[ballenf]

What if number types were Optionals after any operation that could result in any kind of unusual number (sqrt(-1), Infinity, NaN)? Or maybe after every operation, since any operation could overflow the type.

Do any languages do that? Seems more consistent (if way more hassle) than giving a mathematically false result out of pragmatism. At least in a strictly typed language.

[JadeNB]

You know what would happen. Math is ubiquitous in lots of code, so syntactic shortcuts would be introduced. Thus, we wouldn't use `a >>= (\x -> 2x) >>= (\x -> x^2)`, but would soon introduce syntactic sugar. For example, we could re-define `[asterisk]` so that it had type `Maybe Number -> Maybe Number -> Maybe Number`. You'd need a `return` (or `Just`) at the beginning, but soon that would be elided too, so that numeric literals would be auto-promoted to `Maybe Number`s. Then the language would add silent mechanisms to allow `Maybe Number`s to be displayed easily. You should check if your `Maybe Number`s are `Just Number`s before letting them out to play, but, if the language doesn't force you, then you know you won't. And then we're right back in the current situation.

[AnIdiotOnTheNet]

Zig defines checked versions of mathematical operators in its std lib [0], which return an Error Union. It's like an Optional (which Zig also has), but with an error instead of null. Your code can choose to handle this error however it wants.

[0] https://ziglang.org/documentation/master/#Standard-Library-M...

[zokier]

Isn't that essentially what floats already are? A sum type of numbers, infinities, and NaN(s).

[Someone]

Yes and no. I think the OP is looking for a strongly typed language where you can’t do any operation on that sum type, forcing you to check results after every operation.

[klodolph]

JavaScript does that…

[ballenf]

How so without optionals or static typing?

[RReverser]

That's usually what NaN is used for (basically "None" for numbers).