descent.
My implementation of Earley's algorithm is called Marpa. For more about Marpa, there is the semi-official web site, maintained by Ron Savage. The official, but more limited, Marpa website is my personal one. Comments on this post can be made in Marpa's Google group, or on our IRC channel: #marpa at freenode.net.
posted at: 11:38 | direct link to this entry