[gnulinux]

Not yet, it's been one of the things I wanted to do for about a year since cubical-agda was released. I dabbled with it but I don't know enough type theory/topology to digest cubical type theory well. I tried a few times, but I didn't understand everything...

The benefits look really promising e.g. proving forall x -> f x == g x -> f == g. I really want to use this theorem in some of my agda projects, but I never needed it desperately enough that I had to drop everything and do this. My usual workaround is implement slowButEasyToUnderstand function. Do a whole bunch of proofs with slowButEasyToUnderstand. Implement fastButComplicated function. Prove forall x slowButEasyToUnderstand x == fastButComplicated x

I think one immediate application I can think of with cubical is, you can implement mergeSort : List X -> List X and then pass this around everywhere. You don't need a Sorter record or whatever since when you implement quickSort, you will be able to prove quickSort == mergeSort, so everything will typecheck. I don't know which will end up getting compiled though.