Well, idris (v2) is very special since it has modalities for compile-time erasure and linearity. This sets it apart from all the other dependently-typed languages. This makes it possible in theory (and currently being experimented with) to implement efficient-by-construction code.
Linearity is exclusive to Idris 2, compile time only values/run-time erasure are supported by all major proof assistants. Coq and Lean have the Prop type (compile time only) while Agda allows annotation of variables as run-time irrelevant.
And how does it compare to Arend? Does anybody know?
Are there any other HOT based languages out there? (Agda seems to have also some support for the "cubic version"; whatever this means, I'm actually clueless).
Cubical type theory is a way to get to a purely constructive foundation for Homotopy Type Theory. Super cool stuff from a foundations of math perspective and has some surprising applications to topological quantum computing but if it isn’t your rabbit hole you can probably not pay too much attention to it.
The whole "foundations of math" part is extremely exciting!
But I'm not an mathematician so I don't understand much (if anything). More in the programming languages "department" of interests.
But if something is "good enough" to describe whole math it could be useful for getting strong guaranties about programs, I guess. So I would be quite interested how this HOT stuff could be useful in practice. What could type systems based on this enable?
My limited understanding is that you get additionally "paths" between types and type constructor which denote equivalence between them.
But I have no clue what one could do with that (besides doing math, of course).
https://arxiv.org/abs/2104.00480