You can't get there from here

Anything

      sub halts {
          my ($source_code, $input) = @_;
          my $newcode = q{sub { my $n = shift;
                                my $f = eval "CODE";
                                $f->("INPUT");
                                return $n * $n;
                               }};
          $newcode =~ s/CODE/$source_code/;
          $newcode =~ s/INPUT/$input/;
          return calculates_squares($newcode);
        }

But there's nothing really special about calculating squares
For example, we can't recognize whether a function will call die:

      sub halts {
          my ($source_code, $input) = @_;
          my $newcode = q{sub { my $f = eval "CODE";
                                eval { $f->("INPUT"); }
                                die "BOOGA BOOGA!";
                               }};
          $newcode =~ s/CODE/$source_code/;
          $newcode =~ s/INPUT/$input/;
          return dies($newcode);
        }

$newcode dies only if the call $f->("...") will halt