I came up with a similar, and arguably neater implementation:

sub sum{ ( shift()//return 0 ) + &sum }

print sum( 1,2,3);;
6

print sum( 1 .. 100 );;
Deep recursion on subroutine "main::sum" at
5050
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but rejected it because 'sum' is a (glob) variable.

In theory, it is possible to avoid the naming of the sub, thereby achieving "anonymous recursion", by using the Y-combinator. And the Y-combinator has been achieved in Perl by a former regular here.

Putting it together you get:

print Y( sub{my$rec=shift; sub{(shift()//return 0) + &$rec }})->(1 .. 
+100);;
5050
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But whilst that achieves the Y-combinators goal of recursion without adding the sub to the permanent namespace, it still requires the naming of the pesky closure $rec.

And of course, requires you to add the Y-combinator to the permanent namespace first:

sub Y {
    my ( $curried_rec ) = @_;
    sub {
        my ( $f1 ) = @_;
        $curried_rec->( sub { $f1->( $f1 )->( @_ ) } )
    }->( sub {
        my ( $f2 ) = @_;
        $curried_rec->( sub { $f2->( $f2 )->( @_ ) } )
    } )
}
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And that's already more obfuscation as I want to wrap my brain around, even in an obfuscation section post!

My final thought is that the simplest mechanism that fits the OPs breif is just:

C:\test>perl -Mstrict -wE"say eval join'+',()"


C:\test>perl -Mstrict -wE"say eval join'+',0"
0

C:\test>perl -Mstrict -wE"say eval join'+',-1"
-1

C:\test>perl -Mstrict -wE"say eval join'+',-1..+3"
5
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