Breaking The Rules II is of interest indeed.

My parser consists of a self made lexer and a recursive descending parser. The code is quite lengthy, but not really complicated.

Parsing and evaluation are different steps indeed, you can do something like

use Data::Dumper;
my $m = Math::Light::Expression->new;
$m->parse($expression);
print Dumper $m->{ast};
for (0 .. 9) {
    print $val->({ a => $_ }), "\n"; # evaluate multiple times
}
[download]

I experimented with a LaTeX emitting backend, but that goes against the grain of keeping modules small and doing exactly what they are meant for.

I considered a PIR emitter as well, but PIR handles precedence on its on, so there is now real need to for my parser ;-)