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Michiel Helvensteijn <[log in to unmask]>
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Mailing list for the LaTeX3 project <[log in to unmask]>
Sat, 26 Oct 2013 16:03:21 +0200
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On Sat, Oct 26, 2013 at 3:35 AM, Bruno Le Floch <[log in to unmask]> wrote:

> Thanks for your interest in l3regex (and thanks to Lars for many
> useful comments, and to Paulo for the undeserved performance praise).

And thank you for your extensive reply.

>> a lexical analyzer package
> It would be helpful if you can describe what you are trying to do more
> precisely.  Do you work with strings of characters only (i.e., the
> category code does not matter, as in most programming languages), or
> tokens (control sequences, usual characters, special characters)?

Good questions. So far I've only needed to define lexemes containing
'letter', 'space' and 'other' catcodes, beginning with a 'letter' or
'other', though I've also hacked in a way to pick up balanced
brace-groups in-between and pass them as arguments to the expansion

I've so far been using it for math-mode only. The idea is to declare
new lexemes like this:

\LexDef {──►} {\longrightarrow}

The package then updates the internal automaton to recognize the
sequence and makes '◄' math-active, set to start scanning whenever it
is encountered. Using 'maximal munch', it will scan ahead to match the
largest lexeme it recognizes, replaces it inline with the proper
output and feeds any extra tokens that were consumed back into the
input stream afterwards.

Here's an example that picks up an argument:

\LexDef {─�─►} {\xrightarrow{#1}}

This would recognize something like ─{x}─► and replace it with
\xrightarrow{x}. I've also used the package to:
* make kerning / style corrections without cluttering the main LaTeX code
* hyperlink a math symbol to where it was defined
* generate a symbol index.

> Is your goal to have a lexer for a specific set of tokens, fixed once and
> for all, or do you want the lexer to be given by its set of regexes by
> the user of your package?

The user defines new regexes (either directly or indirectly).

> Is the end-goal only to lex, or is there a parsing step afterwards?

For the foreseeable future it will stay at lexing. (Though
interestingly, if it ever does turn into a full-fledged parser, we
could even perform rudimentary type-checking on the math.)

>> I'd like to match against a compiled regex, but feed it one token at a
>> time, rather than the entire token list at once.
> This is doable but more difficult than it seems.  Essentially, you
> want to run some code between calls to l3regex, while keeping the data
> of l3regex from one call to the next.
> The data of l3regex (list of states for the current branches and
> subgroup info) is stored into various TeX registers (\toks, \dimen,
> \skip, \muskip...), hence during the operation of l3regex, none of the
> usual \..._dim, \..._skip, or \..._muskip variables have their correct
> values (even \c_zero_dim, which is just one of the \dimen registers
> behind the scenes).  Because of this, all of the work must be done
> within a group, and the data is discarded at the end of the group,
> before returning the appropriate result to the user.

Doesn't that break recommended expl3 practice? There are no registers,
there are no macros. There are only variables. ;-)

> A completely different approach would be that I ask you how the tokens
> are generated.  If it is from the input stream (e.g., you are using
> \futurelet or the \peek_... functions to find tokens to feed l3regex),
> then l3regex could directly provide tools to read tokens from the
> input stream until the regex cannot match anymore.  This avoids the
> business above of storing data, because we are not running arbitrary
> user code, so everything can be done within the same group.

This would be fine. Though I'm forced to wonder if there would be
anything left for my own package to do. ;-)

>> At each point in
>> between, I want to know whether a match is still possible. If not, I
>> want to go back one step and retrieve the captured groups (and perhaps
>> other available meta-data).
> You change this later on to "going back all the way to the previous
> accepting state".  This is rather straightforward, given that the
> "previous accepting state" is essentially stored somewhere.  The main
> question will be what the best interface is, and I currently have
> absolutely no idea.  Proposals welcome.

Usually an array is made available, in which the 0th element contains
the full match and subsequent elements contain the submatches. That
may be a bit overkill here, but what about something like this:

"\regex_run:NnN" to run compiled regex #1 on token list #2 and package
all pertinent results in variable #3. Then "\regex_get_match:Nn" would
leave the #2th match stored in variable #1 in the input stream.

A variation like "\regex_run:NN" would read from the input stream instead.

>> Is there a particular reason you're not translating
>> it into a DFA (Deterministic Finite Automaton) during the compilation
>> phase, i.e., applying the powerset construction?
> Yes: I couldn't even figure out how to keep track of subgroup info and
> remove epsilon transitions from my NFA.  Shifting to a DFA would make
> things even more tricky.  Also, I'm not sure about the gain when
> keeping track of subgroups, because a given state of the DFA still
> requires storing multiple sets of subgroup info (one for each NFA
> state that the DFA state corresponds to).

I admit I'm not an expert on automata theory. But I suspect that much
of the 'keeping track' and 'branch priority' stuff that you now do at
runtime could be used to generate a DFA that can do the same
on-the-fly. I haven't really looked into this, however. Perhaps you do
lose subgroup information in the translation to a DFA.

> I'd rather not make the code longer than it is, but in principle, I
> could decide to only convert to a DFA if no subgroup info is tracked.
> If I do that, a lazy powerset construction should be best suited, as
> Lars notes.  I'm just not clear whether this construction interacts
> well with ranges:  Given the (silly) regex ( \d+ | [A-F0-9a-f]+ HEX ),
> the first time I encounter a digit, I'll add a transition in the DFA
> from the empty set to a pair of NFA states (one for each side of the
> alternative).  If another use of the same NFA/DFA hybrid also receives
> a digit (other than the first) as its first character, will I add a
> distinct transition from the empty set to the same two-NFA-states
> state, with a different label?  Or should I try to detect that the
> intersection of \d and [A-F0-9a-f] is [0-9]?

I've been pondering the same thing. Ideally, computing the
intersections of all relevant character-classes and taking those to be
your alphabet would be best. But this requires knowing the full regex
at compile-time. No additional regexes can be 'compiled into it'
afterwards, as it may contain new partially overlapping
character-classes. Though I suppose that's acceptable.

> Do you really need to merge NFA's on the fly, or could you simply use
> an alternation such as ( \d+ | [a-zA-Z]\w* | ... ) ?  Then we would
> simply need a way to extract the information of which alternative was
> taken.  Doable, but I have no idea what syntax would be good.  I agree
> with Lars concerning performance.  Branches in the NFA will very
> quickly die if the word does not match the corresponding alternative.

Presumably a 'regex unit' could accumulate named alternatives, and
then be given the command to compile:

\regex_new:N \my_regex
\regex_insert_pattern:Nnn \my_regex {pattern 1} {\d+}
\regex_insert_pattern:Nnn \my_regex {pattern 2} {[A-F0-9a-f]+}
\regex_insert_pattern:Nnn \my_regex {pattern 3} {hello world}
\regex_compile:NN \my_regex \compiled_regex

But there are many other ways to do it, like assuming the root of the
regex to be a list of alternatives "a | b | c | ..." and then
identifying them by index.