Notice that usually the issue is with the parsing algorithm itself, that does not support left-recursive rules. So the parser generator may transform rules written as left-recursive in the proper way to make them work with its algorithm. In this sense, left-recursive support may be very useful syntactic sugar. The specific way in which the rules are transformed vary from one parser generator to the other, however the logic remains the same. The expressions are divided in two groups: the ones with an operator and two operands and the atomic ones.
That is because in mathematics parentheses are used to increase the precedence of an expression. Once you have these two groups: you maintain the order of the members of the second group and reverse the order of the members of the first group.
The reason is that humans reason on a first come, first serve basis: it is easier to write the expressions in their order of precedence. However the final form of the parsing is a tree, which operates on a different principle: you start working on the leaves and rise up. So that at the end of this process the root node contains the final result. Which means that in the parsing tree the atomic expressions are at the bottom, while the ones with operators appear in the inverse order to the one in which they are applied.
Predicates , sometimes called syntactic or semantic predicates , are special rules that are matched only if a certain condition is met. The condition is defined with code in a programming language supported by the tool for which the grammar is written. Their advantage is that they allow some form of context-sensitive parsing, which is sometime unavoidable to match certain elements.
For instance, they can be used to determine if a sequence of characters that defines a soft keyword is used in a position where it would be a keyword e. The disadvantages are that they slow parsing down and they make the grammar dependent on said programming language.
That is because the condition is expressed in a programming language and must be checked. And, of course, to check this condition you must execute the code in the corresponding programming language. Embedded actions identify code that is executed every time the rule is matched.
They have the clear disadvantage that they make the grammar harder to read, since the rules are surrounded by code.
Furthermore, just like predicates, they break the separation between a grammar that describes the language and the code that manipulates the results of the parsing. Actions are frequently used by less sophisticated parsing generators as the only way to easily execute some code when a node is matched.
Using these parser generations, the only alternative would be to traverse the tree and execute the proper code yourself. More advanced tools allow to use the visitor pattern instead to execute arbitrary code when needed, and also to govern the traversing of the tree.
They can also be used to add certain tokens or change the generated tree. While ugly, this might be the only practical way to deal with complicated languages, like C, or specific issues, like whitespace in Python.
Many tools implement their own variants of these ideal formats. Some tools use custom formats altogether. A frequent custom format consists of a three parts grammar: options together with custom code, followed by the lexer section and finally the parser section. Given that a BNF-like format is usually the foundation of a context-free grammar you could also see it identified like the CFG format.
However it is quite simple, and thus it is not often used in its basic form. A more powerful variant is typically used. The first issue is that you have to list all the alternatives individually; you cannot use character classes like you do with regular expressions. This is annoying, but usually manageable, unless of course you have to list all Unicode characters.
A much harder problem is that there is no easy way to denote optional elements or repetitions. So if you want to do that you have to rely on boolean logic and the alternative symbol. BNF has many other limitations: it makes complicated to use empty strings or the symbols used by the format e. EBNF is the most used form in contemporary parsing tools, although tools might deviate from the standard notation.
EBNF has a much cleaner notation and adopts more operators to deal with concatenation or optional elements. The resulting parse tree would also be simpler.
The standard EBNF still presents some problems, like the unfamiliar syntax. To overcome this issue most parsing tools adopt a syntax inspired by regular expressions and also support additional elements like characters classes. If you need an in-depth coverage of the format you can read our article on EBNF. For example, until recently the standard dictated that strings were matched in a case-insensitive way, which would have been a problem for matching identifiers in many programming languages.
For instance, there is no need for a concatenation operator. It also has a few more feature than standard EBNF. This is also used by the designers themselves, to include standard character classes-like basic rules that the end user can use. However a simple way to describe is: EBNF in the real world. In fact it looks similar to EBNF, but also directly supports widely used features, like character ranges character classes.
The previous example could be written this way with PEG. As you can see, this is the most obvious way a programmer would write it, with character classes and regular expression operators.
The pragmatic approach is the foundation of the PEG formalism: it was created to describe programming languages more naturally. That is because context-free grammar has its origin in the work to describe natural languages.
The first should be a sort of recipe to generate only the valid sentences in the language described by the grammar. It does not have to be related to the parsing algorithm. Instead the second kind directly define the structure and semantics of a parser for that language. The practical implications of this theoretical difference are limited: PEG is more closely associated to the packrat algorithm, but that is basically it. For instance, generally PEG packrat does not permit left recursion.
Although the algorithm itself can be modified to support it, this eliminates the linear-time parsing property. Also, PEG parsers are generally scannerless parsers. If there are many possible valid ways to parse an input, a CFG will be ambiguous and thus will usually return an error.
By usually we mean that some parsers that adopt CFGs can deal with ambiguous grammars. For instance, by providing all possible valid results to the developer and letting him sort it out. Instead PEG eliminates ambiguity altogether because the first applicable choice will be chosen, thus a PEG can never be ambiguous.
The disadvantage of this approach is that you have to be more careful in listing possible alternatives, because otherwise you could have unexpected consequences. That is to say some choices could never be matched. In the following example doge will never be matched, since dog comes first it will be picked each time. It is an open area of research whether PEG can describe all grammars that can be defined with CFG, but for all practical purposes it does.
In theory parsing is a solved problem, but it is the kind of problem that keeps being solved again and again. That is to say that there are many different algorithms, each one with strong and weak points, and they are still being improved by academics. In this section we are not going to teach how to implement every one of the parsing algorithm, but we are going to explain their features.
The goal is that you can choose with more awareness which parsing tool to use, or which algorithm to study better and implement for your custom parser. There are two strategies for parsing: top-down parsing and bottom-up parsing. Both terms are defined in relation to the parse tree generated by the parser. In simple terms:. The same tree would be generated in a different order by a top-down and a bottom-up parser. In the following images the number indicate the order in which the nodes are created.
Traditionally top-down parsers were easier to build, but bottom-up parsers were more powerful. Now the situation is more balanced, mostly because of advancement in top-down parsing strategies.
The concept of derivation is closely associated to the strategies. Derivation indicates the order in which the nonterminal elements that appears in the rule, on the right, are applied to obtain the nonterminal symbol, on the left.
The two possibilities are: leftmost derivation and rightmost derivation. The first indicates that the rule are applied from left to right, while the second indicates the opposite. A simple example: imagine that you are trying to parse the symbol result which is defined as such in the grammar. In the case of leftmost derivation you pick the first option, while for rightmost derivation you pick the second one.
It is important to understand that the derivation is applied depth-first or recursively. That is to say, it is applied on the starting expression then it is applied again on the intermediate result that is obtained. Derivation is associated with the two strategies, because for bottom-up parsing you would apply rightmost derivation, while for top-down parsing you would choose leftmost derivation. Note that this has no effect on the final parsing tree, it just affects the intermediate elements and the algorithm used.
Parsers built with top-down and bottom-up strategies shares a few elements that we can talk about. The terms lookadhead and backtracking do not have a different meaning in parsing than the one they have in the larger computer science field.
Lookahead indicates the number of elements, following the current one, that are taken into consideration to decide which current action to take. A simple example: a parser might check the next token to decide which rule to apply now. When the proper rule is matched the current token is consumed, but the next one remains in the queue. Backtracking is a technique of an algorithm. It consists of finding a solution to a complex problems by trying partial solutions, and then keep checking for the most promising one.
If the one that is currently being tested fails, then the parser backtracks i. Lookahead is especially relevant to LL , LR and LALR parsing algorithms, because parsers for languages that just needs one lookahead token are easier to build and quicker to run. The lookahead tokens used by such algorithms are indicated between parentheses after the name of the algorithm e. Chart parsers are a family of parsers that can be bottom-up e. Chart parsers essentially try to avoid backtracking, which can be expensive, by using dynamic programming.
Dynamic programming , or dynamic optimization, is a general method to break down larger problem in smaller subproblems. A common dynamic programming algorithm used by chart parser is the Viterbi algorithm. The goal of the algorithm is to find the most likely hidden states given the sequence of known events. Basically given the tokens that we know, we try to find the most probable rules that have produced them.
The name chart parser derives from the fact that the partial results are stored in a structure called chart usually the chart is a table. The particular technique of storing partial results is called memoization. Memoization is also used by other algorithms, unrelated to chart parsers, like packrat.
Before discussing parsing algorithms we would like to talk about the use of automatons in parsing algorithms. Automaton s are a family of abstract machines, among which there is the well known Turing machine. Since they define abstract machines, usually they are not directly related to an actual algorithm. Rather, they describe in a formal way the level of complexity that an algorithm must be able to deal with.
However since DFAs are state machines in the case of a lexer the distinction is frequently moot. That is because state machines are relatively straightforward to implement i. That is why we are going to briefly talk about DFA and why they are frequently used for lexers. DFA is a finite- state machine, a concept with which we assume you are familiar. Basically, a state machine has many possible states and a transition function for each of them.
These transition functions govern how the machine can move from one state to a different one in response to an event. When used for lexing, the machine is fed the input characters one at a time until it reaches an accepted state i. An online algorithm is one that does not need the whole input to work. In the case of a lexer, it means that it can recognize a token as soon as its characters are seen by the algorithm.
The alternative would be that it would need the whole input to identify each token. In addition to these properties it is fairly easy to transform a set of regular expressions into a DFA, which makes it possible to input the rules in a simple way that is familiar to many developers. Then you can automatically convert them into a state machine that can work on them efficiently.
We provide a table to offer a summary of the main information needed to understand and implement a specific parser algorithm. You can find more implementations by reading our articles that present parsing tools and libraries for Java , C , Python and JavaScript. To understand how a parsing algorithm works you can also look at the syntax analytic toolkit.
It is an educational parser generator that describes the steps that the generated parser takes to accomplish its objective. It implements a LL and a LR algorithm. The technology should not be overkill using techniques much more complex and costly than needed , nor should it be at the limit of its power, thus requiring technical contortions to achieve the desired goal. That is why "It seems fashionable to hate regular expressions".
Though they can do a lot, they sometimes require very unreadable coding to achieve it, not to mention the fact that various extensions and restrictions in implementation somewhat reduce their theoretical simplicity. Lexers do not usually do that, and are usually a simple, efficient, and appropriate technology to parse token.
Using CF parsers for token would be overkill, though it is possible. Another reason not to use CF formalism for lexers is that it might then be tempting to use the full CF power. But that might raise sructural problems regarding the reading of programs.
Fundamentally, most of the structure of program text, from which meaning is extracted, is a tree structure. It expresses how the parse sentence program is generated from syntax rules.
Semantics is derived by compositional techniques homomorphism for the mathematically oriented from the way syntax rules are composed to build the parse tree.
Hence the tree structure is essential. The fact that tokens are identified with a regular set based lexer does not change the situation, because CF composed with regular still gives CF I am speaking very loosely about regular transducers, that transform a stream of characters into a stream of token. So CF is not the appropriate tool for lexers, even though it can be used.
One of the major differences between regular and CF is that regular languages and transducers compose very well with almost any formalism in various ways, while CF languages and transducers do not, not even with themselves with a few exceptions. Note that regular transducers may have others uses, such as formalization of some syntax error handling techniques.
It can always be transformed into an equivalent pure BNF. However, the regular notation is often used in EBNF only to emphasize these parts of the syntax that correspond to the structure of lexical elements, and should be recognized with the lexer, while the rest with be rather presented in straight BNF. But it is not an absolute rule. To summarize, the simpler structure of token is better analyzed with the simpler technology of regular languages, while the tree oriented structure of the language of program syntax is better handled by CF grammars.
I would suggest also looking at AHR's answer. It is a fundamental algebraic tool to define the semantics of mathematical formalisms.
Note that AST are often different from parse tree because the parsing technology used by many professionals Such as LL or LR applies only to a subset of CF grammars, thus forcing grammatical distorsions which are later corrected in AST. This can be avoided with more general parsing technology based on dynamic programming that accepts any CF grammar. Statement about the fact that programming languages are context-sensitive CS rather than CF are arbitrary and disputable.
The problem is that the separation of syntax and semantics is arbitrary. Checking declarations or type agreement may be seen as either part of syntax, or part of semantics. The same would be true of gender and number agreement in natural languages. But there are natural languages where plural agreement depends on the actual semantic meaning of words, so that it does not fit well with syntax. Many definitions of programming languages in denotational semantics place declarations and type checking in the semantics.
So stating as done by Ira Baxter that CF parsers are being hacked to get a context sensitivity required by syntax is at best an arbitrary view of the situation. It may be organized as a hack in some compilers, but it does not have to be.
Also it is not just that CS parsers in the sense used in other answers here are hard to build, and less efficient. They are are also inadequate to express perspicuously the kinf of context-sensitivity that might be needed. And they do not naturally produce a syntactic structure such as parse-trees that is convenient to derive the semantics of the program, i. There are a number of reasons why the analysis portion of a compiler is normally separated into lexical analysis and parsing syntax analysis phases.
Abo Columbia University Monica S. Ullman Stanford University. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Asked 11 years, 6 months ago. Active 2 years, 10 months ago. Viewed k times. Are lexers and parsers really that different in theory? When is lexing enough, when do you need EBNF? Has anyone used the tokens produced by these lexers with bison or antlr parser generators?
Improve this question. All Workers Are Essential Naveen Naveen 5, 5 5 gold badges 28 28 silver badges 36 36 bronze badges. I am trying to parse autohotkey. I was able to build a syntax highlighter using pygments really fast. But antlr is taking much longer I haven't seen a lot of cross pollination between the two tools.
Its only fashionable to hate regular expressions when they are misused. Many people try to use regular expressions when context-free parsing is needed. They always fail. And they blame regular expression technology. That's much like complaining that your hammer is a crummy saw. True, but you won't get a lot of sympathy. I am starting to pick up some speed with antlr, thankfully. Consider this file, written in the DOT language, as used by the Graphviz graph visualizer teamwork.
Here we have a 'program' and we wish to give effect to the author's intention by rendering this as an image:. What's required to do that? As above, lex, parse , render. Using Graphviz's dot command to carry out these 3 tasks, we would run:. This is significant, since it's usually straight-forward to translate a BNF description of a language into code within a lexer and parser.
Let's say we feel the Graphviz language is too complex, and hence we write a wrapper around it, so end users can code in a simplified version of that language. This has been done, with the original effort available in the now-obsolete Perl module Graph::Easy.
Tels, the author, devised his own very clever little language , which he called Graph::Easy. The manual for that is on-line here. When I took over maintenance of Graph::Easy , I found the code too complex to read, let alone work on, so I wrote another implementation of the lexer and parser, released as Graph::Easy::Marpa. I'll have much more to say about that in the next article in this 2-part series, so for now we'll just examine the above graph re-cast in Graph::Easy teamwork.
Simpler for sure, but how does Graph::Easy::Marpa work? As always: lex, parse , render. More samples of Graph::Easy::Marpa 's work are here.
It should be clear by now that lexing and parsing are in fact widespread, although they often operate out of sight, with just their rendered output visible to the average programmer and web surfer. What all such problems have in common is complex but well-structured source text formats, with a bit of hand-waving over the tacky details available to authors of documents in HTML.
And, in each case, it is the responsibility of the programmer writing the lexer and parser to honour the intention of the original text's author. And we can only do that by recognizing each token in the input as embodying some meaning e.
With all that I can safely claim that it's the ubiquity and success of lexing and parsing which justify their recognition as vital constituents in the world of software engineering. And with that we're done answering the question posed above: Why study them? But there's another - significant - reason to discuss lexing and parsing. And that's to train programmers, without expertise in such matters, to resist the understandable urge to opt for using tools they are already familiar with, with regexps being the 'obvious' choice.
Sure, regexps suit many simple cases, and the old standbys of flex and bison are always available, but now there's a new kid on the block: Marpa. The Perl and C-based interface to the most recent version of libmarpa.
This is the version I use. The newest and thinnest interface to libmarpa, which documents how to make Marpa accessible to non-Perl languages. Once you get used to it, of course!
And if you're having trouble, just post on the Google Group. Actually, if you've ever worked with flex and bison, you'll be astonished at how simple it is to drive Marpa. This is a bit surprising, since new technology usually needs some time to surpass established technology while delivering the all-important stability.
What's important is that this work is on-going, and we can expect a series of incremental improvements for some time to come. However, this is not an article on Marpa but the next one is , so let's return to discussing lexing and parsing.
As mentioned, the stages, conveniently, run in English alphabetical order, so we lex and then we parse. Here, I'm using lexing to mean the comparatively simple process of tokenising a stream of text, which means chopping that input stream into discrete tokens, and identifying the type of each token.
The output is a new stream, this time of stand-alone tokens. And I say 'comparatively' because I see parsing as complex compared to lexing. And no, lexing does not do anything more than identify tokens. Therefore questions about the meanings of those tokens, or their acceptable order, are matters for the parser.
So, the lexer will say: I have found another token, and have identified it as being of some type T. Hence, for each recognized token, 2 items will be output:. Since the process happens repeatedly, the output will be an array of token elements, with each element needing at least these 2 components: type and value. The advantage of Set::Array over Set::Tiny is that the former preserves the ordering of the elements. See also this report comparing a range of set-handling modules. The 'count' field, apparently redundant, is sometimes employed in the clean-up phase of the lexer, which may need to combine tokens unnecessarily split by the regexp-based approach.
Also, it is available to the parser if needed, so I always include it in the hashref. The 'name' field really is unused, but gives people who fork or sub-class my code a place to work with their own requirements, without worrying that their edits will affect the fundamental code.
The parser then, concerns itself with the context in which each token appears, which is a way of saying it cares about whether or not the sequence and combination of tokens actually detected fits the expected grammar.
Ideally, the grammar is provided in BNF Form. This makes it easy to translate into the form acceptable to Marpa. If it's not in that form, you're work is probably going to be harder, simply because someone else has not done the hard work formalizing the grammar.
An example grammar was mentioned above: DOT. But, how are we to understand a block of text written in BNF? Well, training is of course required when taking on such a task, and to that I'd add what I've gleaned from this work, as follows. To us beginners eventually comes the realization that grammars, no matter how formally defined or otherwise, contain within them 2 sub-grammars:. One sub-grammar specifies what a token looks like, meaning what range of forms it can assume in the input stream.
If an incomprehensible candidate it detected, the lexer can generate an error, or it can activate a strategy called - by Jeffrey Kegler, the author of Marpa - Ruby Slippers which has no relation to the Ruby programming language. Put simply, the Ruby Slippers strategy fiddles the current token, or perhaps an even larger section of the input stream, in a way that satisfies the grammar, and restarts processing at the new current token.
Marpa is arguably unique in being able to do this. The other sub-grammar specifies how these tokens are allowed to combine, meaning if they don't conform to the grammar, the code generates a syntax error of some sort. It is: We will encode the first sub-grammar into the lexer and the second into the parser. Modern software development is a fast and iterative process aimed at delivering amazing products and experiences to customers.
To get the most out of our time, we rely a lot on the tools and utilities we use every day. An IDE comes with a series of tools including:.
These tools all share a very common but often overlooked trait; they parse your code to infer meaning as part of their function. It used to be the case that writing a good language recognizer and parser was a rather complicated affair, but today there are several great tools that help do a lot of the work for you.
It makes it effortless to parse nontrivial text inputs such as a programming language syntax. This holds true even if you plan on targeting a language other than Java. Before we begin generating a lexer and parser for our hypothetical syntax or language we must describe its structure by putting together a grammar.
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