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Bruno Le Floch <[log in to unmask]>
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Mailing list for the LaTeX3 project <[log in to unmask]>
Sat, 26 Oct 2013 03:35:27 +0200
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Hello Michiel,

Thanks for your interest in l3regex (and thanks to Lars for many
useful comments, and to Paulo for the undeserved performance praise).
I've been focusing on l3fp lately (finishing up the code for inverse
trigonometric functions, which should be done in a week or two).  I'll
try to answer most things raised in this thread, but I might miss
some.  Also, I should say that I haven't looked at l3regex in a loong
time, so it will take me some time before I can modify the code (don't
expect changes before the end of November).

> 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)?  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?  Is the end-goal only to lex, or is there a
parsing step afterwards?  In that case, it may be better to use a PEG
packrat parser, rather than a combination of a lexer and a more
conventional parser (for context free/context sensitive grammars...).

> 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.

Running arbitrary user code within this group would lead to weird bugs
as soon as the user's code involves any register (this may happen
behind the scenes, as some functions may expect \c_max_int to have its
appropriate value, for instance).  The other option is to provide
functions which save the data in a csname, and functions which accept
a regex and starting data as an input.  Should the data be stored
together with the regex, i.e., should I introduce a "partially applied
regex" type?  Should the regex and the data be independent arguments
(I think not, as the data is only consistent with the particular regex
that "fathered" it)?

In any case, another difficulty is that you will not be able to feed
unbalanced tokens (braces) to l3regex, only balanced token lists (no
problem there, doing a few tokens at a time rather than just one
should be as easy).

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.

> 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).

Going just one step back would lead to a partially matched regex only,
and the notion of captured group is a bit fuzzy: I don't know what
matching "abcZ" against the regex "a(bcd)e" should give as a captured
group once "Z" is seen to allow no match.

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.

> You're now running a regex as a NFA (Nondeterministic
> Finite Automaton), keeping track of all active branches while matching
> against an input.

Not quite: I don't keep track of branches (that would allow me to do
backreferences, but would be very expensive), only of states which are
reached by those branches, and only one set of subgroup info per
reached state.

> 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'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 thinking about that. Why not memoize a
> regex-to-minimized-DFA translation in an auxiliary file? That way you
> only have to compile a new regex once, even across LaTeX runs.

We have not decided what we'd do for auxiliary files in expl3 (and
later on LaTeX3) yet, so I'm not using the .aux file.

>> One possible alternative is to
>> use a NFA and applying Thompson's construction or a similar algorithm
> I assume this is what l3regex already does, to construct the NFA.


>>> (2) I would also need the ability to merge new (N|D)FA's into an
>>> existing one and mark the corresponding accepting states with an
>>> identifier. I could then query this identifier when a match was found,
>>> so I could know which original pattern(s) matched.
>> Doable, but whichever way you do it, you effectively end up executing all
>> the component automata in parallel. With DFAs, the new state space is the
>> cartesian product of the component state spaces. With NFAs, you have a
>> set
>> of active branches for each component automaton. So if you're anyway
>> feeding
>> data to your automaton one token at a time, then you might as well feed
>> each
>> token to a sequence of automata instead.
> Properly merging DFA's will gain you plenty if some rudimentary
> optimizations are performed. But not so much for NFA's, as you say,
> which is a shame. I've defined near 200 separate math-mode lexemes in
> my thesis so far. I wouldn't want to start up 200 automata for every
> potential occurrence. My current implementation uses a trie, i.e., a
> very primitive DFA.

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.

Best regards,