I once had a statistics professor (teaching a programming class using, IIRC, SAS) in college who worked as a data analyst in the federal government, possibly the Labor Department. Part of his job was working with polling and form data. After class he once tried to explain a paper he wrote arguing for an additional null-like type in the formal analytics system in his domain. I was young and stupid (took it as an easy programming course; was not skilled at abstract math) and impatient (wanted to meet up with friends at a pub) so didn't follow along well enough to even properly remember his argument, let alone understand it. But I've always distinctly recalled that he was arguing for a 4th, or possibly 5th type, yet whenever I survey the literature I've only found at most such 2 types. But I've probably been looking in the wrong places.

For context, NULL/missing was a type. N/A was a type (i.e. a question irrelevant to someone). I can't remember the 3rd, and of course not the additional (4th or 5th) type he was proposing. If anyone knows a good resource that describes this problem domain, that would be much appreciated. I've been haunted for over 20 years by the regret of not fully appreciating what he was trying to explain to me, both because I could've learned something that day, but also because I almost immediately felt like an a*hole for not showing enough interest in and respect for a piece of scholarly work he was clearly proud of and wanted to share with me.

EDIT: I think the third pre-existing type was for a situation where someone abstains from answering a question like, "Sex: male/female", because they consider themselves neither. So something like an Other type. In retrospect this was presumably related to set theory, and he felt there was a gap in the pre-existing formal models.

Alas, Wittgenstein can only explain it like you are 0.5.

> Heck, there's also a symbol for twenty, 廿, and it exists despite the number system being base 10.

I'm not sure that if you intend to captured the structure of chinese symbols, you wouldn't to make the radicals something below symbols. Then 廿 wouldn't count as a single symbol here, but rather as a concatenation of two 十, i.e. the same as XX is 20 in roman numerals.

> 5147 would be 五千一百四十七

"Five thousand one hundred four tens seven". So each order of magnitude is explicitly labeled. Where's the positional part?

But we only have words for them. We don't have special symbols for them, kind of*

* Technically you could read "k" as a symbol for thousand, "M" for million, "B" for billion, and "T" for trillion.

You want a character that stands in for theres no character here?

Have you also looked at Snap! (https://snap.berkeley.edu/), by any chance? It's basically Scratch but with the artificial limitations removed, e.g. you can pass lists to functions, and blocks (functions) are treated as first-class objects so you can store them in data structures, pass them as input to other functions, and basically teach students proper functional-programming thinking (to find the odd numbers in this list, just pass the "is odd?" block as input to the "filter" block and you're done).

Function arguments are unfilled holes. So are interface declarations.

Both are (fairly) programming language agnostic, but in the context of an editor, would become specific. The editor would have to know _how_ to represent them in the code’s language.

Delimited continuations? Though I'm not totally clear what you're asking for. Semantics or syntax?