What do you mean by generalized sorting and how isn't this affected by the comparison sorting lower bound?
Do you have a source?
Secondly, I've tried to get the white paper exposed here and it generally goes over like a lead balloon but:
http://www.diku.dk/hjemmesider/ansatte/henglein/papers/hengl...
Is the technique. It's an imposing 80 page paper even dedicated educators like Edward Kmett has trouble explaining trivially, but there is a talk here by the author to help sum it up: https://www.youtube.com/watch?v=sz9ZlZIRDAg
We've had some of Henglein's associates here to talk about it, too.
There is a Haskell implementation and it can really speed up certain types of operations. It's tricky to get the constants low in Haskell, but Kmett seems to have done a pretty good job.
Do you have something I can read? I'm curious specifically what you mean by this.
It's pretty cool because you can essentially ad hoc extend the type system to understand all transitions valid for types, then prove then.
Idris is different from Agda in that it has great introducory literature (the Idris book is just fantastic) and it also has F# style type providers that let you do things like query the AWS API with a given account's creds then extend the type system with a series of descriptive types for all valid operations for every asset.
It means that you can (and I find this really surprising) assert code totality on very real world use cases like code that orchestrates containers, binary parsers, or network protocols.
I spent my Christmas break studying Idris and what really delighted me most was that in many cases systems like that end up being simpler to use (even though their "Verified" constructions often involve simple inductive proofs to the compiler. You don't have to prove everything, but things that are proven are safe to use
What's really wild is that they even got the rough proportion of security cost for losing it down to 5% of the numbers were seeing with today's security patches.
I submitted this because I think their technique is preferred for lots of stuff distributed systems developers do with crypto primitives (as opposed to retpoline).
There are lots of well-known things no one seems to know outside of Academia, like how generalized sorting is O(n) and compilers that can prove the correctness of real world code when it's written a specific way