Wow, this is completely wrong.
Perl has two different kinds of strings. We'll call them 'binary' and 'unicode' strings.
Awful names, and they have nothing to do with binary or Unicode.
They are respectively strings of 8-bit chars and string of 72-bit chars.
it sometimes try to convert Unicode strings to binary, which also doesn't work very well
No, the problem is that you told it to encode text that was already encoded. It has nothing to do with the internal string formats.
Binary string "Я" got mangled in Unicode context.
No, you created garbage by concatenating UTF-8 and text. It has nothing to do with the internal string formats.
When you do $number + $letters, Perl doesn't mangle anything; you did.
When you do $text + $utf8, Perl doesn't mangle anything; you did.
Conclusion: to use Perl, you must either be an American, or an expert in Unicode and Perl internals.
Just like you wouldn't insert text into SQL without conversion, insert text into HTML without conversion, or insert text into a command line without conversion; all you have to do is not insert text into UTF-8 (or vice-versa) without conversion.
It doesn't take an American to understand that 4 + apple is going to be garbage. Decode inputs. Encode inputs. That's it.
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