Brace expansion

Brace expansion
You are encouraged to solve this task according to the task description, using any language you may know.

Brace expansion is a type of parameter expansion made popular by Unix shells, where it allows users to specify multiple similar string parameters without having to type them all out. E.g. the parameter enable_{audio,video} would be interpreted as if both enable_audio and enable_video had been specified.

Task

Write a function that can perform brace expansion on any input string, according to the following specification.
Demonstrate how it would be used, and that it passes the four test cases given below.

Specification

In the input string, balanced pairs of braces containing comma-separated substrings (details below) represent alternations that specify multiple alternatives which are to appear at that position in the output. In general, one can imagine the information conveyed by the input string as a tree of nested alternations interspersed with literal substrings, as shown in the middle part of the following diagram:

It{{em,alic}iz,erat}e{d,}	parse  ―――――▶ ‌	It ⎧ ⎨ ⎩ ⎧ ⎨ ⎩ em ⎫ ⎬ ⎭ alic iz ⎫ ⎬ ⎭ erat e ⎧ ⎨ ⎩ d ⎫ ⎬ ⎭ ‌	expand  ―――――▶ ‌	Itemized Itemize Italicized Italicize Iterated Iterate
input string		alternation tree		output (list of strings)

This tree can in turn be transformed into the intended list of output strings by, colloquially speaking, determining all the possible ways to walk through it from left to right while only descending into one branch of each alternation one comes across (see the right part of the diagram). When implementing it, one can of course combine the parsing and expansion into a single algorithm, but this specification discusses them separately for the sake of clarity.

Expansion of alternations can be more rigorously described by these rules:

a ⎧ ⎨ ⎩ 2 ⎫ ⎬ ⎭ 1 b ⎧ ⎨ ⎩ X ⎫ ⎬ ⎭ Y X c

⟶

a2bXc a2bYc a2bXc a1bXc a1bYc a1bXc

• An alternation causes the list of alternatives that will be produced by its parent branch to be increased 𝑛-fold, each copy featuring one of the 𝑛 alternatives produced by the alternation's child branches, in turn, at that position.
• This means that multiple alternations inside the same branch are cumulative  (i.e. the complete list of alternatives produced by a branch is the string-concatenating "Cartesian product" of its parts).
• All alternatives (even duplicate and empty ones) are preserved, and they are ordered like the examples demonstrate  (i.e. "lexicographically" with regard to the alternations).
• The alternatives produced by the root branch constitute the final output.

Parsing the input string involves some additional complexity to deal with escaped characters and "incomplete" brace pairs:

a\\{\\\{b,c\,d}	⟶	a\\ ⎧ ⎨ ⎩ \\\{b ⎫ ⎬ ⎭ c\,d
{a,b{c{,{d}}e}f	⟶	{a,b{c ⎧ ⎨ ⎩ ‌ ⎫ ⎬ ⎭ {d} e}f

• An unescaped backslash which precedes another character, escapes that character (to force it to be treated as literal). The backslashes are passed along to the output unchanged.
• Balanced brace pairs are identified by, conceptually, going through the string from left to right and associating each unescaped closing brace that is encountered with the nearest still unassociated unescaped opening brace to its left (if any). Furthermore, each unescaped comma is associated with the innermost brace pair that contains it (if any). With that in mind:
  • Each brace pair that has at least one comma associated with it, forms an alternation (whose branches are the brace pair's contents split at its commas). The associated brace and comma characters themselves do not become part of the output.
  • Brace characters from pairs without any associated comma, as well as unassociated brace and comma characters, as well as all characters that are not covered by the preceding rules, are instead treated as literals.

For every possible input string, your implementation should produce exactly the output which this specification mandates. Please comply with this even when it's inconvenient, to ensure that all implementations are comparable. However, none of the above should be interpreted as instructions (or even recommendations) for how to implement it. Try to come up with a solution that is idiomatic in your programming language. (See #Perl for a reference implementation.)

Test Cases

Input (single string)	Ouput (list/array of strings)
~/{Downloads,Pictures}/*.{jpg,gif,png}	~/Downloads/*.jpg ~/Downloads/*.gif ~/Downloads/*.png ~/Pictures/*.jpg ~/Pictures/*.gif ~/Pictures/*.png
It{{em,alic}iz,erat}e{d,}, please.	Itemized, please. Itemize, please. Italicized, please. Italicize, please. Iterated, please. Iterate, please.
{,{,gotta have{ ,\, again\, }}more }cowbell!	cowbell! more cowbell! gotta have more cowbell! gotta have\, again\, more cowbell!
{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}	{}} some }{,{\\ edge \,}{ cases, {here} \\\\\} {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

---

AutoHotkey

This example is incorrect. Please fix the code and remove this message. Details: Output for edge cases is wrong.

<lang autohotkey>; AutoHotkey runs Perl-compatible regular expressions no problem t=~/{Downloads,Pictures}/ *.{jpg,gif,png} ; Note I added a space so the RosettaCode syntax highlighting will work. The AutoHotkey interpreter handles it no problem. msgbox % expand(t) t=It{{em,alic}iz,erat}e{d,}, please. msgbox % expand(t) t={,{,gotta have{ ,\, again\, }}more }cowbell! msgbox % expand(t) t={}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\} msgbox % expand(t)

expand(t) { t:=RegExReplace(t, "\\\\", "\!") ; if you want to use these character combinations literally in your string, just switch these susbstitutions to something unicode ,t:=RegExReplace(t, "\\,", "\#") ,t:=RegExReplace(t, "\\\{", "\@") ,t:=RegExReplace(t, "\\\}", "\&") a=1 While a or b ; expand (braces with multiple commas) which are (apparently inside something else) t:=RegExReplace(t, "Sxm)^(.*) ([{,]) ([^{},]*) \{ ([^{},]*) , ([^{},]* , [^{}]*) \} ([^{},]*?) ([},]) (.*)$", "$1$2$3$4$6,$3{$5}$6$7$8", a) ; expand (braces with single commas) which are (apparently inside something else) ,t:=RegExReplace(t, "Sxm)^(.*) ([{,]) ([^{},]*) \{ ([^{},]*) , ([^{},]*) \} ([^{},]*?) ([},]) (.*)$", "$1$2$3$4$6,$3$5$6$7$8", b) a=1 While a or b ; expand braces with single commas t:=RegExReplace(t, "Sxm)^(.*) \{ ([^{},]*) , ([^{},]*) \} (.*)$", "$1$2$4`r`n$1$3$4", a) ; expand braces with multiple commas ,t:=RegExReplace(t, "Sxm)^(.*) \{ ([^{},]*) , ([^{},]* , [^{}]*) \} (.*)$", "$1$2$4`r`n$1{$3}$4", b) t:=RegExReplace(t, "\\!", "\\") ,t:=RegExReplace(t, "\\#", "\,") ,t:=RegExReplace(t, "\\@", "\{") ,t:=RegExReplace(t, "\\&", "\}") Return t }</lang>

Output:

~/Downloads/*.jpg
~/Downloads/*.gif
~/Downloads/*.png
~/Pictures/*.jpg
~/Pictures/*.gif
~/Pictures/*.png

Itemized, please.
Itemize, please.
Italicized, please.
Italicize, please.
Iterated, please.
Iterate, please.

cowbell!
more cowbell!
gotta have more cowbell!
gotta have\, again\, more cowbell!

{}} some {\\edge }{ cases, here\\\}
{}} some {\\edgy }{ cases, here\\\}

C++

C++11 solution:

<lang cpp>#include <iostream>

1. include <iterator>
2. include <string>
3. include <utility>
4. include <vector>

namespace detail {

template <typename ForwardIterator> class tokenizer {

ForwardIterator _tbegin, _tend, _end;

public:

tokenizer(ForwardIterator begin, ForwardIterator end) : _tbegin(begin), _tend(begin), _end(end) { }

template <typename Lambda> bool next(Lambda istoken) { if (_tbegin == _end) { return false; } _tbegin = _tend; for (; _tend != _end && !istoken(*_tend); ++_tend) { if (*_tend == '\\' && std::next(_tend) != _end) { ++_tend; } } if (_tend == _tbegin) { _tend++; } return _tbegin != _end; }

ForwardIterator begin() const { return _tbegin; } ForwardIterator end() const { return _tend; } bool operator==(char c) { return *_tbegin == c; }

};

template <typename List> void append_all(List & lista, const List & listb) { if (listb.size() == 1) { for (auto & a : lista) { a += listb.back(); } } else { List tmp; for (auto & a : lista) { for (auto & b : listb) { tmp.push_back(a + b); } } lista = std::move(tmp); } }

template <typename String, typename List, typename Tokenizer> List expand(Tokenizer & token) {

std::vector<List> alts{ { String() } };

while (token.next([](char c) { return c == '{' || c == ',' || c == '}'; })) {

if (token == '{') { append_all(alts.back(), expand<String, List>(token)); } else if (token == ',') { alts.push_back({ String() }); } else if (token == '}') { if (alts.size() == 1) { for (auto & a : alts.back()) { a = '{' + a + '}'; } return alts.back(); } else { for (std::size_t i = 1; i < alts.size(); i++) { alts.front().insert(alts.front().end(), std::make_move_iterator(std::begin(alts[i])), std::make_move_iterator(std::end(alts[i]))); } return std::move(alts.front()); } } else { for (auto & a : alts.back()) { a.append(token.begin(), token.end()); } }

}

List result{ String{ '{' } }; append_all(result, alts.front()); for (std::size_t i = 1; i < alts.size(); i++) { for (auto & a : result) { a += ','; } append_all(result, alts[i]); } return result; }

} // namespace detail

template < typename ForwardIterator, typename String = std::basic_string< typename std::iterator_traits<ForwardIterator>::value_type >, typename List = std::vector<String> > List expand(ForwardIterator begin, ForwardIterator end) { detail::tokenizer<ForwardIterator> token(begin, end); List list{ String() }; while (token.next([](char c) { return c == '{'; })) { if (token == '{') { detail::append_all(list, detail::expand<String, List>(token)); } else { for (auto & a : list) { a.append(token.begin(), token.end()); } } } return list; }

template < typename Range, typename String = std::basic_string<typename Range::value_type>, typename List = std::vector<String> > List expand(const Range & range) { using Iterator = typename Range::const_iterator; return expand<Iterator, String, List>(std::begin(range), std::end(range)); }

int main() {

for (std::string string : { R"(~/{Downloads,Pictures}/*.{jpg,gif,png})", R"(It{{em,alic}iz,erat}e{d,}, please.)", R"({,{,gotta have{ ,\, again\, }}more }cowbell!)", R"({}} some {\\{edge,edgy} }{ cases, here\\\})", R"(a{b{1,2}c)", R"(a{1,2}b}c)", R"(a{1,{2},3}b)", R"(a{b{1,2}c{}})", R"(more{ darn{ cowbell,},})", R"(ab{c,d\,e{f,g\h},i\,j{k,l\,m}n,o\,p}qr)", R"({a,{\,b}c)", R"(a{b,Template:C)", R"({a{\}b,c}d)", R"({a,b{{1,2}e}f)", R"({}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\})", R"({{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{)", }) { std::cout << string << '\n'; for (auto expansion : expand(string)) { std::cout << " " << expansion << '\n'; } std::cout << '\n'; }

return 0; }</lang>

Common Lisp

<lang lisp>(defstruct alternation

 (alternatives nil :type list))

(defun alternatives-end-positions (string start)

 (assert (char= (char string start) #\{))
 (loop with level = 0
       with end-positions
       with escapep and commap
       for index from start below (length string)
       for c = (char string index)
       do (cond (escapep
                 (setf escapep nil))
                ((char= c #\\)
                 (setf escapep t))
                ((char= c #\{)
                 (incf level))
                ((char= c #\})
                 (decf level)
                 (when (zerop level)
                   (push index end-positions)
                   (loop-finish)))
                ((and (char= c #\,) (= level 1))
                 (setf commap t)
                 (push index end-positions)))
       finally (return (and (zerop level) commap (nreverse end-positions)))))

(defun parse-alternation (string start)

 (loop with end-positions = (alternatives-end-positions string start)
       for %start = (1+ start) then (1+ %end)
       for %end in end-positions
       collect (parse string :start %start :end %end) into alternatives
       finally (return (and alternatives
                            (values (make-alternation :alternatives alternatives) (1+ %end))))))

(defun parse (string &key (start 0) (end (length string)))

 (loop with result and escapep
       for index = start then next
       while (< index end)
       for c = (char string index)
       for next = (1+ index)
       do (cond (escapep
                 (push c result)
                 (setf escapep nil))
                ((char= c #\\)
                 (push c result)
                 (setf escapep t))
                ((char= c #\{)
                 (multiple-value-bind (alternation next-index)
                     (parse-alternation string index)
                   (cond (alternation
                          (push alternation result)
                          (setf next next-index))
                         (t
                          (push c result)))))
                (t
                 (push c result)))
       finally (return (nreverse result))))

(defun traverse-alternation (alternation)

 (mapcan #'traverse (alternation-alternatives alternation)))

(defun traverse (parsed)

 (let ((results (list nil)))
   (dolist (element parsed results)
     (etypecase element
       (character
        (setf results (loop for r in results
                            collect (nconc r (list element)))))
       (alternation
        (setf results (loop for r in results
                            nconc (loop for ar in (traverse-alternation element)
                                        collect (append r ar)))))))))

(defun expand (string)

 (loop for result in (traverse (parse string))
       collect (coerce result 'string)))

(defun main ()

 (dolist (input '("~/{Downloads,Pictures}/*.{jpg,gif,png}"
                  "It{{em,alic}iz,erat}e{d,}, please."
                  "{,{,gotta have{ ,\\, again\\, }}more }cowbell!"
                  "{}} some }{,{\\\\{ edge, edge} \\,}{ cases, {here} \\\\\\\\\\}"))
   (write-line input)
   (dolist (output (expand input))
     (format t "    ~A~%" output))
   (terpri)))</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
    ~/Downloads/*.jpg
    ~/Downloads/*.gif
    ~/Downloads/*.png
    ~/Pictures/*.jpg
    ~/Pictures/*.gif
    ~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
    Itemized, please.
    Itemize, please.
    Italicized, please.
    Italicize, please.
    Iterated, please.
    Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
    cowbell!
    more cowbell!
    gotta have more cowbell!
    gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
    {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
    {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

D

Translation of: Python

This code is not UTF-corrected, because it uses slicing instead of front, popFront, etc. <lang d>import std.stdio, std.typecons, std.array, std.range, std.algorithm, std.string;

Nullable!(Tuple!(string[], string)) getGroup(string s, in uint depth) pure nothrow @safe {

   string[] sout;
   auto comma = false;

   while (!s.empty) {
       // {const g, s} = getItems(s, depth);
       const r = getItems(s, depth);
       const g = r[0];
       s = r[1];

       if (s.empty)
           break;
       sout ~= g;

       if (s[0] == '}') {
           if (comma)
               return typeof(return)(tuple(sout, s[1 .. $]));
           return typeof(return)(tuple(
               sout.map!(a => '{' ~ a ~ '}').array, s[1 .. $]));
       }

       if (s[0] == ',') {
           comma = true;
           s = s[1 .. $];
       }
   }
   return typeof(return)();

}

Tuple!(string[], string) getItems(string s, in uint depth=0) pure @safe nothrow {

   auto sout = [""];

   while (!s.empty) {
       auto c = s[0 .. 1];
       if (depth && (c == "," || c == "}"))
           return tuple(sout, s);

       if (c == "{") {
           /*const*/ auto x = getGroup(s.dropOne, depth + 1);
           if (!x.isNull) {
               sout = cartesianProduct(sout, x[0])
                      .map!(ab => ab[0] ~ ab[1])
                      .array;
               s = x[1];
               continue;
           }
       }

       if (c == "\\" && s.length > 1) {
           c ~= s[1];
           s = s[1 .. $];
       }

       sout = sout.map!(a => a ~ c).array;
       s = s[1 .. $];
   }
   return tuple(sout, s);

}

void main() @safe {

   immutable testCases = r"~/{Downloads,Pictures}/*.{jpg,gif,png}

It{{em,alic}iz,erat}e{d,}, please. {,{,gotta have{ ,\, again\, }}more }cowbell! {}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\} a{b{1,2}c a{1,2}b}c a{1,{2},3}b a{b{1,2}c{}} more{ darn{ cowbell,},} ab{c,d\,e{f,g\h},i\,j{k,l\,m}n,o\,p}qr {a,{\,b}c a{b,Template:C {a{\}b,c}d {a,b{{1,2}e}f";

   foreach (const s; testCases.splitLines)
       writefln("%s\n%-(    %s\n%)\n", s, s.getItems[0]);

}</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
    ~/Downloads/*.jpg
    ~/Downloads/*.gif
    ~/Downloads/*.png
    ~/Pictures/*.jpg
    ~/Pictures/*.gif
    ~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
    Itemized, please.
    Itemize, please.
    Italicized, please.
    Italicize, please.
    Iterated, please.
    Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
    cowbell!
    more cowbell!
    gotta have more cowbell!
    gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
    {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
    {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

a{b{1,2}c
    a{b1c
    a{b2c

a{1,2}b}c
    a1b}c
    a2b}c

a{1,{2},3}b
    a1b
    a{2}b
    a3b

a{b{1,2}c{}}
    a{b1c{}}
    a{b2c{}}

more{ darn{ cowbell,},}
    more darn cowbell
    more darn
    more

ab{c,d\,e{f,g\h},i\,j{k,l\,m}n,o\,p}qr
    abcqr
    abd\,efqr
    abd\,eg\hqr
    abi\,jknqr
    abi\,jl\,mnqr
    abo\,pqr

{a,{\,b}c
    {a,{\,b}c

a{b,{{c}}
    a{b,{{c}}

{a{\}b,c}d
    {a\}bd
    {acd

{a,b{{1,2}e}f
    {a,b{1e}f
    {a,b{2e}f

Elixir

Translation of: Ruby

<lang elixir>defmodule Brace_expansion do

 def getitem(s), do: getitem(String.codepoints(s), 0, [""])
 
 defp getitem([], _, out), do: {out,[]}
 defp getitem([c|_]=s, depth, out) when depth>0 and (c == "," or c == "}"), do: {out,s}
 defp getitem([c|t], depth, out) do
   x = getgroup(t, depth+1, [], false)
   if (c == "{") and x do
     {y, z} = x
     out2 = for a <- out, b <- y, do: a<>b
     getitem(z, depth, out2)
   else
     if c == "\\" and length(t) > 0 do
       c2 = c <> hd(t)
       getitem(tl(t), depth, Enum.map(out, fn a -> a <> c2 end))
     else 
       getitem(t, depth, Enum.map(out, fn a -> a <> c end))
     end
   end
 end
 
 defp getgroup([], _, _, _), do: nil
 defp getgroup(s, depth, out, comma) do
   {g, s2} = getitem(s, depth, [""])
   if s2 == [] do
     nil
   else
     out2 = out ++ g
     case hd(s2) do
       "}" -> if comma, do: {out2, tl(s2)},
                      else: {Enum.map(out2, &"{#{&1}}"), tl(s2)}
       "," -> getgroup(tl(s2), depth, out2, true)
       _   -> getgroup(s2, depth, out2, comma)
     end
   end
 end

end

test_cases = ~S""" ~/{Downloads,Pictures}/*.{jpg,gif,png} It{{em,alic}iz,erat}e{d,}, please. {,{,gotta have{ ,\, again\, }}more }cowbell! {}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\} """ |> String.split("\n", trim: true)

Enum.each(test_cases, fn s ->

 IO.puts s
 Brace_expansion.getitem(s)
 |> elem(0)
 |> Enum.each(fn str -> IO.puts "\t#{str}" end)
 IO.puts ""

end)</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
        ~/Downloads/*.jpg
        ~/Downloads/*.gif
        ~/Downloads/*.png
        ~/Pictures/*.jpg
        ~/Pictures/*.gif
        ~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
        Itemized, please.
        Itemize, please.
        Italicized, please.
        Italicize, please.
        Iterated, please.
        Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
        cowbell!
        more cowbell!
        gotta have more cowbell!
        gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
        {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
        {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Haskell

"Here is a direct translation to Haskell using parsec" (of an earlier version of the Perl 6 solution):

<lang haskell>import Control.Applicative (liftA2, pure, (<$>), (<*>)) import Control.Monad (forever) import Text.Parsec

parser :: Parsec String u [String] parser = expand <$> many (try alts <|> try alt1 <|> escape <|> pure . pure <$> anyChar)

   where
       alts = concat <$> between (char '{') (char '}') (alt `sepBy2` char ',')
       alt1 = (:[]).('{':).(++"}") <$> between (char '{') (char '}') (many $ noneOf ",{}")
       alt = expand <$> many (try alts <|> try alt1 <|> escape <|> pure . pure <$> noneOf ",}")
       escape = pure <$> sequence [char '\\', anyChar]
       expand = foldr (liftA2 (++)) [""]
       p `sepBy2` sep = liftA2 (:) p (many1 (sep >> p))

main :: IO () main = forever $ parse parser [] <$> getLine >>= either print (mapM_ putStrLn)</lang>

Output:

$ ./bracex
~/{Downloads,Pictures}/*.{jpg,gif,png}
~/Downloads/*.jpg
~/Downloads/*.gif
~/Downloads/*.png
~/Pictures/*.jpg
~/Pictures/*.gif
~/Pictures/*.png
It{{em,alic}iz,erat}e{d,}, please.
Itemized, please.
Itemize, please.
Italicized, please.
Italicize, please.
Iterated, please.
Iterate, please.
{,{,gotta have{ ,\, again\, }}more }cowbell!
cowbell!
more cowbell!
gotta have more cowbell!
gotta have\, again\, more cowbell!
{}} some {\\{edge,edgy} }{ cases, here\\\}
{}} some {\\edge }{ cases, here\\\}
{}} some {\\edgy }{ cases, here\\\}
a{b{1,2}c
a{b1c
a{b2c
a{1,2}b}c
a1b}c
a2b}c
a{1,{2},3}b
a1b
a{2}b
a3b
a{b{1,2}c{}}
a{b1c{}}
a{b2c{}}
^D
bracex: <stdin>: hGetLine: end of file

Go

expand.go: <lang go>package expand

// Expander is anything that can be expanded into a slice of strings. type Expander interface { Expand() []string }

// Text is a trivial Expander that expands to a slice with just itself. type Text string

func (t Text) Expand() []string { return []string{string(t)} }

// Alternation is an Expander that expands to the union of its // members' expansions. type Alternation []Expander

func (alt Alternation) Expand() []string { var out []string for _, e := range alt { out = append(out, e.Expand()...) } return out }

// Sequence is an Expander that expands to the combined sequence of its // members' expansions. type Sequence []Expander

func (seq Sequence) Expand() []string { if len(seq) == 0 { return nil } out := seq[0].Expand() for _, e := range seq[1:] { out = combine(out, e.Expand()) } return out }

func combine(al, bl []string) []string { out := make([]string, 0, len(al)*len(bl)) for _, a := range al { for _, b := range bl { out = append(out, a+b) } } return out }

// Currently only single byte runes are supported for these. const ( escape = '\\' altStart = '{' altEnd = '}' altSep = ',' )

type piT struct{ pos, cnt, depth int }

type Brace string

// Expand takes an input string and returns the expanded list of // strings. The input string can contain any number of nested // alternation specifications of the form "{A,B}" which is expanded to // the strings "A", then "B". // // E.g. Expand("a{2,1}b{X,Y,X}c") returns ["a2bXc", "a2bYc", "a2bXc", // "a1bXc", "a1bYc", "a1bXc"]. // // Unmatched '{', ',', and '}' characters are passed through to the // output. The special meaning of these characters can be escaped with // '\', (which itself can be escaped). // Escape characters are not removed, but passed through to the output. func Expand(s string) []string { return Brace(s).Expand() } func (b Brace) Expand() []string { return b.Expander().Expand() } func (b Brace) Expander() Expander { s := string(b) //log.Printf("Exapand(%#q)\n", s) var posInfo []piT var stack []int // indexes into posInfo removePosInfo := func(i int) { end := len(posInfo) - 1 copy(posInfo[i:end], posInfo[i+1:]) posInfo = posInfo[:end] }

inEscape := false for i, r := range s { if inEscape { inEscape = false continue } switch r { case escape: inEscape = true case altStart: stack = append(stack, len(posInfo)) posInfo = append(posInfo, piT{i, 0, len(stack)}) case altEnd: if len(stack) == 0 { continue } si := len(stack) - 1 pi := stack[si] if posInfo[pi].cnt == 0 { removePosInfo(pi) for pi < len(posInfo) { if posInfo[pi].depth == len(stack) { removePosInfo(pi) } else { pi++ } } } else { posInfo = append(posInfo, piT{i, -2, len(stack)}) } stack = stack[:si] case altSep: if len(stack) == 0 { continue } posInfo = append(posInfo, piT{i, -1, len(stack)}) posInfo[stack[len(stack)-1]].cnt++ } } //log.Println("stack:", stack) for len(stack) > 0 { si := len(stack) - 1 pi := stack[si] depth := posInfo[pi].depth removePosInfo(pi) for pi < len(posInfo) { if posInfo[pi].depth == depth { removePosInfo(pi) } else { pi++ } } stack = stack[:si] } return buildExp(s, 0, posInfo) }

func buildExp(s string, off int, info []piT) Expander { if len(info) == 0 { return Text(s) } //log.Printf("buildExp(%#q, %d, %v)\n", s, off, info) var seq Sequence i := 0 var dj, j, depth int for dk, piK := range info { k := piK.pos - off switch s[k] { case altStart: if depth == 0 { dj = dk j = k depth = piK.depth } case altEnd: if piK.depth != depth { continue } if j > i { seq = append(seq, Text(s[i:j])) } alt := buildAlt(s[j+1:k], depth, j+1+off, info[dj+1:dk]) seq = append(seq, alt) i = k + 1 depth = 0 } } if j := len(s); j > i { seq = append(seq, Text(s[i:j])) } if len(seq) == 1 { return seq[0] } return seq }

func buildAlt(s string, depth, off int, info []piT) Alternation { //log.Printf("buildAlt(%#q, %d, %d, %v)\n", s, depth, off, info) var alt Alternation i := 0 var di int for dk, piK := range info { if piK.depth != depth { continue } if k := piK.pos - off; s[k] == altSep { sub := buildExp(s[i:k], i+off, info[di:dk]) alt = append(alt, sub) i = k + 1 di = dk + 1 } } sub := buildExp(s[i:], i+off, info[di:]) alt = append(alt, sub) return alt }</lang> expand_test.go <lang go>package expand

import ( "fmt" "reflect" "testing" )

// These could be in expand.go but for now they're only used for debugging. func (t Text) String() string { return fmt.Sprintf("%#q", string(t)) } func (alt Alternation) String() string { return fmt.Sprintf("ALT:%v", []Expander(alt)) }

// From http://rosettacode.org/wiki/Brace_expansion var testCases = []struct { input string expected []string }{ {"", []string{""}}, {"a{2,1}b{X,Y,X}c", []string{ "a2bXc", "a2bYc", "a2bXc", "a1bXc", "a1bYc", "a1bXc"}}, {`a\\{\\\{b,c\,d}`, []string{ `a\\\\\{b`, `a\\c\,d`}}, {"{a,b{c{,{d}}e}f", []string{ "{a,b{ce}f", "{a,b{c{d}e}f"}}, {"~/{Downloads,Pictures}/*.{jpg,gif,png}", []string{ "~/Downloads/*.jpg", "~/Downloads/*.gif", "~/Downloads/*.png", "~/Pictures/*.jpg", "~/Pictures/*.gif", "~/Pictures/*.png"}}, {"It{{em,alic}iz,erat}e{d,}, please.", []string{ "Itemized, please.", "Itemize, please.", "Italicized, please.", "Italicize, please.", "Iterated, please.", "Iterate, please."}}, {`{,{,gotta have{ ,\, again\, }}more }cowbell!`, []string{ "cowbell!", "more cowbell!", "gotta have more cowbell!", `gotta have\, again\, more cowbell!`}}, {`{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}`, []string{ `{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}`, `{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}`}}, }

//func ml(l []string) string { return "\n\t" + strings.Join(l, "\n\t") } func ml(l []string) string { var result string for _, s := range l { result += fmt.Sprintf("\n\t%#q", s) } return result }

func TestExpand(t *testing.T) { for _, d := range testCases { if g := Expand(d.input); !reflect.DeepEqual(g, d.expected) { t.Errorf("unexpected result\n Expand(%#q) gave:%v\nExpected:%v", d.input, ml(g), ml(d.expected)) } else { // Normally Go tests aren't this verbose, but for rosettacode t.Logf("as expected\n Expand(%#q):%v", d.input, ml(g)) } } }

func BenchmarkExpand(b *testing.B) { input := testCases[5].input //b.Logf("Benchmarking Expand(%#q)\n", input) b.ReportAllocs() for i := 0; i < b.N; i++ { Expand(input) } }</lang>

Output:

% go test -v -bench=.
=== RUN TestExpand
--- PASS: TestExpand (0.00 seconds)
	expand_test.go:72: as expected
		 Expand(``):
			``
	expand_test.go:72: as expected
		 Expand(`a{2,1}b{X,Y,X}c`):
			`a2bXc`
			`a2bYc`
			`a2bXc`
			`a1bXc`
			`a1bYc`
			`a1bXc`
	expand_test.go:72: as expected
		 Expand(`a\\{\\\{b,c\,d}`):
			`a\\\\\{b`
			`a\\c\,d`
	expand_test.go:72: as expected
		 Expand(`{a,b{c{,{d}}e}f`):
			`{a,b{ce}f`
			`{a,b{c{d}e}f`
	expand_test.go:72: as expected
		 Expand(`~/{Downloads,Pictures}/*.{jpg,gif,png}`):
			`~/Downloads/*.jpg`
			`~/Downloads/*.gif`
			`~/Downloads/*.png`
			`~/Pictures/*.jpg`
			`~/Pictures/*.gif`
			`~/Pictures/*.png`
	expand_test.go:72: as expected
		 Expand(`It{{em,alic}iz,erat}e{d,}, please.`):
			`Itemized, please.`
			`Itemize, please.`
			`Italicized, please.`
			`Italicize, please.`
			`Iterated, please.`
			`Iterate, please.`
	expand_test.go:72: as expected
		 Expand(`{,{,gotta have{ ,\, again\, }}more }cowbell!`):
			`cowbell!`
			`more cowbell!`
			`gotta have more cowbell!`
			`gotta have\, again\, more cowbell!`
	expand_test.go:72: as expected
		 Expand(`{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}`):
			`{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}`
			`{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}`
PASS
BenchmarkExpand	  500000	      6562 ns/op	    2467 B/op	      64 allocs/op
ok  	rosetta_code/Brace_expansion	3.347s

J

Implementation:

<lang J> NB. legit { , and } do not follow a legit backslash: legit=: 1,_1}.4>(3;(_2[\"1".;._2]0 :0);('\';a.);0 _1 0 1)&;:&.(' '&,)

2 1   1 1 NB. result 0 or 1: initial state
2 2   1 2 NB. result 2 or 3: after receiving a non backslash
1 2   1 2 NB. result 4 or 5: after receiving a backslash

)

expand=:3 :0

 Ch=. u:inv y
 M=. N=. 1+>./ Ch
 Ch=. Ch*-_1^legit y
 delim=. 'left comma right'=. u:inv '{,}'
 J=. i.K=. #Ch
 while. M=. M+1 do.
   candidates=. i.0 2
   for_check.I. comma=Ch do.
     begin=. >./I. left=check{. Ch
     end=. check+<./I. right=check}. Ch
     if. K>:end-begin do.
       candidates=. candidates,begin,end
     end.
   end.
   if. 0=#candidates do. break. end.
   'begin end'=. candidates{~(i.>./) -/"1 candidates
   ndx=. I.(begin<:J)*(end>:J)*Ch e. delim
   Ch=. M ndx} Ch 
 end.
 T=. ,<Ch
 for_mark. |.N}.i.M  do.
   T=. ; mark divide each T
 end.
 u: each |each T

)

divide=:4 :0

 if. -.x e. y do. ,<y return. end.
 mask=. x=y
 prefix=. < y #~ -.+./\ mask
 suffix=. < y #~ -.+./\. mask
 options=. }:mask <;._1 y
 prefix,each options,each suffix

)</lang>

Examples:

<lang J> >expand t1 ~/Downloads/*.jpg ~/Downloads/*.gif ~/Downloads/*.png ~/Pictures/*.jpg ~/Pictures/*.gif ~/Pictures/*.png

  > expand t2

Itemized, please. Itemize, please. Italicized, please. Italicize, please. Iterated, please. Iterate, please.

  >expand t3

cowbell! more cowbell! gotta have more cowbell! gotta have\, again\, more cowbell!

  >expand t4

{}} some {\\edge }{ cases, here\\\} {}} some {\\edgy }{ cases, here\\\}</lang>

Explanation:

Instead of working directly with text, work with a string of numeric unicode values. Negate the numbers for characters which are "off limits" because of preceding backslashes (we will take the absolute value and convert back to unicode for the final result). Also, find a limit value larger than that of the largest in-use character.

Then, iteratively: for each relevant comma, find the location of the closest surrounding braces. From these candidates, pick a pair of braces that's the shortest distance apart. Mark those braces and their contained relevant commas by replacing their character codes with an integer larger than any previously used (all of them in the set get marked with the same number). Repeat until we cannot find any more possibilities.

Finally, for each integer that we've used to mark delimiter locations, split out each of the marked options (each with a copy of that group's prefix and suffix). (Then when all that is done, take the absolute values convert back to unicode for the final result.)

Java

Should be able to handle all printable Unicode. <lang java>public class BraceExpansion {

   public static void main(String[] args) {
       for (String s : new String[]{"It{{em,alic}iz,erat}e{d,}, please.",
           "~/{Downloads,Pictures}/*.{jpg,gif,png}",
           "{,{,gotta have{ ,\\, again\\, }}more }cowbell!",
           "{}} some }{,{\\\\{ edge, edge} \\,}{ cases, {here} \\\\\\\\\\}"}) {
           System.out.println();
           expand(s);
       }
   }

   public static void expand(String s) {
       expandR("", s, "");
   }

   private static void expandR(String pre, String s, String suf) {
       int i1 = -1, i2 = 0;
       String noEscape = s.replaceAll("([\\\\]{2}|[\\\\][,}{])", "  ");
       StringBuilder sb = null;

       outer:
       while ((i1 = noEscape.indexOf('{', i1 + 1)) != -1) {
           i2 = i1 + 1;
           sb = new StringBuilder(s);
           for (int depth = 1; i2 < s.length() && depth > 0; i2++) {
               char c = noEscape.charAt(i2);
               depth = (c == '{') ? ++depth : depth;
               depth = (c == '}') ? --depth : depth;
               if (c == ',' && depth == 1) {
                   sb.setCharAt(i2, '\u0000');
               } else if (c == '}' && depth == 0 && sb.indexOf("\u0000") != -1)
                   break outer;
           }
       }
       if (i1 == -1) {
           if (suf.length() > 0)
               expandR(pre + s, suf, "");
           else
               System.out.printf("%s%s%s%n", pre, s, suf);
       } else {
           for (String m : sb.substring(i1 + 1, i2).split("\u0000", -1))
               expandR(pre + s.substring(0, i1), m, s.substring(i2 + 1) + suf);
       }
   }

}</lang>

Itemized, please.
Itemize, please.
Italicized, please.
Italicize, please.
Iterated, please.
Iterate, please.

~/Downloads/*.jpg
~/Downloads/*.gif
~/Downloads/*.png
~/Pictures/*.jpg
~/Pictures/*.gif
~/Pictures/*.png

cowbell!
more cowbell!
gotta have more cowbell!
gotta have\, again\, more cowbell!

{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

JavaScript

ES5 Functional

Without importing Node.js libraries, JavaScript doesn't immediately have access to anything like Haskell's Parsec, but using a functional idiom of JavaScript, and emphasising clarity more than optimisation, we can separate out the tokenizing from the parsing, and the parsing from the generation of strings, to build a function which:

1. returns the set of expansions for each brace expression, and
2. logs a pretty-printed abstract syntax tree for each expression to the console (in a JSON format).

Each node of the parse tree consists of one of two simple functions (AND: syntagmatic concatenation, OR: flattening of paradigms) with a set of arguments, each of which may be a plain string or an AND or OR subtree. The expansions are derived by evaluating the parse tree as an expression.

<lang JavaScript>(function () {

 'use strict'

 // Index of any closing brace matching the opening brace at iPosn
 // with the indices of any immediately-enclosed commas
 function bracePair(tkns, iPosn, iNest, lstCommas) {
   if (iPosn >= tkns.length || iPosn < 0) return null;

   var t = tkns[iPosn],
     n = (t === '{') ? iNest + 1 : (t === '}' ? iNest - 1 : iNest),
     lst = (t === ',' && iNest === 1) ? lstCommas.concat(iPosn) : lstCommas;

   return n ? bracePair(tkns, iPosn + 1, n, lst) : {
     close: iPosn,
     commas: lst
   };
 }

 // Parse of a SYNTAGM subtree
 function andTree(dctSofar, tkns) {
   if (!tkns.length) return [dctSofar, []];

   var dctParse = dctSofar ? dctSofar : {
       fn: and,
       args: []
     },

     head = tkns[0],
     tail = head ? tkns.slice(1) : [],

     dctBrace = head === '{' ? bracePair(
       tkns, 0, 0, []
     ) : null,

     lstOR = dctBrace && dctBrace.close && dctBrace.commas.length ? (
       splitAt(dctBrace.close + 1, tkns)
     ) : null;

   return andTree({
     fn: and,
     args: dctParse.args.concat(
       lstOR ? orTree(dctParse, lstOR[0], dctBrace.commas) : head
     )
   }, lstOR ? lstOR[1] : tail);
 }

 // Parse of a PARADIGM subtree
 function orTree(dctSofar, tkns, lstCommas) {
   if (!tkns.length) return [dctSofar, []];
   var iLast = lstCommas.length;

   return {
     fn: or,
     args: splitsAt(
       lstCommas, tkns
     ).map(function (x, i) {
       var ts = x.slice(1, i === iLast ? -1 : void 0);

       return ts.length ? ts : [];
     }).map(function (ts) {
       return ts.length > 1 ? andTree(null, ts)[0] : ts[0];
     })
   };
 }

 // List of unescaped braces and commas, and remaining strings
 function tokens(str) {
   // Filter function excludes empty splitting artefacts
   var toS = function (x) {
     return x.toString();
   };

   return str.split(/(\\\\)/).filter(toS).reduce(function (a, s) {
     return a.concat(s.charAt(0) === '\\' ? s : s.split(
       /(\\*[{,}])/
     ).filter(toS));
   }, []);
 }

 // PARSE TREE OPERATOR (1 of 2)
 // Each possible head * each possible tail
 function and(args) {
   var lng = args.length,
     head = lng ? args[0] : null,
     lstHead = "string" === typeof head ? [head] : head;

   return lng ? (
     1 < lng ? lstHead.reduce(function (a, h) {
       return a.concat(and(args.slice(1)).map(function (t) {
         return h + t;
       }));
     }, []) : lstHead
   ) : [];
 }

 // PARSE TREE OPERATOR (2 of 2)
 // Each option flattened
 function or(args) {
   return args.reduce(function (a, b) {
     return a.concat(b);
   }, []);
 }

 // One list split into two (first sublist length n)
 function splitAt(n, lst) {
   return n < lst.length + 1 ? [lst.slice(0, n), lst.slice(n)] : [lst, []];
 }

 // One list split into several (sublist lengths [n])
 function splitsAt(lstN, lst) {
   return lstN.reduceRight(function (a, x) {
     return splitAt(x, a[0]).concat(a.slice(1));
   }, [lst]);
 }

 // Value of the parse tree
 function evaluated(e) {
   return typeof e === 'string' ? e :
     e.fn(e.args.map(evaluated));
 }

 // JSON prettyprint (for parse tree, token list etc)
 function pp(e) {
   return JSON.stringify(e, function (k, v) {
     return typeof v === 'function' ? (
       '[function ' + v.name + ']'
     ) : v;
   }, 2)
 }

 // MAIN

 // s -> [s]
 function expansions(s) {
   // BRACE EXPRESSION PARSED
   var dctParse = andTree(null, tokens(s))[0];

   // ABSTRACT SYNTAX TREE LOGGED
   console.log(pp(dctParse));

   // AST EVALUATED TO LIST OF STRINGS
   return evaluated(dctParse);
 }

 // Sample expressions, double-escaped for quotation in source code.
 var lstTests = [
   '~/{Downloads,Pictures}/*.{jpg,gif,png}',
   'It{{em,alic}iz,erat}e{d,}, please.',
   '{,{,gotta have{ ,\\, again\\, }}more }cowbell!',
   '{}} some }{,{\\\\{ edge, edge} \\,}{ cases, {here} \\\\\\\\\\}'
 ];

 // 1. Return each expression with an indented list of its expansions, while
 // 2. logging each parse tree to the console.log() stream

 return lstTests.map(function (s) {
   return s + '\n\n' + expansions(s).map(function (x) {
     return '   ' + x;
   }).join('\n');
 }).join('\n\n');

})();</lang>

Value returned by function:

~/{Downloads,Pictures}/*.{jpg,gif,png}

   ~/Downloads/*.jpg
   ~/Downloads/*.gif
   ~/Downloads/*.png
   ~/Pictures/*.jpg
   ~/Pictures/*.gif
   ~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.

   Itemized, please.
   Itemize, please.
   Italicized, please.
   Italicize, please.
   Iterated, please.
   Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!

   cowbell!
   more cowbell!
   gotta have more cowbell!
   gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}

   {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
   {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Sample of parse trees logged to the console:

<lang JavaScript>{

 "fn": "[function and]",
 "args": [
   "It",
   {
     "fn": "[function or]",
     "args": [
       {
         "fn": "[function and]",
         "args": [
           {
             "fn": "[function or]",
             "args": [
               "em",
               "alic"
             ]
           },
           "iz"
         ]
       },
       "erat"
     ]
   },
   "e",
   {
     "fn": "[function or]",
     "args": [
       "d",
       ""
     ]
   },
   ",",
   " please."
 ]

}</lang>

Julia

Translation of: Python

<lang> function getitem(s, depth=0)

   out = [""]
   while s != ""
       c = s[1]
       if depth > 0 && (c == ',' || c == '}')
           return out, s
       elseif c == '{'
           x = getgroup(s[2:end], depth+1)
           if x != ""
               out, s = [a * b for a in out, b in x[1]], x[2]
               continue
           end
       elseif c == '\\' && length(s) > 1
           s, c = s[2:end], c * s[2]
       end
       out, s = [a * c for a in out], s[2:end]
   end
   return out, s

end

function getgroup(s, depth)

   out, comma = "", false
   while s != ""
       g, s = getitem(s, depth)
       if s == "" 
           break
       end
       out = vcat([out...], [g...])
       if s[1] == '}'
           if comma
               return out, s[2:end]
           end
           return ["{" * a * "}" for a in out], s[2:end]
       end
       if s[1] == ','
           comma, s = true, s[2:end]
       end
   end
   return ""

end

const teststrings = [raw"~/{Downloads,Pictures}/*.{jpg,gif,png}",

                   raw"It{{em,alic}iz,erat}e{d,}, please.",
                   raw"{,{,gotta have{ ,\, again\, }}more }cowbell!",
                   raw"{}} some }{,{\\\\{ edge, edge} \,}{ cases, {here} \\\\\\\\\}"]
   

for s in teststrings

   println("\n", s, "\n--------------------------------------------")
   for ans in getitem(s)[1]
       println(ans)
   end

end </lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
--------------------------------------------
~/Downloads/*.jpg
~/Pictures/*.jpg
~/Downloads/*.gif
~/Pictures/*.gif
~/Downloads/*.png
~/Pictures/*.png
It{{em,alic}iz,erat}e{d,}, please.
--------------------------------------------
Itemized, please.
Italicized, please.
Iterated, please.
Itemize, please.
Italicize, please.
Iterate, please.
{,{,gotta have{ ,\, again\, }}more }cowbell!
--------------------------------------------
cowbell!
more cowbell!
gotta have more cowbell!
gotta have\  again\  more cowbell!
{}} some }{,{\\\\{ edge, edge} \,}{ cases, {here} \\\\\\\\\}'''
--------------------------------------------
{}} some }{,{\\\{ edge \}}{ cases, {here} \\\\\\\\\''''
{}} some }{,{\\\{ edge \}}{ cases, {here} \\\\\\\\\''''

Kotlin

Translation of: Java

<lang scala>// version 1.1.2

object BraceExpansion {

   fun expand(s: String) = expandR("", s, "")

   private val r = Regex("""([\\]{2}|[\\][,}{])""")

   private fun expandR(pre: String, s: String, suf: String) {
       val noEscape = s.replace(r, "  ")
       var sb = StringBuilder("")
       var i1 = noEscape.indexOf('{')
       var i2 = 0

       outer@ while (i1 != -1) {
           sb = StringBuilder(s)
           var depth = 1
           i2 = i1 + 1
           while (i2 < s.length && depth > 0) {
               val c = noEscape[i2]

               if (c == '{') depth++
               else if (c == '}') depth--

               if (c == ',' && depth == 1) sb[i2] = '\u0000'
               else if (c == '}' && depth == 0 && sb.indexOf("\u0000") != -1) break@outer
               i2++
           }
           i1 = noEscape.indexOf('{', i1 + 1)
       }
       if (i1 == -1) {
           if (suf.isNotEmpty()) expandR(pre + s, suf, "")
           else println("$pre$s$suf")
       } else {
           for (m in sb.substring(i1 + 1, i2).split('\u0000')) {
               expandR(pre + s.substring(0, i1), m, s.substring(i2 + 1) + suf)
           }
       }
   }

}

fun main(args: Array<String>) {

   val strings = arrayOf(
       """~/{Downloads,Pictures}/*.{jpg,gif,png}""",
       """It{{em,alic}iz,erat}e{d,}, please.""",
       """{,{,gotta have{ ,\, again\, }}more }cowbell!""",
       """{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}"""
   )
   for (s in strings) {
       println()
       BraceExpansion.expand(s)
   }

}</lang>

Output:

~/Downloads/*.jpg
~/Downloads/*.gif
~/Downloads/*.png
~/Pictures/*.jpg
~/Pictures/*.gif
~/Pictures/*.png

Itemized, please.
Itemize, please.
Italicized, please.
Italicize, please.
Iterated, please.
Iterate, please.

cowbell!
more cowbell!
gotta have more cowbell!
gotta have\, again\, more cowbell!

{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Perl

Perl has a built-in glob function which does brace expansion, but it can't be used to solve this task because it also does shell-like word splitting, wildcard expansion, and tilde expansion at the same time. The File::Glob core module gives access to the more low-level bsd_glob function which actually supports exclusive brace expansion, however it does not comply with this task's specification when it comes to preserving backslashes and handling unbalanced brace characters.

So here is a manual solution that implements the specification precisely:

<lang perl>sub brace_expand {

   my $input = shift;
   my @stack = ([my $current = []]);
   
   while ($input =~ /\G ((?:[^\\{,}]++ | \\(?:.|\z))++ | . )/gx) {
       if ($1 eq '{') {
           push @stack, [$current = []];
       }
       elsif ($1 eq ',' && @stack > 1) {
           push @{$stack[-1]}, ($current = []);
       }
       elsif ($1 eq '}' && @stack > 1) {
           my $group = pop @stack;
           $current = $stack[-1][-1];
           
           # handle the case of brace pairs without commas:
           @{$group->[0]} = map { "{$_}" } @{$group->[0]} if @$group == 1;
           
           @$current = map {
               my $c = $_;
               map { map { $c . $_ } @$_ } @$group;
           } @$current;
       }
       else { $_ .= $1 for @$current; }
   }
   
   # handle the case of missing closing braces:
   while (@stack > 1) {
       my $right = pop @{$stack[-1]};
       my $sep;
       if (@{$stack[-1]}) { $sep = ',' }
       else               { $sep = '{'; pop @stack }
       $current = $stack[-1][-1];
       @$current = map {
           my $c = $_;
           map { $c . $sep . $_ } @$right;
       } @$current;
   }
   
   return @$current;

}</lang>

Usage demonstration: <lang perl>while (my $input = ) {

   chomp($input);
   print "$input\n";
   print "    $_\n" for brace_expand($input);
   print "\n";

}

__DATA__ ~/{Downloads,Pictures}/*.{jpg,gif,png} It{{em,alic}iz,erat}e{d,}, please. {,{,gotta have{ ,\, again\, }}more }cowbell! {}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
    ~/Downloads/*.jpg
    ~/Downloads/*.gif
    ~/Downloads/*.png
    ~/Pictures/*.jpg
    ~/Pictures/*.gif
    ~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
    Itemized, please.
    Itemize, please.
    Italicized, please.
    Italicize, please.
    Iterated, please.
    Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
    cowbell!
    more cowbell!
    gotta have more cowbell!
    gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
    {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
    {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Perl 6

The task description allows the taking of shortcuts, but please note that we are not taking any shortcuts here. The solution is short because this particular problem happens to map quite naturally to the strengths of Perl 6.

First, the parsing is handled with a grammar that can backtrack in the few places this problem needs it. The + quantifier matches one or more alternatives (we handle the case of a single alternative in the walk now), and the % modifier requires a comma between each quantified item to its left. Note that the * quantifiers do not backtrack here, because the token keyword suppresses that; all the backtracking here fails over to a different alternative in an outer alternation (that is, things separated by the | character in the grammar. Most of these failovers just nibble an uninteresting character and continue.)

On the other end, we recursively walk the parse tree returning expanded sublists, and we do the cartesian concatenation of sublists at each level by use of the X~ operator, which is a "cross" metaoperator used on a simple ~ concatenation. As a list infix operator, X~ does not care how many items are on either side, which is just what you want in this case, since some of the arguments are strings and some are lists. Here we use a fold or reduction form in square brackets to interpose the cross-concat between each value generated by the map, which returns a mixture of lists and literal strings. One other thing that might not be obvious: if we bind to the match variable, $/, we automatically get all the syntactic sugar for its submatches. In this case, $0 is short for $/[0], and represents all the submatches captured by 0th set of parens in either TOP or alt. $<meta> is likewise short for $/<meta>, and retrieves what was captured by that named submatch. <lang perl6>grammar BraceExpansion {

   token TOP  { ( <meta> | . )* }
   token meta { '{' <alts> '}' | \\ .  }
   token alts { <alt>+ % ',' }
   token alt  { ( <meta> | <-[ , } ]> )* }

}

sub crosswalk($/) {

   [X~] , $0.map: -> $/ { ([$<meta><alts><alt>.&alternatives]) or ~$/ }

}

sub alternatives($_) {

   when :not { () }
   when 1    { '{' X~ $_».&crosswalk X~ '}' }
   default   { $_».&crosswalk }

}

sub brace-expand($s) { crosswalk BraceExpansion.parse($s) }

1. Testing:

sub bxtest(*@s) {

   for @s -> $s {
       say "\n$s";
       for brace-expand($s) {
           say "    ", $_;
       }
   }

}

bxtest Q:to/END/.lines;

   ~/{Downloads,Pictures}/*.{jpg,gif,png}
   It{{em,alic}iz,erat}e{d,}, please.
   {,{,gotta have{ ,\, again\, }}more }cowbell!
   {}} some {\\{edge,edgy} }{ cases, here\\\}
   a{b{1,2}c
   a{1,2}b}c
   a{1,{2},3}b
   a{b{1,2}c{}}
   more{ darn{ cowbell,},}
   ab{c,d\,e{f,g\h},i\,j{k,l\,m}n,o\,p}qr
   {a,{\,b}c
   a{b,Template:C
   {a{\}b,c}d
   {a,b{{1,2}e}f
   END</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
    ~/Downloads/*.jpg
    ~/Downloads/*.gif
    ~/Downloads/*.png
    ~/Pictures/*.jpg
    ~/Pictures/*.gif
    ~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
    Itemized, please.
    Itemize, please.
    Italicized, please.
    Italicize, please.
    Iterated, please.
    Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
    cowbell!
    more cowbell!
    gotta have more cowbell!
    gotta have\, again\, more cowbell!

{}} some {\\{edge,edgy} }{ cases, here\\\}
    {}} some {\\edge }{ cases, here\\\}
    {}} some {\\edgy }{ cases, here\\\}

a{b{1,2}c
    a{b1c
    a{b2c

a{1,2}b}c
    a1b}c
    a2b}c

a{1,{2},3}b
    a1b
    a{2}b
    a3b

a{b{1,2}c{}}
    a{b1c{}}
    a{b2c{}}

more{ darn{ cowbell,},}
    more darn cowbell
    more darn
    more

ab{c,d\,e{f,g\h},i\,j{k,l\,m}n,o\,p}qr
    abcqr
    abd\,efqr
    abd\,eg\hqr
    abi\,jknqr
    abi\,jl\,mnqr
    abo\,pqr

{a,{\,b}c
    {a,{\,b}c

a{b,{{c}}
    a{b,{{c}}

{a{\}b,c}d
    {a\}bd
    {acd

{a,b{{1,2}e}f
    {a,b{1e}f
    {a,b{2e}f

Phix

Fairly straightforward recursive solution <lang Phix>-- -- demo\rosetta\Brace_expansion.exw -- ================================ -- function pair(sequence stems, sequence brest)

   sequence res = {}
   for i=1 to length(stems) do
       for j=1 to length(brest) do
           res = append(res,stems[i]&brest[j])
       end for
   end for
   return res

end function

function brarse(string s) integer idx = 1

   while idx<=length(s) do
       integer ch = s[idx]
       if ch='{' then
           sequence alts = {idx}
           idx += 1
           integer l0 = idx
           bool nest = false
           integer level = 1
           while idx<=length(s) do
               switch s[idx] do
                   case '{': level += 1
                             nest = true
                   case '}': level -= 1
                             if level=0 then exit end if
                   case ',': if level=1 then
                               alts = append(alts,idx)
                             end if
                   case '\\': idx += 1
               end switch
               idx += 1
           end while
           if length(alts)>1 and level=0 then
               alts &= idx
               sequence stems = {}
               string stem = s[1..alts[1]-1]
               for i=2 to length(alts) do
                   string rest = s[alts[i-1]+1..alts[i]-1]
                   if nest then
                       sequence inners = brarse(rest)
                       for j=1 to length(inners) do
                           stems = append(stems,stem&inners[j])
                       end for
                   else
                       stems = append(stems,stem&rest)
                   end if
               end for
               return pair(stems,brarse(s[idx+1..$]))
           elsif nest then
               return pair({s[1..l0-1]},brarse(s[l0..$]))
           end if
       end if
       idx += 1
   end while
   return {s}

end function

-- (since ? and pp() add their own backslash escapes:) procedure edump(sequence x)

   for i=1 to length(x) do
       printf(1,"%s\n",{x[i]})
   end for

end procedure

edump(brarse("~/{Downloads,Pictures}/*.{jpg,gif,png}")) edump(brarse("It{{em,alic}iz,erat}e{d,}, please.")) edump(brarse(`{,{,gotta have{ ,\, again\, }}more }cowbell!`)) edump(brarse(`{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}`))</lang>

Output:

~/Downloads/*.jpg
~/Downloads/*.gif
~/Downloads/*.png
~/Pictures/*.jpg
~/Pictures/*.gif
~/Pictures/*.png
Itemized, please.
Itemize, please.
Italicized, please.
Italicize, please.
Iterated, please.
Iterate, please.
cowbell!
more cowbell!
gotta have more cowbell!
gotta have\, again\, more cowbell!
{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

PicoLisp

<lang PicoLisp>(de braceExpand (Str)

  (let Lst
     (make
        (for (Lst (chop Str)  Lst)
           (case (pop 'Lst)
              ("\\" (link (pop 'Lst)))
              ("{"
                 (recur ()
                    (let L
                       (make
                          (while
                             (case (pop 'Lst)
                                ("\\" (link (pop 'Lst)) Lst)
                                ("{" (recurse) Lst)
                                ("}" NIL)
                                ("," (link 0) Lst)  # Replace commata with '0'
                                (T (link @) Lst) ) ) )
                       (if (= "}" @)  # Was closing brace
                          (if (member 0 L)  # Has comma(ta)
                             (link (split L 0))
                             (chain (list "{") (replace L 0 ",") (list "}")))
                          (chain (list "{") (replace L 0 ",")) ) ) ) )
              (T (link @)) ) ) )
     (recur (Lst)
        (ifn (find pair Lst)
           (list (pack Lst))
           (let R (recurse (cdr Lst))
              (mapcan
                 '((A) (mapcar '((B) (pack A B)) R))
                 (if (pair (car Lst))
                    (mapcan recurse (car Lst))
                    (list (car Lst)) ) ) ) ) ) ) )</lang>

Test: <lang PicoLisp>(test

  (quote
     "~/Downloads/*.jpg"
     "~/Downloads/*.gif"
     "~/Downloads/*.png"
     "~/Pictures/*.jpg"
     "~/Pictures/*.gif"
     "~/Pictures/*.png" )
  (braceExpand "~/{Downloads,Pictures}/*.{jpg,gif,png}") )

(test

  (quote
     "Itemized, please."
     "Itemize, please."
     "Italicized, please."
     "Italicize, please."
     "Iterated, please."
     "Iterate, please." )
  (braceExpand "It{{em,alic}iz,erat}e{d,}, please.") )

(test

  (quote
     "cowbell!"
     "more cowbell!"
     "gotta have more cowbell!"
     "gotta have\, again\, more cowbell!" )
  (braceExpand "{,{,gotta have{ ,\\, again\\, }}more }cowbell!") )

(test

  (quote
     "{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}"
     "{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}" )
  (braceExpand "{}} some }{,{\\\\{ edge, edge} \\,}{ cases, {here} \\\\\\\\\\}") )</lang>

PowerShell

Works with: PowerShell version 2

<lang PowerShell> function Expand-Braces ( [string]$String )

   {
   $Escaped = $False
   $Stack = New-Object System.Collections.Stack
   $ClosedBraces = $BracesToParse = $Null

   ForEach ( $i in 0..($String.Length-1) )
       {
       Switch ( $String[$i] )
           {
           '\' {
               $Escaped = -not $Escaped
               break
               }

           '{' {
               If ( -not $Escaped ) { $Stack.Push( [pscustomobject]@{ Delimiters = @( $i ) } ) }
               }

           ',' {
               If ( -not $Escaped -and $Stack.Count ) { $Stack.Peek().Delimiters += $i }
               }

           '}' {
               If ( -not $Escaped -and $Stack.Count )
                   {
                   $Stack.Peek().Delimiters += $i
                   $ClosedBraces = $Stack.Pop()
                   If ( $ClosedBraces.Delimiters.Count -gt 2 )
                       {
                       $BracesToParse = $ClosedBraces
                       }
                   }
               }

           default { $Escaped = $False }
           }
       }

       If ( $BracesToParse )
           {
           $Start = $String.Substring( 0, $BracesToParse.Delimiters[0] )
           $End   = $String.Substring( $BracesToParse.Delimiters[-1] + 1 )

           ForEach ( $i in 0..($BracesToParse.Delimiters.Count-2) )
               {
               $Option = $String.Substring( $BracesToParse.Delimiters[$i] + 1, $BracesToParse.Delimiters[$i+1] - $BracesToParse.Delimiters[$i] - 1 )
               Expand-Braces ( $Start + $Option + $End )
               }
           }
       Else
           {
           $String
           }
   }

</lang> <lang PowerShell> $TestStrings = @(

   'It{{em,alic}iz,erat}e{d,}, please.'
   '~/{Downloads,Pictures}/*.{jpg,gif,png}'
   '{,{,gotta have{ ,\, again\, }}more }cowbell!'
   '{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}'
   )

ForEach ( $String in $TestStrings )

   {
   
   $String
   '------'
   Expand-Braces $String
   }

</lang>

Output:

It{{em,alic}iz,erat}e{d,}, please.
------
Itemized, please.
Italicized, please.
Iterated, please.
Itemize, please.
Italicize, please.
Iterate, please.

~/{Downloads,Pictures}/*.{jpg,gif,png}
------
~/Downloads/*.jpg
~/Pictures/*.jpg
~/Downloads/*.gif
~/Pictures/*.gif
~/Downloads/*.png
~/Pictures/*.png

{,{,gotta have{ ,\, again\, }}more }cowbell!
------
cowbell!
more cowbell!
gotta have more cowbell!
gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
------
{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Python

<lang python>def getitem(s, depth=0):

   out = [""]
   while s:
       c = s[0]
       if depth and (c == ',' or c == '}'):
           return out,s
       if c == '{':
           x = getgroup(s[1:], depth+1)
           if x:
               out,s = [a+b for a in out for b in x[0]], x[1]
               continue
       if c == '\\' and len(s) > 1:
           s, c = s[1:], c + s[1]

       out, s = [a+c for a in out], s[1:]

   return out,s

def getgroup(s, depth):

   out, comma = [], False
   while s:
       g,s = getitem(s, depth)
       if not s: break
       out += g

       if s[0] == '}':
           if comma: return out, s[1:]
           return ['{' + a + '}' for a in out], s[1:]

       if s[0] == ',':
           comma,s = True, s[1:]

   return None

1. stolen cowbells from perl6 example

for s in ~/{Downloads,Pictures}/*.{jpg,gif,png} It{{em,alic}iz,erat}e{d,}, please. {,{,gotta have{ ,\, again\, }}more }cowbell! {}} some }{,{\\\\{ edge, edge} \,}{ cases, {here} \\\\\\\\\}.split('\n'):

   print "\n\t".join([s] + getitem(s)[0]) + "\n"</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
        ~/Downloads/*.jpg
        ~/Downloads/*.gif
        ~/Downloads/*.png
        ~/Pictures/*.jpg
        ~/Pictures/*.gif
        ~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
        Itemized, please.
        Itemize, please.
        Italicized, please.
        Italicize, please.
        Iterated, please.
        Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
        cowbell!
        more cowbell!
        gotta have more cowbell!
        gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
        {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
        {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Racket

Translation of: Python

<lang racket>#lang racket/base (require racket/match) (define (merge-lists as . bss)

 (match bss
   ['() as]
   [(cons b bt)
    (apply merge-lists
           (for*/list ((a (in-list as)) (b (in-list b))) (append a b))
           bt)]))

(define (get-item cs depth)

 (let loop ((out '(())) (cs cs))
   (match cs
     ['() (values out cs)]
     [`(,(or #\, #\}) . ,more) #:when (positive? depth) (values out cs)]
     [`(#\{ . ,more)
      (=> no-group-match)
      (define-values (group-out group-rem) (get-group more (add1 depth) no-group-match))
      (loop (merge-lists out group-out) group-rem)]
     [(or `(#\\ ,c ,more ...) `(,c . ,more)) (loop (merge-lists out (list (list c))) more)])))

(define (get-group cs depth no-group-match)

 (let loop ((out '()) (cs cs) (comma? #f))
   (when (null? cs) (no-group-match))
   (define-values (item-out item-rem) (get-item cs depth))
   (when (null? item-rem) (no-group-match))
   (let ((out (append out item-out)))
     (match item-rem
       [`(#\} . ,more) #:when comma? (values out more)]
       [`(#\} . ,more) (values (merge-lists '((#\{)) out '((#\}))) more)]
       [`(#\, . ,more) (loop out more #t)]
       [_ (no-group-match)]))))

(define (brace-expand s)

 (let-values (([out rem] (get-item (string->list s) 0))) (map list->string out)))

(module+ test

 (define patterns
   (list
    "~/{Downloads,Pictures}/*.{jpg,gif,png}"
    "It{{em,alic}iz,erat}e{d,}, please."
    #<<P

{,{,gotta have{ ,\, again\, }}more }cowbell! P

    #<<P

{}} some }{,{\\\\{ edge, edge} \,}{ cases, {here} \\\\\\\\\} P

    ))
 (for ((s (in-list patterns)) #:when (printf "expand: ~a~%" s) (x (in-list (brace-expand s))))
   (printf "\t~a~%" x)))</lang>

Output:

expand: ~/{Downloads,Pictures}/*.{jpg,gif,png}
	~/Downloads/*.jpg
	~/Downloads/*.gif
	~/Downloads/*.png
	~/Pictures/*.jpg
	~/Pictures/*.gif
	~/Pictures/*.png
expand: It{{em,alic}iz,erat}e{d,}, please.
	Itemized, please.
	Itemize, please.
	Italicized, please.
	Italicize, please.
	Iterated, please.
	Iterate, please.
expand: {,{,gotta have{ ,\, again\, }}more }cowbell!
	cowbell!
	more cowbell!
	gotta have more cowbell!
	gotta have, again, more cowbell!
expand: {}} some }{,{\\\\{ edge, edge} \,}{ cases, {here} \\\\\\\\\}
	{}} some }{,{\\ edge ,}{ cases, {here} \\\\}
	{}} some }{,{\\ edge ,}{ cases, {here} \\\\}

REXX

<lang rexx>/*---------------------------------------------------------------------

• Brace expansion
• 26.07.2016
• s.* holds the set of strings
• --------------------------------------------------------------------*/

text.1='{,{,gotta have{ ,\, again\, }}more }cowbell!' text.2='~/{Downloads,Pictures}/*.{jpg,gif,png}' text.3='It{{em,alic}iz,erat}e{d,}, please. ' text.4='{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\} ' text.5='x{,a,b,c}{d,e}y' text.6='aa{,{,11}cc}22' text.7='{}' Parse Arg dbg oid='brace.xxx'; 'erase' oid Do case=1 To 7

 Call brac text.case
 End

Return brac:

 s.=0
 Parse Arg s
 Say 
 Say '  's
 s.1.0=1                            /* first iteration              */
 s.1.1=s                            /* the initial string           */
 Do it=1 To 10 Until todo=0         /* Iterate until all done       */
   todo=0                           /* will be 1 if more to be done */
   Call dbg 'Iteration' it
   do di=1 To s.it.0                /* show current state           */
     Call dbg 's.'it'.'di  s.it.di
     End
   ita=it+1                         /* index for next set of strings*/
   xp=0
   do di=1 To s.it.0                /* loop over all strings        */
     Call dbg it'.'di s.it.di
     Call bra s.it.di               /* analyze current string       */
     If braces=1 Then Do            /* If brace groups were found   */
       Do bgi=1 To bgdata.0         /* loop over grace groups       */
         If end.bgi=0 Then Iterate  /* Incomplete bg (... )         */
         clist=
         Do cj=1 To ci.bgi.0
           clist=clist ci.bgi.cj
           End
         Call dbg bgdata.bgi '->' clist
         If ccount.bgi>0 Then Do    /* comma(s) founf in bg         */
           Call expand bgi          /* expand this bg               */
           xp=1                     /* indicate that we worked      */
           Leave
           End
         End
       If xp=0 Then Do              /* nothing done                 */
         z=s.ita.0+1                /* copy string to next iteration*/
         s.ita.z=s.it.di
         End
       End
     Else Do                        /* no brace group               */
       z=s.ita.0+1                  /* copy string to next iteration*/
       s.ita.z=s
       s.ita.0=z
       End
     End
   Do dd=1 To s.ita.0               /* log current set of strings   */
     Call dbg ita dd s.ita.dd
     End
   End
 Do dd=1 To s.it.0                  /* show final set of strings    */
   Say dd s.it.dd
   End
 Return

bra: /*---------------------------------------------------------------------

• Analyze the given string
• Input: s
• Output:
• bgdata.* Array of data about brace groups:
• level start column comma positions end column
• --------------------------------------------------------------------*/

parse Arg s Call dbg 'bra:' s level=0 bgdata.=0 bgn=0 bgnmax=0 ccount.=0 ol= ci.=0 bgnl= braces=0 end.=0 escape=0 Do i=1 To length(s)

 c=substr(s,i,1)
 Select
   When escape Then
     escape=0
   When c='\' Then
     escape=1
   When c='{' Then Do
     level=level+1
     Call bm c
     co=level
     End
   When c='}' Then Do
     If level>0 Then Do
       co=level
       Call bm c
       level=level-1
       End
     End
   When c=',' Then Do
     co=level
     If co>0 Then Do
       ccount.bgn=ccount.bgn+1
       z=ccount.bgn
       ci.bgn.0=z
       ci.bgn.z=i
       End
     If ccount.bgn>0 Then
       braces=1
     End
   Otherwise
     co=level
   End
 ol=ol||co
 bgnl=bgnl||bgn
 End

Call dbg s Call dbg ol Call dbg left(copies('123456789.',10),length(s)) Call dbg bgnl Do bgi=1 To bgdata.0

 If end.bgi=1 Then Do
   cl=
   Do cii=1 To ci.bgi.0
     cl=cl ci.bgi.cii
     End
   Parse Var bgdata.bgi level a e
   Call dbg bgi level a cl e
   End
 End

Return

bm: /*---------------------------------------------------------------------

• Brace Management
• for '{' create a new brace group )record level and start column
• for '}' look for corresponding bg and add end column
• Input: column and character ( '{' or '}' )
• Output: bgdata.* level start-column [end-column]
• --------------------------------------------------------------------*/

 Parse Arg oc
 Call dbg oc i level
 If oc='{' Then Do
   z=bgdata.0+1
   bgdata.z=level i
   bgdata.0=z
   bgn=bgnmax+1
   bgnmax=bgn
   End
 Else Do
   Do bgi=bgdata.0 To 1 By -1
     If level=word(bgdata.bgi,1) Then Do
       bgdata.bgi=bgdata.bgi i
       end.bgi=1
       Leave
       End
     End
   bgn=bgn-1
   Call dbg bgdata.bgi 'bgn='bgn
   End
 Return

expand: /*---------------------------------------------------------------------

• Expand a brace group in string s
• --------------------------------------------------------------------*/

 Parse Arg bgi
 Parse Var bgdata.bgi . start end
 clist=start clist end
 If words(clist)>0 Then Do          /* commas in brace group        */
   left=left(s,start-1)             /* part of s before the '{'     */
   rite=substr(s,end+1)             /* part of s after the '}'      */
   Do k=1 To words(clist)-1         /* Loop over comma positions    */
     a=word(clist,k)                /* start position               */
     e=word(clist,k+1)              /* end position                 */
     choice.k=substr(s,a+1,e-a-1)   /* one of the choices           */
     z=s.ita.0+1                    /* add new string to next set   */
     s.ita.z=left||choice.k||rite   /* construct new string         */
     s.ita.0=z
     todo=1                         /* maybe more to be done        */
     End
   End
 Else Do                            /* no commas                    */
   z=s.ita.0+1                      /* copy string as is to next set*/
   s.ita.z=s
   s.ita.0=z
   End
 Do zz=1 To s.ita.0
   Call dbg zz s.ita.zz
   End
 Return

dbg: /* handle debug output */

 If dbg<> Then                    /* argument given               */
   Say arg(1)                       /* show on screen               */
 Call lineout oid,arg(1)            /* write to file                */
 Return</lang>

Output:

J:\>rexx braces

  {,{,gotta have{ ,\, again\, }}more }cowbell!
1 cowbell!
2 more cowbell!
3 gotta have more cowbell!
4 gotta have\, again\, more cowbell!

  ~/{Downloads,Pictures}/*.{jpg,gif,png}
1 ~/Downloads/*.jpg
2 ~/Downloads/*.gif
3 ~/Downloads/*.png
4 ~/Pictures/*.jpg
5 ~/Pictures/*.gif
6 ~/Pictures/*.png

  It{{em,alic}iz,erat}e{d,}, please.
1 Itemized, please.
2 Itemize, please.
3 Italicized, please.
4 Italicize, please.
5 Iterated, please.
6 Iterate, please.

  {}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
1 {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
2 {}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

  x{,a,b,c}{d,e}y
1 xdy
2 xey
3 xady
4 xaey
5 xbdy
6 xbey
7 xcdy
8 xcey

  aa{,{,11}cc}22
1 aa22
2 aacc22
3 aa11cc22

  {}
1 {}

Ruby

Translation of: Python

<lang ruby>def getitem(s, depth=0)

 out = [""]
 until s.empty?
   c = s[0]
   break  if depth>0 and (c == ',' or c == '}')
   if c == '{' and x = getgroup(s[1..-1], depth+1)
     out = out.product(x[0]).map{|a,b| a+b}
     s = x[1]
   else
     s, c = s[1..-1], c + s[1]  if c == '\\' and s.size > 1
     out, s = out.map{|a| a+c}, s[1..-1]
   end
 end
 return out, s

end

def getgroup(s, depth)

 out, comma = [], false
 until s.empty?
   g, s = getitem(s, depth)
   break  if s.empty?
   out += g
   case s[0]
     when '}' then return (comma ? out : out.map{|a| "{#{a}}"}), s[1..-1]
     when ',' then comma, s = true, s[1..-1]
   end
 end

end

strs = <<'EOS' ~/{Downloads,Pictures}/*.{jpg,gif,png} It{{em,alic}iz,erat}e{d,}, please. {,{,gotta have{ ,\, again\, }}more }cowbell! {}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\} EOS

strs.each_line do |s|

 puts s.chomp!
 puts getitem(s)[0].map{|str| "\t"+str}
 puts

end</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
	~/Downloads/*.jpg
	~/Downloads/*.gif
	~/Downloads/*.png
	~/Pictures/*.jpg
	~/Pictures/*.gif
	~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
	Itemized, please.
	Itemize, please.
	Italicized, please.
	Italicize, please.
	Iterated, please.
	Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
	cowbell!
	more cowbell!
	gotta have more cowbell!
	gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
	{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
	{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Scala

Works with: Scala version 2.11

<lang scala> import collection.mutable.ListBuffer case class State(isChild: Boolean, alts: ListBuffer[String], rem: List[Char]) def expand(s: String): Seq[String] = {

 def parseGroup(s: State): State = s.rem match {
   case Nil =>  s.copy(alts = ListBuffer("{" + s.alts.mkString(",")))
   case ('{' | ',')::sp =>
     val newS = State(true, ListBuffer(""), rem = sp)
     val elem = parseElem(newS)
     elem.rem match {
       case Nil =>     elem.copy(alts = elem.alts.map(a => "{" + s.alts.map(_ + ",").mkString("") + a))
       case elemrem => parseGroup(s.copy(alts = (s.alts ++= elem.alts), rem = elem.rem))
     }
   case '}'::sp =>
     if (s.alts.isEmpty)          s.copy(alts = ListBuffer("{}"), rem = sp)
     else if(s.alts.length == 1)  s.copy(alts = ListBuffer("{"+s.alts.head + "}"), rem = sp)
     else                         s.copy(rem = sp)
   case _ => throw new Exception("parseGroup should be called only with delimitors")
 }
 def parseElem(s: State): State = s.rem match {
   case Nil =>  s
   case '{'::sp =>
     val ys = parseGroup(State(true, ListBuffer(), s.rem))
     val newAlts = for { x <- s.alts; y <- ys.alts} yield x + y
     parseElem(s.copy(alts = newAlts, rem = ys.rem))
   case (',' | '}')::_ if s.isChild => s
   case '\\'::c::sp => parseElem(s.copy(alts = s.alts.map(_ + '\\' + c), rem = sp))
   case c::sp =>       parseElem(s.copy(alts = s.alts.map(_ + c), rem = sp))
 }
 parseElem(State(false, ListBuffer(""), s.toList)).alts

} </lang> Demonstrating: <lang scala> println(expand("""~/{Downloads,Pictures}/*.{jpg,gif,png}""") mkString "\n") println(expand("It{{em,alic}iz,erat}e{d,}, please.") mkString "\n") println(expand("""{,{,gotta have{ ,\, again\, }}more }cowbell!""") mkString "\n") println(expand("""{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}""") mkString "\n") </lang>

Output:

~/Downloads/*.jpg
~/Downloads/*.gif
~/Downloads/*.png
~/Pictures/*.jpg
~/Pictures/*.gif
~/Pictures/*.png
Itemized, please.
Itemize, please.
Italicized, please.
Italicize, please.
Iterated, please.
Iterate, please.
cowbell!
more cowbell!
gotta have more cowbell!
gotta have\, again\, more cowbell!
{}} some }{,\\ edge \,{ cases, {here} \\\\\}
{}} some }{,\\ edge \,{ cases, {here} \\\\\}

Sidef

Translation of: Perl

<lang ruby>func brace_expand (input) {

   var current = []
   var stack = current

   loop {
       var t = input.match(
           /\G ((?:[^\\{,}]++ | \\(?:.|\z))++ | . )/gx
       )[0] \\ break

       if (t == '{') {
           stack << [current = []]
       }
       elsif ((t == ',') && (stack.len > 1)) {
           stack[-1] << (current = [])
       }
       elsif ((t == '}') && (stack.len > 1)) {
           var group = stack.pop
           current   = stack[-1][-1]

           # handle the case of brace pairs without commas:
           group[0][] = group[0].map{ '{'+_+'}' }... if (group.len == 1)

           current[] = current.map { |c|
               group.map { .map { c + _ }... }...
           }...
       }
       else {
           current[] = current.map { _ + t }...
       }
   }

   # handle the case of missing closing braces:
   while (stack.len > 1) {

       var right = stack[-1].pop
       var sep = ','

       if (stack[-1].is_empty) {
           sep = '{'
           stack.pop
       }

       current = stack[-1][-1]
       current[] = current.map  { |c|
           right.map { c + sep + _ }...
       }...
   }

   return current

}

DATA.each { |line|

   say line
   brace_expand(line).each { "\t#{_}".say }
   say 

}

__DATA__ ~/{Downloads,Pictures}/*.{jpg,gif,png} It{{em,alic}iz,erat}e{d,}, please. {,{,gotta have{ ,\, again\, }}more }cowbell! {}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
	~/Downloads/*.jpg
	~/Downloads/*.gif
	~/Downloads/*.png
	~/Pictures/*.jpg
	~/Pictures/*.gif
	~/Pictures/*.png

It{{em,alic}iz,erat}e{d,}, please.
	Itemized, please.
	Itemize, please.
	Italicized, please.
	Italicize, please.
	Iterated, please.
	Iterate, please.

{,{,gotta have{ ,\, again\, }}more }cowbell!
	cowbell!
	more cowbell!
	gotta have more cowbell!
	gotta have\, again\, more cowbell!

{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
	{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
	{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

Tcl

Works with: Tcl version 8.6

<lang tcl>package require Tcl 8.6

proc combine {cases1 cases2 {insert ""}} {

   set result {}
   foreach c1 $cases1 {

foreach c2 $cases2 { lappend result $c1$insert$c2 }

   }
   return $result

} proc expand {string *expvar} {

   upvar 1 ${*expvar} expanded
   set a {}
   set result {}
   set depth 0
   foreach token [regexp -all -inline {(?:[^\\{},]|\\.)+|[\\{},]} $string] {

switch $token { "," { if {$depth == 0} { lappend result {*}[commatize $a] set a {} set expanded 1 continue } } "\{" {incr depth 1} "\}" {incr depth -1} } append a $token

   }
   lappend result {*}[commatize $a]
   return $result

} proc commatize {string} {

   set current {{}}
   set depth 0
   foreach token [regexp -all -inline {(?:[^\\{},]|\\.)+|[\\{},]} $string] {

switch $token { "\{" { if {[incr depth] == 1} { set collect {} continue } } "\}" { if {[incr depth -1] == 0} { set foundComma 0 set exp [expand $collect foundComma] if {!$foundComma} { set exp [lmap c [commatize $collect] {set c \{$c\}}] } set current [combine $current $exp] continue } elseif {$depth < 0} { set depth 0 } } } if {$depth} { append collect $token } else { set current [lmap s $current {set s $s$token}] }

   }
   if {$depth} {

set current [combine $current [commatize $collect] "\{"]

   }
   return $current

}</lang> Demonstrating: <lang tcl>foreach testcase {

   "~/{Downloads,Pictures}/*.{jpg,gif,png}"
   "It{{em,alic}iz,erat}e{d,}, please."
   "{,{,gotta have{ ,\\, again\\, }}more }cowbell!"
   "\{\}\} some \}\{,\{\\\\\{ edge, edge\} \\,\}\{ cases, \{here\} \\\\\\\\\\\}"

} {

   puts $testcase\n\t[join [commatize $testcase] \n\t]

}</lang>

Output:

~/{Downloads,Pictures}/*.{jpg,gif,png}
	~/Downloads/*.jpg
	~/Downloads/*.gif
	~/Downloads/*.png
	~/Pictures/*.jpg
	~/Pictures/*.gif
	~/Pictures/*.png
It{{em,alic}iz,erat}e{d,}, please.
	Itemized, please.
	Itemize, please.
	Italicized, please.
	Italicize, please.
	Iterated, please.
	Iterate, please.
{,{,gotta have{ ,\, again\, }}more }cowbell!
	cowbell!
	more cowbell!
	gotta have more cowbell!
	gotta have\, again\, more cowbell!
{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}
	{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}
	{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}

zkl

This is a two pass algorithm (2*length(string)), one pass to find valid {} pairs, the next pass to expand them. <lang zkl>fcn eyeball(code,ps=L(),brace=False){ //-->indexes of valid braces & commas

  cs:=L();
  foreach c in (code){ // start fresh or continue (if recursing)
     switch(c){

case("\\"){ __cWalker.next(); } case(",") { if(brace) cs.append(__cWalker.n); } // maybe valid case("{") { // this is real only if there is matching } and a comma n:=__cWalker.n; _,cz:=self.fcn(__cWalker,ps,True); if(cz){ ps.append(n,__cWalker.n); ps.extend(cz) } // valid {} pair } case("}"){ if(brace) return(ps,cs); }

     }
  }
  return(ps,False)

}

fcn expando(code,strings=T("")){

  reg [const] stack=List(); reg roots,cs; bs,_:=eyeball(code);
  foreach c in (code){
     if(bs.holds(__cWalker.n)){
        if     (c=="{") { stack.append(cs); cs=0; roots=strings;       }

else if(c==",") { stack.append(strings); strings=roots; cs+=1; } else if(c=="}") { do(cs){ strings=stack.pop().extend(strings); } cs=stack.pop(); }

     }else   if(c=="\\"){

c="\\"+__cWalker.next(); strings=strings.apply('+(c));

     }
     else strings=strings.apply('+(c));
  }
  strings

}</lang> <lang zkl>foreach bs in (T("It{{em,alic}iz,erat}e{d,}", "~/{Downloads,Pictures}/*.{jpg,gif,png}",

  "It{{em,alic}iz,erat}e{d,}, please.",  "a{2,1}b{X,Y,X}c",  0'|a\\{\\\{b,c\,d}|,
  "{a,b{c{,{d}}e}f",  0'|{,{,gotta have{ ,\, again\, }}more }cowbell!|,
  0'|{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\}|))

{

  "%s expands to\n   %s".fmt(bs,expando(bs)).println();

}</lang>

Output:

It{{em,alic}iz,erat}e{d,} expands to
   L("Itemized","Italicized","Iterated","Itemize","Italicize","Iterate")
~/{Downloads,Pictures}/*.{jpg,gif,png} expands to
   L("~/Downloads/*.jpg","~/Pictures/*.jpg","~/Downloads/*.gif","~/Pictures/*.gif","~/Downloads/*.png","~/Pictures/*.png")
It{{em,alic}iz,erat}e{d,}, please. expands to
   L("Itemized, please.","Italicized, please.","Iterated, please.","Itemize, please.","Italicize, please.","Iterate, please.")
a{2,1}b{X,Y,X}c expands to
   L("a2bXc","a1bXc","a2bYc","a1bYc","a2bXc","a1bXc")
a\\{\\\{b,c\,d} expands to
   L("a\\\\\{b","a\\c\,d")
{a,b{c{,{d}}e}f expands to
   L("{a,b{ce}f","{a,b{c{d}e}f")
{,{,gotta have{ ,\, again\, }}more }cowbell! expands to
   L("cowbell!","more cowbell!","gotta have more cowbell!","gotta have\, again\, more cowbell!")
{}} some }{,{\\{ edge, edge} \,}{ cases, {here} \\\\\} expands to
   L("{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}","{}} some }{,{\\ edge \,}{ cases, {here} \\\\\}")