This one will handle nested parens:
#!/usr/bin/perl -w
use strict;
$_ = '$a ($a (hi) $a) $a (()$a)';
my $re;
$re = qr/(?:[^\(\)]*|\((??{$re})\))+/;
s/(\($re\))|\$a/$1?$1:'$b'/eg;
print;
Update: should've referred to perlre manpage instead of relying on
memory, the version there makes it somewhat nicer:
my $re;
$re = qr/\((?:(?>[^()]*)|(??{$re}))*\)/;
s/($re)|\$a/$1?$1:'$b'/eg;
Update: It appears to broken in 5.6.0 (gives output as tachyon
shows below), but it works for me with 5.6.1.
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