Here's a variation on the above solution, using named recursive subpatterns and named captures.
Nowadays I write all my non-trivial regexes this way.

use 5.010;

my $source = 'function convert(beg string, end string, read_date date,
+ step char(6)) returns (date, date, char(1))';

my $matched =
    $source =~ m{
        \A \s*+
        (?<access>  private  | public        )?+  \s*+
        (?<keyword> function | report        )    \s*+
        (?<name>    (?&identifier)           )    \s*+
        (?<params>  (?&list)                 )    \s*+
        (returns \s*+ (?<returns> (?&list) ) )?+
        \s*+ \z

        (?(DEFINE)
            (?<identifier> [^\W\d]\w*+                              )
            (?<list>       [(] [^()]*+ (?: (?&list) [^()]*+ )*+ [)] )
        )
    }xms;

if ($matched) {
    my %components = %+;
    use Data::Dumper 'Dumper';
    say Dumper \%components;
}
else {
   say 'parse failed';
}
[download]

which outputs:

$VAR1 = {
  keyword => 'function',
  name    => 'convert',
  params  => '(beg string, end string, read_date date, step char(6))',
  returns => '(date, date, char(1))',
};
[download]