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Jeffrey Kegler's blog about Marpa, his new parsing algorithm, and other topics of interest

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The Ocean of Awareness blog: home page, chronological index, and annotated index.

Tue, 23 Aug 2016


Parsing: an expanded timeline

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.

Marpa: an afterword

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.

References, comments, etc.

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: 08:38 | direct link to this entry

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Tue, 22 Mar 2016


Introduction to Marpa Book in progress

What follows is a summary of the features of the Marpa algorithm, followed by a discussion of potential applications. It refers to itself as a "monograph", because it is a draft of part of the introduction to a technical monograph on the Marpa algorithm. I hope the entire monograph will appear in a few weeks.

The Marpa project

The Marpa project was intended to create a practical and highly available tool to generate and use general context-free parsers. Tools of this kind had long existed for LALR and regular expressions. But, despite an encouraging academic literature, no such tool had existed for context-free parsing. The first stable version of Marpa was uploaded to a public archive on Solstice Day 2011. This monograph describes the algorithm used in the most recent version of Marpa, Marpa::R2. It is a simplification of the algorithm presented in my earlier paper.

A proven algorithm

While the presentation in this monograph is theoretical, the approach is practical. The Marpa::R2 implementation has been widely available for some time, and has seen considerable use, including in production environments. Many of the ideas in the parsing literature satisfy theoretical criteria, but in practice turn out to face significant obstacles. An algorithm may be as fast as reported, but may turn out not to allow adequate error reporting. Or a modification may speed up the recognizer, but require additional processing at evaluation time, leaving no advantage to compensate for the additional complexity.

In this monograph, I describe the Marpa algorithm as it was implemented for Marpa::R2. In many cases, I believe there are better approaches than those I have described. But I treat these techniques, however solid their theory, as conjectures. Whenever I mention a technique that was not actually implemented in Marpa::R2, I will always explicitly state that that technique is not in Marpa as implemented.

Features

General context-free parsing

As implemented, Marpa parses all "proper" context-free grammars. The proper context-free grammars are those which are free of cycles, unproductive symbols, and inaccessible symbols. Worst case time bounds are never worse than those of Earley's algorithm, and therefore never worse than O(n**3).

Linear time for practical grammars

Currently, the grammars suitable for practical use are thought to be a subset of the deterministic context-free grammars. Using a technique discovered by Joop Leo, Marpa parses all of these in linear time. Leo's modification of Earley's algorithm is O(n) for LR-regular grammars. Leo's modification also parses many ambiguous grammars in linear time.

Left-eidetic

The original Earley algorithm kept full information about the parse --- including partial and fully recognized rule instances --- in its tables. At every parse location, before any symbols are scanned, Marpa's parse engine makes available its information about the state of the parse so far. This information is in useful form, and can be accessed efficiently.

Recoverable from read errors

When Marpa reads a token which it cannot accept, the error is fully recoverable. An application can try to read another token. The application can do this repeatedly as long as none of the tokens are accepted. Once the application provides a token that is accepted by the parser, parsing will continue as if the unsuccessful read attempts had never been made.

Ambiguous tokens

Marpa allows ambiguous tokens. These are often useful in natural language processing where, for example, the same word might be a verb or a noun. Use of ambiguous tokens can be combined with recovery from rejected tokens so that, for example, an application could react to the rejection of a token by reading two others.

Using the features

Error reporting

An obvious application of left-eideticism is error reporting. Marpa's abilities in this respect are ground-breaking. For example, users typically regard an ambiguity as an error in the grammar. Marpa, as currently implemented, can detect an ambiguity and report specifically where it occurred and what the alternatives were.

Event driven parsing

As implemented, Marpa::R2 allows the user to define "events". Events can be defined that trigger when a specified rule is complete, when a specified rule is predicted, when a specified symbol is nulled, when a user-specified lexeme has been scanned, or when a user-specified lexeme is about to be scanned. A mid-rule event can be defined by adding a nulling symbol at the desired point in the rule, and defining an event which triggers when the symbol is nulled.

Ruby slippers parsing

Left-eideticism, efficient error recovery, and the event mechanism can be combined to allow the application to change the input in response to feedback from the parser. In traditional parser practice, error detection is an act of desperation. In contrast, Marpa's error detection is so painless that it can be used as the foundation of new parsing techniques.

For example, if a token is rejected, the lexer is free to create a new token in the light of the parser's expectations. This approach can be seen as making the parser's "wishes" come true, and I have called it "Ruby Slippers Parsing".

One use of the Ruby Slippers technique is to parse with a clean but oversimplified grammar, programming the lexical analyzer to make up for the grammar's short-comings on the fly. As part of Marpa::R2, the author has implemented an HTML parser, based on a grammar that assumes that all start and end tags are present. Such an HTML grammar is too simple even to describe perfectly standard-conformant HTML, but the lexical analyzer is programmed to supply start and end tags as requested by the parser. The result is a simple and cleanly designed parser that parses very liberal HTML and accepts all input files, in the worst case treating them as highly defective HTML.

Ambiguity as a language design technique

In current practice, ambiguity is avoided in language design. This is very different from the practice in the languages humans choose when communicating with each other. Human languages exploit ambiguity in order to design highly flexible, powerfully expressive languages. For example, the language of this monograph, English, is notoriously ambiguous.

Ambiguity of course can present a problem. A sentence in an ambiguous language may have undesired meanings. But note that this is not a reason to ban potential ambiguity --- it is only a problem with actual ambiguity.

Syntax errors, for example, are undesired, but nobody tries to design languages to make syntax errors impossible. A language in which every input was well-formed and meaningful would be cumbersome and even dangerous: all typos in such a language would be meaningful, and parser would never warn the user about errors, because there would be no such thing.

With Marpa, ambiguity can be dealt with in the same way that syntax errors are dealt with in current practice. The language can be designed to be ambiguous, but any actual ambiguity can be detected and reported at parse time. This exploits Marpa's ability to report exactly where and what the ambiguity is. Marpa::R2's own parser description language, the SLIF, uses ambiguity in this way.

Auto-generated languages

In 1973, Čulik and Cohen pointed out that the ability to efficiently parse LR-regular languages opens the way to auto-generated languages. In particular, Čulik and Cohen note that a parser which can parse any LR-regular language will be able to parse a language generated using syntax macros.

Second order languages

In the literature, the term "second order language" is usually used to describe languages with features which are useful for second-order programming. True second-order languages --- languages which are auto-generated from other languages --- have not been seen as practical, since there was no guarantee that the auto-generated language could be efficiently parsed.

With Marpa, this barrier is raised. As an example, Marpa::R2's own parser description language, the SLIF, allows "precedenced rules". Precedenced rules are specified in an extended BNF. The BNF extensions allow precedence and associativity to be specified for each RHS.

Marpa::R2's precedenced rules are implemented as a true second order language. The SLIF representation of the precedenced rule is parsed to create a BNF grammar which is equivalent, and which has the desired precedence. Essentially, the SLIF does a standard textbook transformation. The transformation starts with a set of rules, each of which has a precedence and an associativity specified. The result of the transformation is a set of rules in pure BNF. The SLIF's advantage is that it is powered by Marpa, and therefore the SLIF can be certain that the grammar that it auto-generates will parse in linear time.

Notationally, Marpa's precedenced rules are an improvement over similar features in LALR-based parser generators like yacc or bison. In the SLIF, there are two important differences. First, in the SLIF's precedenced rules, precedence is generalized, so that it does not depend on the operators: there is no need to identify operators, much less class them as binary, unary, etc. This more powerful and flexible precedence notation allows the definition of multiple ternary operators, and multiple operators with arity above three.

Second, and more important, a SLIF user is guaranteed to get exactly the language that the precedenced rule specifies. The user of the yacc equivalent must hope their syntax falls within the limits of LALR.

References, comments, etc.

Marpa has a 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: 17:56 | direct link to this entry

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Wed, 09 Mar 2016


What parser do birds use?

"Here we provide, to our knowledge, the first unambiguous experimental evidence for compositional syntax in a non-human vocal system." -- "Experimental evidence for compositional syntax in bird calls", Toshitaka N. Suzuki, David Wheatcroft & Michael Griesser Nature Communications 7, Article number: 10986

In this post I look at a subset of the language of the Japanese great tit, also known as Parus major. The above cited article presents evidence that bird brains can parse this language. What about standard modern computer parsing methods? Here is the subset -- probably a tiny one -- of the language actually used by Parus major.

      S ::= ABC
      S ::= D
      S ::= ABC D
      S ::= D ABC
    

Classifying the Parus major grammar

Grammophone is a very handy new tool for classifying grammars. Its own parser is somewhat limited, so that it requires a period to mark the end of a rule. The above grammar is in Marpa's SLIF format, which is smart enough to use the "::=" operator to spot the beginning and end of rules, just as the human eye does. Here's the same grammar converted into a form acceptable to Grammophone:

      S -> ABC .
      S -> D .
      S -> ABC D .
      S -> D ABC .
    

Grammophone tells us that the Parus major grammar is not LL(1), but that it is LALR(1).

What does this mean?

LL(1) is the class of grammar parseable by top-down methods: it's the best class for characterizing most parsers in current use, including recursive descent, PEG, and Perl 6 grammars. All of these parsers fall short of dealing with the Parus major language.

LALR(1) is probably most well-known from its implementations in bison and yacc. While able to handle this subset of Parus's language, LALR(1) has its own, very strict, limits. Whether LALR(1) could handle the full complexity of Parus language is a serious question. But it's a question that in practice would probably not arise. LALR(1) has horrible error handling properties.

When the input is correct and within its limits, an LALR-driven parser is fast and works well. But if the input is not perfectly correct, LALR parsers produce no useful analysis of what went wrong. If Parus hears "d abc d", a parser like Marpa, on the other hand, can produce something like this:

# * String before error: abc d\s
# * The error was at line 1, column 7, and at character 0x0064 'd', ...
# * here: d
    

Parus uses its language in predatory contexts, and one can assume that a Parus with a preference for parsers whose error handling is on an LALR(1) level will not be keeping its alleles in the gene pool for very long.

References, comments, etc.

Those readers content with sub-Parus parsing methods may stop reading here. Those with greater parsing ambitions, however, may wish to learn more about Marpa. A Marpa test script for parsing the Parus subset is in a Github gist. Marpa has a 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: 19:13 | direct link to this entry

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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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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.

Comments

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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