As others have mentioned, functional programming is indeed interesting and worth looking into. That having been said, you don't really have to learn another language to do it. You can write Perl in a functional style. If you want to understand closures, you might as well do it in Perl, a language you already know, as learn a whole other language with its own version of print, etc.

You might look at Prolog for a programming style you really don't see in Perl (at least not until another monk comes along and points us to a CPAN module that lets you write code that way).