I've recently being trying to teach myself how parsers (for languages/context-free grammars) work, and most of it seems to be making sense, except for one thing. I'm focusing my attention in particular on LL(k) grammars, for which the two main algorithms seem to be the LL parser (using stack/parse table) and the Recursive Descent parser (simply using recursion).
As far as I can see, the recursive descent algorithm works on all LL(k) grammars and possibly more, whereas an LL parser works on all LL(k) grammars. A recursive descent parser is clearly much simpler than an LL parser to implement, however (just as an LL one is simpler than an LR one).
So my question is, what are the advantages/problems one might encounter when using either of the algorithms? Why might one ever pick LL over recursive descent, given that it works on the same set of grammars and is trickier to implement?
LL is usually a more efficient parsing technique than recursive-descent. In fact, a naive recursive-descent parser will actually be O(k^n) (where n is the input size) in the worst case. Some techniques such as memoization (which yields a Packrat parser) can improve this as well as extend the class of grammars accepted by the parser, but there is always a space tradeoff. LL parsers are (to my knowledge) always linear time.
On the flip side, you are correct in your intuition that recursive-descent parsers can handle a greater class of grammars than LL. Recursive-descent can handle any grammar which is LL(*) (that is, unlimited lookahead) as well as a small set of ambiguous grammars. This is because recursive-descent is actually a directly-encoded implementation of PEGs, or Parser Expression Grammar(s). Specifically, the disjunctive operator (a | b) is not commutative, meaning that a | b does not equal b | a. A recursive-descent parser will try each alternative in order. So if a matches the input, it will succeed even if b would have matched the input. This allows classic "longest match" ambiguities like the dangling else problem to be handled simply by ordering disjunctions correctly.
With all of that said, it is possible to implement an LL(k) parser using recursive-descent so that it runs in linear time. This is done by essentially inlining the predict sets so that each parse routine determines the appropriate production for a given input in constant time. Unfortunately, such a technique eliminates an entire class of grammars from being handled. Once we get into predictive parsing, problems like dangling else are no longer solvable with such ease.
As for why LL would be chosen over recursive-descent, it's mainly a question of efficiency and maintainability. Recursive-descent parsers are markedly easier to implement, but they're usually harder to maintain since the grammar they represent does not exist in any declarative form. Most non-trivial parser use-cases employ a parser generator such as ANTLR or Bison. With such tools, it really doesn't matter if the algorithm is directly-encoded recursive-descent or table-driven LL(k).
As a matter of interest, it is also worth looking into recursive-ascent, which is a parsing algorithm directly encoded after the fashion of recursive-descent, but capable of handling any LALR grammar. I would also dig into parser combinators, which are a functional way of composing recursive-descent parsers together.
Related
Is there an online algorithm which converts certain grammar to the most efficient parser possible?
For example: SLR/LR(k) such as k>=0
For the class of grammars you are discussing (xLR(k)), they are all linear time anyway, and it is impossible to do sublinear time if you have to examine every character.
If you insist on optimizing parse time, you should get a very fast LR parsing engine. LRStar used to be the cat's meow on this topic, but the guy behind it got zero reward from the world of "I want it for free" and pulled all instances of it off the net. You can settle for Bison.
Frankly most of your parsing time will be determined by how fast your parser can process individual characters, e.g., the lexer. Tune that first and you may discover there's no need to tune the parser.
First let's distinguish LR(k) grammars and LR(k) languages. A grammar may not be LR(1), but let's say, for example, LR(2). But the language it generates must have an LR(1) grammar -- and for that matter, it must have an LALR(1) grammar. The table size for such a grammar is essentially the same as for SLR(1) and is more powerful (all SLR(1) grammars are LALR(1) but not vice versa). So, there is really no reason not to use an LALR(1) parser generator if you are looking to do LR parsing.
Since parsing represents only a fraction of the compilation time in modern compilers when lexical analysis and code generation that contains peephole and global optimizations are taken into consideration, I would just pick a tool considering its entire set of features. You should also remember that one parser generator may take a little longer than another to analyze a grammar and to generate the parsing tables. But once that job is done, the table-driven parsing algorithm that will run in the actual compiler thousands of times should not vary significantly from one parser generator to another.
As far as tools for converting arbitrary grammars to LALR(1), for example (in theory this can be done), you could do a Google search (I have not done this). But since semantics are tied to the productions, I would want to have complete control over the grammar being used for parsing and would probably eschew such conversion tools.
Given an ambiguous grammar, to remove operator precedence problems we would convert the grammar to follow the operator precedence rules. To solve the operator associativity problem, we convert the grammar into left recursive or right recursive by considering the operator it is associated with.
Now when the computer has to do the parsing, suppose if it uses the recursive descent algorithm, should the grammar be unambiguous in the first place? Or the grammar should have different requirements according to the algorithm?
If the grammar is left recursive, the recursive descent algorithm doesn't terminate. Now how do I give an unambiguous grammar(with associativity problems solved) to the algorithm as the input?
The grammar must be LL(k) to use the standard efficient recursive descent algorithm with no backtracking. There are standard transformations useful for taking a general LR grammar (basically any grammar parsable by a deterministic stack-based algorithm) to LL(k) form. They include left recursion elimination and left factoring. These are extensive topics I won't attempt to cover here. But they are covered well in most any good compiler text and reasonably well in online notes available thru search. Aho Sethi and Ullman Compiler Design is a great reference for this and most other compiler basics.
I am wondered why there is no generalized parser combinators for Bottom-up parsing in Haskell like a Parsec combinators for top down parsing.
( I could find some research work went during 2004 but nothing after
https://haskell-functional-parsing.googlecode.com/files/Ljunglof-2002a.pdf
http://www.di.ubi.pt/~jpf/Site/Publications_files/technicalReport.pdf )
Is there any specific reason for not achieving it?
This is because of referential transparency. Just as no function can tell the difference between
let x = 1:x
let x = 1:1:1:x
let x = 1:1:1:1:1:1:1:1:1:... -- if this were writeable
no function can tell the difference between a grammar which is a finite graph and a grammar which is an infinite tree. Bottom-up parsing algorithms need to be able to see the grammar as a graph, in order to enumerate all the possible parsing states.
The fact that top-down parsers see their input as infinite trees allows them to be more powerful, since the tree could be computationally more complex than any graph could be; for example,
numSequence n = string (show n) *> option () (numSequence (n+1))
accepts any finite ascending sequence of numbers starting at n. This has infinitely many different parsing states. (It might be possible to represent this in a context-free way, but it would be tricky and require more understanding of the code than a parsing library is capable of, I think)
A bottom up combinator library could be written, though it is a bit ugly, by requiring all parsers to be "labelled" in such a way that
the same label always refers to the same parser, and
there is only a finite set of labels
at which point it begins to look a lot more like a traditional specification of a grammar than a combinatory specification. However, it could still be nice; you would only have to label recursive productions, which would rule out any infinitely-large rules such as numSequence.
As luqui's answer indicates a bottom-up parser combinator library is not a realistic. On the chance that someone gets to this page just looking for haskell's bottom up parser generator, what you are looking for is called the Happy parser generator. It is like yacc for haskell.
As luqui said above: Haskell's treatment of recursive parser definitions does not permit the definition of bottom-up parsing libraries. Bottom-up parsing libraries are possible though if you represent recursive grammars differently. With apologies for the self-promotion, one (research) parser library that uses such an approach is grammar-combinators. It implements a grammar transformation called the uniform Paull transformation that can be combined with the top-down parser algorithm to obtain a bottom-up parser for the original grammar.
#luqui essentially says, that there are cases in which sharing is unobservable. However, it's not the case in general: many approaches to observable sharing exist. E.g. http://www.ittc.ku.edu/~andygill/papers/reifyGraph.pdf mentions a few different methods to achieve observable sharing and proposes its own new method:
This looping structure can be used for interpretation, but not for
further analysis, pretty printing, or general processing. The
challenge here, and the subject of this paper, is how to allow trees
extracted from Haskell hosted deep DSLs to have observable back-edges,
or more generally, observable sharing. This a well-understood problem,
with a number of standard solutions.
Note that the "ugly" solution of #liqui is mentioned by the paper under the name of explicit labels. The solution proposed by the paper is still "ugly" as it uses so called "stable names", but other solutions such as http://www.cs.utexas.edu/~wcook/Drafts/2012/graphs.pdf (which relies on PHOAS) may work.
I am confused by the following quote from Wikipedia:
In other words, if a language was reasonable enough to allow an
efficient one-pass parser, it could be described by an LR(k) grammar.
And that grammar could always be mechanically transformed into an
equivalent (but larger) LR(1) grammar. So an LR(1) parsing method was,
in theory, powerful enough to handle any reasonable language. In
practice, the natural grammars for many programming languages are
close to being LR(1).[citation needed]
This means that a parser generator, like bison, is very powerful (since it can handle LR(k) grammars), if one is able to convert a LR(k) grammar to a LR(1) grammar. Do some examples of this exist, or a recipe on how to do this? I'd like to know this since I have a shift/reduce conflict in my grammar, but I think this is because it is a LR(2) grammar and would like to convert it to a LR(1) grammar. Side question: is C++ an unreasonable language, since I've read, that bison-generated parsers cannot parse it.
For references on the general purpose algorithm to find a covering LR(1) grammar for an LR(k) grammar, see Real-world LR(k > 1) grammars?
The general purpose algorithm produces quite large grammars; in fact, I'm pretty sure that the resulting PDA is the same size as the LR(k) PDA would be. However, in particular cases it's possible to come up with simpler solutions. The general principle applies, though: you need to defer the shift/reduce decision by unconditionally shifting until the decision can be made with a single lookahead token.
One example: Is C#'s lambda expression grammar LALR(1)?
Without knowing more details about your grammar, I can't really help more than that.
With regard to C++, the things that make it tricky to parse are the preprocessor and some corner cases in parsing (and lexing) template instantiations. The fact that the parse of an expression depends on the "kind" (not type) of a symbol (in the context in which the symbol occurs) makes precise parsing with bison complicated. [1] "Unreasonable" is a value judgement which I'm not comfortable making; certainly, tool support (like accurate syntax colourizers and tab-completers) would have been simple with a different grammar, but the evidence is that it is not that hard to write (or even read) good C++ code.
Notes:
[1] The classic tricky parse, which also applies to C, is (a)*b, which is a cast of a dereference if a represents a type, and otherwise a multiplication. If you were to write it in the context: c/(a)*b, it would be clear that an AST cannot be constructed without knowing whether it's a cast or a product, since that affects the shape of the AST,
A more C++-specific issue is: x<y>(z) (or x<y<z>>(3)) which parse (and arguably tokenise) differently depending on whether x names a template or not.
I've seen some claims that optimized PEG parsers in general cannot be faster than optimized LALR(1) or LL(k) parsers. (Of course, performance of parsing would depend on a particular grammar.)
I'd like to know if there are any specific limitations of PEG parsers, either valid in general or for some subsets of PEG grammars that would make them inferior to LALR(1) or
LL(k) performance-wise.
In particular, I'm interested in parser generators, but assume that their output can be tweaked for performance in any particular case. I also assume that parsers are optimized and it is possible to tweak a particular grammar a bit if that's needed to improve performance.
Found a good answer about Packrat vs LALR parsing. Some quotes from it:
L(AL)R parsers are linear time parsers, too. So in theory, neither packrat nor L(AL)R parsers are "faster".
What matters, in practice, of course, is implementation. L(AL)R state transitions can be executed in very few machine instructions ("look token code up in vector, get next state and action") so they can be extremely fast in practice.
An observation: most language front-ends don't spend most of their time "parsing"; rather, they spend a lot of time in lexical analysis. Optimize that ..., and the parser speed won't matter much.
PEG parsers can use unlimited lookahead (while maintaining linear parse time on average, via packrat) unlike (default) LL(k), or LR(k) parsers which use limited lookahead, while maintining linear parse time.
Lately (2014-2015) ANTLR4 has made extensions to handle arbitrary lookahead (as in PEG) while maintaining linear parse time on average (said to be more efficient than packrat algorithm), however this is incorporates new extensions and variations of the LR parsing algorithm (and not the default LR algorithm).
The packrat parser (and associated parsers for LL, LR) is not necesarily practical, but provides theoretical bounds on parsing so comparison can be made.
But note that unlimited lookahead can be used to parse grammars/languages in linear time (e.g via packrat or antlr) which are not possible to parse via LL(k) or LR(k) even in non-linear time, So it is important to understand what is compared to what.