Re: Dealing with empty strings in regexp.

On 18 June 2013, Paul Isambert <zappathustra@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

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