But that is clearly not so - *including* the parentheses in the above script alters the output (and restores commutativity):

Of course it alters the output. You are allowed to use predeclared subroutines without parenthesis, but the docs don't say that you always get the same result as with parens -- in the case without parens, you need to be aware of the precedence of your expressions.

In particular non_commutative + 10 parses as non_commutative( +10 ). You meant non_commutative() + 10, but perl can't know that; you'd have to write (non_commutative) + 10 to disambiguate.

In case you wonder what the *10 is: as a term that's the glob syntax that you might know from *STDOUT.

The precedence of subroutines without parenthesis is described in perlop as "list operators (rightward)", and looser than + and *.

Another option is to declare the sub with a prototoype:

sub non_commutative() { 17 }
[download]

Which is described in perlsub.