| > The biggest "blocker" for using dependent types is that programs must be /total/, because that program has to be evaluated for it to typecheck! Totality is orthogonal to dependent types. You can absolutely have non-total programs at the type level: Rust has such programs today in fact! > Generally this means that recursion is only allowed if its structural, and there can be no run-forever loops, i.e., no servers. You can have an infinite loop in a total language like Agda or Idris: coinduction is the mechanism. > Dependent types are, by their nature, proof carrying[2], and there are times when you want this, but for a general-purpose programming language, also times that you do not. This doesn't make a whole lot of sense to me. Dependent types are "proof carrying" in the sense that any program of the type: Int -> Int
Is a proof that there exists a function of type `Int -> Int`, nothing more. I don't know what "opting out" of the "carrying" there would mean.> You can't be total over IO (or any effect for that matter), so, yeah, skip it when arg-parsing, but then opt-in when you're processing your financial transactions or actuating your robot. You can be total over IO, and effects do not imply non-totality either. |
Absolutely, the talk I linked to gets at this to some extent. In rust, partiality causes type checking to fail. You could use it on purpose!
> You can have an infinite loop in a total language like Agda or Idris: coinduction is the mechanism.
For sure, but the totality checker is appeased by sized-types, or at least that's how I know to do it in Agda. I've heard it can be done without them, but I'm not familiar with the approach. This is what I intended w/r/t structural recursion.
> This doesn't make a whole lot of sense to me.
This is because, as the authors state, to type check the program is to evaluate it, so before it can run you have proof that it is correct.
By opting out I'm more talking about the converse, to opt in when you need it. Kind of the opposite of Idris's %partial directive.
> You can be total over IO, and effects do not imply non-totality either.
That's fair, you're right. This is poorly stated.