Dealing with empty strings in regexp.

[Paul Isambert]

Hello all,

The following issue has been recently discussed on the Lua mailing list:
http://lua-users.org/lists/lua-l/2013-04/msg00812.html

(It has also been independantly raised on the LuaTeX list:
http://tug.org/pipermail/luatex/2013-June/004418.html)

If I understand correctly, any string can be represented with
interspersed empty substrings. E.g. “abc” is really “ϵaϵbϵcϵ”, where
“ϵ” is the empty string. Now, there seems to be two ways to deal with
those empty strings in regexps, especially regarding the “*” operator:

- The Perl way: “X*” matches as many “X” as possible, and does not
include the following empty string.
- The Python (or sed) way: “X*” matches as many “X” as possible, and
includes the following empty string.

Starting empty strings are always included. So, the Perl way gives (I
use Ruby, since I can’t speak Perl):

puts 'abc'.gsub(/[ac]*/, '(\0)')
# returns “(a)()b(c)()”, really “(ϵa)(ϵ)b(ϵc)(ϵ)”

And the Python way:

import re
print re.sub(re.compile('(a*)'), '(\\1)', 'abc')
# returns “(a)b(c)”, really “(ϵaϵ)b(ϵcϵ)”

(Note that adding “$” to the patterns doesn’t change anything.)

Now, VimL works in the Perl way, except that “*” includes the empty
string if it is the last one in the string:

echo substitute('abc', '[ac]*', '(\0)', 'g')
" returns “(a)()b(c)”, really “(ϵa)(ϵ)b(ϵcϵ)”

As far as I’m concerned, I find the Perl way quite counter-intuitive,
but what I’m interested in here is whether VimL is consistent or not.
I.e., shouldn’t it work clearly one way or the other?

Best,
Paul

[Paul Isambert]

Sorry, this

> print re.sub(re.compile('(a*)'), '(\\1)', 'abc')

should be

print re.sub(re.compile('([ac]*)'), '(\\1)', 'abc')

Paul

[John Little]

On Tuesday, June 18, 2013 11:19:43 PM UTC+12, Paul Isambert wrote:

> I.e., shouldn’t it work clearly one way or the other?

I don't understand this "interspersed empty substrings" way of looking at regexes; I suspect that it doesn't make sense some of the time, and is not useful, but my suspicions may obviously stem from my incomprehension.

A pattern like [ac]* on its own matches everywhere; so vim does the substitution everywhere. Why is that not intuitive? Anyway, as I see it, vim is consistent.

Doing substitutions with a pattern that matches the empty string is not useful, in real editing tasks it's not what is wanted. One is always trying to match *something*.

Regards, John Little

[Paul Isambert]

John Little <John.B...@gmail.com> a écrit:

> On Tuesday, June 18, 2013 11:19:43 PM UTC+12, Paul Isambert wrote:
>
> > I.e., shouldn’t it work clearly one way or the other?
>
> I don't understand this "interspersed empty substrings" way of
> looking at regexes; I suspect that it doesn't make sense some of the
> time, and is not useful, but my suspicions may obviously stem from my
> incomprehension.

The empty substrings are only a means to account for the difference
between Perl-like and Python-like languages; it is interesting only
inasmuch as it achieves that, and shouldn’t be extended to understand
regexps any further. (Dirk Laurie formalizes that with open/closed
intervals here: http://lua-users.org/lists/lua-l/2013-04/msg00869.html.)

> A pattern like [ac]* on its own matches everywhere; so vim does the
> substitution everywhere. Why is that not intuitive? Anyway, as I see
> it, vim is consistent.

The issue is what “everywhere” means. Perl-like languages include
“just after a successful match”, hence “(a)()b(c)()”, Python-like
ones do not, hence “(a)b(c)”. The presumed inconsistency in VimL is
that it includes “just after a successful match”, unless we’re at the
end of the string, hence “(a)()b(c)”.

> Doing substitutions with a pattern that matches the empty string is
> not useful, in real editing tasks it's not what is wanted. One is
> always trying to match *something*.

The “*” operator should be banned, then!

Best,
Paul

[Erik Christiansen]

On 18.06.13 14:51, Paul Isambert wrote:
> The “*” operator should be banned, then!

Does the problem with matching empty strings arise from using "*" when
"+" should be used instead? You are presumably aware that¹:

* = 0 or more of the preceding atom.
+ = 1 or more of the preceding atom.

Thus "(a|b)+" means one or more a or b characters, and cannot match the
empty string. Use "*" instead, and you've instructed it to also match "".

There are many regex dialects - enough to fill a fat O'Reilly book, and
enough to make anyone's head hurt. One way to minimise the confusion is
to cultivate fluency in one dialect, and eschew the others.

Having long ago found posix BREs annoyingly full of superfluous
backslashes, I've settled for the more concise and powerful posix EREs.
Also, "man 7 regex" agrees that BREs are obsolete. (To get away from
obsolete regexes in vim, prefix regexes with "\v". That is a good
approximation of posix EREs, and so is consistent with many *nix
utilities, so you can effortlessly switch from awk, bash, egrep,
procmail, etc, etc, to vim with "\v".)

Erik

¹ In posix EREs, and most others, though in some vim modes, "+" isn't
"magic". Those obsolete regex modes are worth avoiding.

--
Leibowitz's Rule:
When hammering a nail, you will never hit your finger if you hold the
hammer with both hands.

[Ben Fritz]

On Tuesday, June 18, 2013 7:51:06 AM UTC-5, Paul Isambert wrote:
>
> > Doing substitutions with a pattern that matches the empty string is
>
> > not useful, in real editing tasks it's not what is wanted. One is
>
> > always trying to match *something*.
>
>
>
> The “*” operator should be banned, then!
>

The * should not be used by itself. But it is very useful in combination with other stuff.

For example, I use a tool which generates variable names automatically from graphically-created GUI widgets. I'm sometimes not sure whether there is a single _, two __, or none at all between two parts of a variable name, so I'll search for something like "firstpart_*secondpart". Other examples (not even auto-generated) are when there might be a word in between, like "firstpart\w*secondpart".

[Paul Isambert]

Erik Christiansen <dva...@internode.on.net> a écrit:

> On 18.06.13 14:51, Paul Isambert wrote:
> > The “*” operator should be banned, then!
>
> Does the problem with matching empty strings arise from using "*" when
> "+" should be used instead? You are presumably aware that¹:
>
> * = 0 or more of the preceding atom.
> + = 1 or more of the preceding atom.
>
> Thus "(a|b)+" means one or more a or b characters, and cannot match the
> empty string. Use "*" instead, and you've instructed it to also match "".

I’ve no problem with the empty string in itself. Rather, my original
question was to know where there was an empty string, and whether VimL
follows Perl or Python in that respect. Of course I use “+” when
necessary.

> There are many regex dialects - enough to fill a fat O'Reilly book, and
> enough to make anyone's head hurt. One way to minimise the confusion is
> to cultivate fluency in one dialect, and eschew the others.
>
> Having long ago found posix BREs annoyingly full of superfluous
> backslashes, I've settled for the more concise and powerful posix EREs.
> Also, "man 7 regex" agrees that BREs are obsolete. (To get away from
> obsolete regexes in vim, prefix regexes with "\v". That is a good
> approximation of posix EREs, and so is consistent with many *nix
> utilities, so you can effortlessly switch from awk, bash, egrep,
> procmail, etc, etc, to vim with "\v".)

Mapping “/” to “/\v” (and, slightly more difficult, “:s/” to “:s/\v”)
is something I’ve thought abouth doing many times but have never done,
for some reason. I wish there were a “verymagic” option by default, I
would have turned it on a long time ago.

Best,
Paul

[LCD 47]

On 18 June 2013, Paul Isambert <zappat...@free.fr> wrote:
> Hello all,
>
> The following issue has been recently discussed on the Lua mailing list:
> http://lua-users.org/lists/lua-l/2013-04/msg00812.html
>
> (It has also been independantly raised on the LuaTeX list:
> http://tug.org/pipermail/luatex/2013-June/004418.html)
>
> If I understand correctly, any string can be represented with
> interspersed empty substrings. E.g. “abc” is really “ϵaϵbϵcϵ”, where
> “ϵ” is the empty string. Now, there seems to be two ways to deal with
> those empty strings in regexps, especially regarding the “*” operator:

You're making up a metaphysics of empty substrings. I humbly submit
that there is no such thing in the programming languages you mention
(don't know about Lua though).

> - The Perl way: “X*” matches as many “X” as possible, and does not
> include the following empty string.

$ echo -n abc | perl -pe 's/[ac]*/($&)/g'
(a)()b(c)()

The key to understanding this is to keep in mind that:

(1) "*" is greedy; and
(2) "/g" is defined as "Global matching, and keep the Current position
after failed matching."

Try something like this if you want the gory details:

$ echo -n abc | perl -Mre=debug -ne 's/[ac]*/($&)/g'

> - The Python (or sed) way: “X*” matches as many “X” as possible, and
> includes the following empty string.
>
> Starting empty strings are always included. So, the Perl way gives (I
> use Ruby, since I can’t speak Perl):
>
> puts 'abc'.gsub(/[ac]*/, '(\0)')
> # returns “(a)()b(c)()”, really “(ϵa)(ϵ)b(ϵc)(ϵ)”

Same thing with Ruby: there's a current position pointer, keeping
track of the current match.

> And the Python way:
>
> import re
> print re.sub(re.compile('(a*)'), '(\\1)', 'abc')
> # returns “(a)b(c)”, really “(ϵaϵ)b(ϵcϵ)”

With Python, re.sub() "return[s] the string obtained by replacing
the leftmost non-overlapping occurrences of pattern in string by the
replacement repl". It's the same thing, except for an optimisation:
"empty matches are included in the result unless they touch the
beginning of another match".

> (Note that adding “$” to the patterns doesn’t change anything.)
>
> Now, VimL works in the Perl way, except that “*” includes the empty
> string if it is the last one in the string:
>
> echo substitute('abc', '[ac]*', '(\0)', 'g')
> " returns “(a)()b(c)”, really “(ϵa)(ϵ)b(ϵcϵ)”

Again the same thing, except the optimisation above is applied only
at the end of the string.

> As far as I’m concerned, I find the Perl way quite counter-intuitive,
> but what I’m interested in here is whether VimL is consistent or not.
> I.e., shouldn’t it work clearly one way or the other?

You came up with the concept of "ϵ", you fix its limitations. :)

My conclusion to the above comparison is that Vim should apply the
same optimisation in full, that is, kill the empty matches that touch
the beginning of another match. As far as I can tell, that would be
safe for both the old and the new regexp engines.

/lcd

[Paul Isambert]

LCD 47 <lcd...@gmail.com> a écrit:

> On 18 June 2013, Paul Isambert <zappat...@free.fr> wrote:
> > Hello all,
> >
> > The following issue has been recently discussed on the Lua mailing list:
> > http://lua-users.org/lists/lua-l/2013-04/msg00812.html
> >
> > (It has also been independantly raised on the LuaTeX list:
> > http://tug.org/pipermail/luatex/2013-June/004418.html)
> >
> > If I understand correctly, any string can be represented with
> > interspersed empty substrings. E.g. “abc” is really “ϵaϵbϵcϵ”, where
> > “ϵ” is the empty string. Now, there seems to be two ways to deal with
> > those empty strings in regexps, especially regarding the “*” operator:
>
> You're making up a metaphysics of empty substrings. I humbly submit
> that there is no such thing in the programming languages you mention
> (don't know about Lua though).

As I’ve already said, the empty strings were just meant to capture the
differences between languages. I did not mean to imply that those
substrings have any kind of reality.

Yes. My question simply was: is it consistent to optimize only at the
end?

> > As far as I’m concerned, I find the Perl way quite counter-intuitive,
> > but what I’m interested in here is whether VimL is consistent or not.
> > I.e., shouldn’t it work clearly one way or the other?
>
> You came up with the concept of "ϵ", you fix its limitations. :)

The “metaphysics of empty substrings”, the “concept of ϵ”... please, I
know I’m French, but that doesn’t mean I subscribe to French Theory! :)

> My conclusion to the above comparison is that Vim should apply the
> same optimisation in full, that is, kill the empty matches that touch
> the beginning of another match. As far as I can tell, that would be
> safe for both the old and the new regexp engines.

I prefer it that way too. But I’d prefer no optimization rather than
conditional optimization, as is the case now.

Best,
Paul

[Erik Christiansen]

On 18.06.13 18:05, Paul Isambert wrote:
> Mapping “/” to “/\v” (and, slightly more difficult, “:s/” to “:s/\v”)
> is something I’ve thought abouth doing many times but have never done,
> for some reason.

Now that's a darned good idea!

> I wish there were a “verymagic” option by default, I would have turned
> it on a long time ago.

+ 1 million

Quite a few years ago, I built Vim with a proper regex library from
another FOSS project. It provided posix ERE behaviour, which worked
beautifully, except that the Vim help broke. Maybe I should have found
the time to debug that.

Erik

--
Nowlan's Theory:
He who hesitates is not only lost, but several miles from the next
freeway exit.