One technique for 'static' variables in Perl (that you should be able to adapt to your underlying problem) is to wrap the sub in a bare block (or possibly a BEGIN block depending on initialization requirements and such). Your pseudo-code example becomes:

#!/usr/bin/perl -w
use strict;
foo(4);
foo();
{
    my $bar;
    sub foo {
        $bar = shift unless defined $bar;
        print "$bar\n";
    }
}
__END__
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Which, in the case of an expensive initialization can be along the lines of:

#!/usr/bin/perl -w
use strict;
print scalar localtime(),"\n";
slow_once(5);
slow_once();

{
    my $expensive_thingy;
    sub slow_once {
        unless (defined $expensive_thingy) {
            # make expensive thingy:
            sleep 5;
            $expensive_thingy = shift;
        }
        print scalar localtime()," :$expensive_thingy:\n";
    }
}
__END__

OUTPUT:
Sat Nov  3 15:55:31 2001
Sat Nov  3 15:55:36 2001 :5:
Sat Nov  3 15:55:36 2001 :5:
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If you wanted to create more than one expensive thingy, go with a parameterized sub that sets up the expensive thingy and returns a closure that does what you want with it.