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When I began to use parser combinators my first reaction was a sense of liberation from what felt like an artificial distinction between parsing and lexing. All of a sudden everything was just parsing!

However, I recently came across this posting on codereview.stackexchange illustrating someone reinstating this distinction. At first I thought this was very silly of them, but then the fact that functions exist in Parsec to support this behavior leads me to question myself.

What are the advantages/disadvantages to parsing over an already lexed stream in parser combinators?

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Please could someone add [parser-combinator] tag? –  Eli Frey Jan 6 '12 at 21:47
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5 Answers

Everyone suggesting that separating lexing and parsing is a "good practice" -- I have to disagree - in many cases performing lexing and parsing in a single pass gives much more power, and performance implications are not as bad as they're presented in the other answers (see Packrat).

This approach shines when one has to mix a number of different languages in a single input stream. This is not only needed by the weird metaprogramming-oriented languages like Katahdin and alike, but for much more mainstream applications as well, like literate programming (mixing latex and, say, C++), using HTML in comments, stuffing Javascript into HTML, and so on.

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In my answer I suggested that it is a "good practice in certain contexts" and not that it is a "better practice in all contexts". –  Giorgio Jan 8 '12 at 11:54
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Under parsing we understand most often analysis of context free languages. A context free language is more powerful than a regular one, hence the parser can (most often) do the job of the lexical analyser right away.

But, this is a) quite unnatural b) often inefficient.

For a), if I think about how for example an if expression looks, I think IF expr THEN expr ELSE expr and not 'i' 'f', maybe some spaces, then any character an expression can start with, etc. you get the idea.

For b) there are powerful tools that do an excellent job recognizing lexical entities, like identifiers, literals, brackets of all kinds, etc. They will do their work in practically no time and give you a nice interface: a list of tokens. No worries about skipping spaces in the parser anymore, your parser will be much more abstract when it deals with tokens and not with characters.

After all, if you think a parser should be busy with low level stuff, why then process characters at all? One could write it also on the level of bits! You see, such a parser that works on the bit level would be almost incomprehensible. It's the same with characters and tokens.

Just my 2 cents.

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Just for the sake of precision: a parser can always do the job of a lexical analyser. –  Giorgio Jan 7 '12 at 11:07
    
Also, regarding efficiency: I am not sure if a parser would be less efficient (slower). I would expect that the resulting grammar would contain a sub-grammar that describes a regular language, and the code for that sub-grammar would be as fast as a corresponding lexical analyser. IMO the real point is (a): how natural, intuitive it is to work with a simpler, more abstract parser. –  Giorgio Jan 7 '12 at 11:22
    
@Giorgio - Regarding your 1st comment: You are right. What I had in mind here are cases where the lexer pragmatically does some work that makes the grammar easier, so that one can use LALR(1) instead of LALR(2). –  Ingo Jan 7 '12 at 11:32
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I have removed my acceptence of your answer after further experimentation and reflection. It seams that you two come from yon world of Antlr et all. Considering the first class nature of parser combinators I often simply end up defining a wrapper parser for my token parsers leaving each token as a single name in the parsing layer of parsers. for instance your if example would look like if = string "if" >> expr >> string "then" >> expr >> string "else" >> expr. –  Eli Frey Jan 8 '12 at 6:04
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Performance is still an open question, I will do some benchmarks. –  Eli Frey Jan 8 '12 at 6:06
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A lexical analyser recognizes a regular language and a parser recognizes a context-free language. Since each regular language is also context free (it can be defined by a so-called right-linear grammar), a parser can also recognize a regular language and the distinction between parser and lexical analyser seems to add some unneeded complexity: a single context-free grammar (parser) could do the job of a parser and a lexical analyser.

On the other hand, it can be useful to capture some elements of a context-free language through a regular language (and therefore a lexical analyser) because

  1. Often these elements appear so often that they can be dealt with in a standard way: recognizing number and string literals, keywords, identifiers, skipping white space, and so on.
  2. Defining a regular language of tokens makes the resulting context-free grammar simpler, e.g. one can reason in terms of identifiers, not in terms of individual characters, or one can ignore white space completely if it is not relevant for that particular language.

So separating parsing from lexical analysis has the advantage that you can work with a simpler context-free grammar and encapsulate some basic (often routine) tasks in the lexical analyser (divide et impera).

EDIT

I am not familiar with parser combinators so I am not sure how the above considerations apply in that context. My impression is that even if with parser combinators one only has one context-free grammar, distinguishing between two levels (lexical analysis / parsing) could help to make this grammar more modular. As said, the lower lexical-analysis layer could contain basic reusable parsers for identifiers, literals, and so on.

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Lexemes falls into regular grammars not naturally, but by convention, since all the lexers are built upon regular expression engines. It is limiting the expressive power of the languages you can design. –  SK-logic Jan 8 '12 at 9:44
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Can you give an example of a language for which it would be appropriate to define lexemes that cannot be described as a regular language? –  Giorgio Jan 8 '12 at 10:03
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for example, in a couple of the domain specific languages I've built, identifiers could have been TeX expressions, which simplified pretty-printing the code, e.g., an expression like \alpha'_1 (K_0, \vec{T}), where \alpha'_1, K_0 and \vec{T} are identifiers. –  SK-logic Jan 8 '12 at 10:56
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Given a context-free grammar you can always take a non-terminal N and treat the words it can derive as units that have a useful meaning in themselves (e.g. an expression, a term, a number, a statement). This can be done regardless of how you parse that unit (parser, parser + lexer, etc). IMO the choice of a parser + lexer is more a technical one (how to implement the parsing) than a semantic one (what is the meaning of the blocks of source code that you parse). Maybe I am overlooking something but the two aspects look orthogonal to me. –  Giorgio Jan 8 '12 at 11:37
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So, I agree with you: if you define some arbitrary basic building blocks (lexemes) and want to use a lexical analyser to recognize them, this is not always possible. I just wonder if this is the goal of a lexer. As far as I understand, the goal of a lexical analyser is more a technical one: taking away some low-level, tedious implementation details from the parser. –  Giorgio Jan 8 '12 at 11:43
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Simply, lexing and parsing should be separated because they're different complexities. Lexing is a DFA (deterministic finite automaton) and a parser is a PDA (push-down automaton). This means that parsing inherently consumes more resources than lexing, and there are specific optimization techniques available to DFAs only. In addition, writing a finite state machine is much less complex, and it's easier to automate.

You're being wasteful by using a parsing algorithm to lex.

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If you use a parser to to do lexical analysis, the PDA would never use the stack, it would basically work as a DFA: just consuming input and jumping between states. I am not 100% sure, but I think that the optimization techniques (reducing the number of states) that can be applied to a DFA can also be applied to a PDA. But yes: it is easier to write the lexical analyser as such without using a more powerful tool, and then to write a simpler parser on top of it. –  Giorgio Jan 7 '12 at 11:39
    
In addition, it makes the whole thing more flexible and maintenable. For instance, suppose we have a parser for the Haskell language without the layout rule (i.e., with semicolons and braces). If we have a separate lexer, we could now add the layout rules by just doing another pass over the tokens, adding braces and semicolons as needed. Or, for an easier example: suppose we started out with a language supporting ASCII characters in identifiers only and now we want to support unicode letters in identifiers. –  Ingo Jan 7 '12 at 12:11
    
@Ingo, and why would you need to do it in a separate lexer? Just factor out those terminals. –  SK-logic Jan 8 '12 at 11:13
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@SK-logic: I am not sure I understand your question. Why a separate lexer may be a good choice I have tried to substantiate in my post. –  Ingo Jan 8 '12 at 14:57
    
Giorgio, no. The stack is a crucial component of a normal LALR style parser. Doing lexing with a parser is a hideous waste of memory (both static storage and dynamically allocated) and will be much slower. The Lexer/Parser model is efficient--use it :) –  Stargazer712 Jan 8 '12 at 17:01
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One of the main advantage of separate parse / lex is the intermediate representation - the token stream. This can be processed in various ways that would otherwise not be possible with a combined lex/parse.

That said, I have found that good 'ol recursive decent can be less complicated and easier to work with vs learning some parser generator, and having to figure out how to express the weakness of the grammer within the rules of the parser generator.

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Could you explain more about grammars that are more easily expressed on a prefabbed stream then performed at parse time? I only have experience implementing toy languages and a scant few data formats, so perhaps I have missed something. Have you noticed any performance characteristics between your hand-rolled RD parser/lex combos and BNF fed (I'm assuming) generators? –  Eli Frey Jan 8 '12 at 7:49
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