That’s impractical. Take binary search and the assumption the list is sorted. Verifying the list is sorted would negate the point of binary search as you would be inspecting every item in the list.
But you make some sort of distinction here.
> Is asserting the assumptions during code execution not standard practice for formally verified code?
Are you using the same definition of "assert" as that post does?
Verify means you checked.
Assert means you are suggesting something is true, but might or might not have checked. Sometimes an assert is "too hard" to verify but you have reason to think it is true. This could be because of low level code, or just that it is possible to verify but would cost too much CPU (runtime, or possibly limits of our ability to prove large systems) Sometimes assert is like a Mafia boss (It is true or I'll shoot - it might or might not really be true but nobody is going to argue the point now. This can sometimes be needed to keep a discussion on a more important topic despite the image)
If you want to assert that a list is sorted, you need some function that checks if it is sorted and returns a boolean.
You can aslo mark certain codepaths as unreachable to hint to the compiler that it can make certain optimisations (e.g., "this argument is never negative"), but if you aren't validating that the assumption is correct I wouldn't call that an assertion -- though a plain reading of your comment would imply you would still call this an "assertion"? AFAIK, no language calls this construct "assert".
This is probably one of those "depends on where you first learned it" bits of nomenclature, but to me the distinction here is between debug assertions (compiled out in production code) and assertions (always run).
This is true, but if you care about correct execution, you would need to re-verify that the list is sorted - bitflips in your DRAM or a buggy piece of code trampling random memory could have de-sorted the list. Then your formally verified application misbehaves even though nothing is wrong with it.
It's also possible to end up with a "sorted" list that isn't actually sorted if your comparison function is buggy, though hopefully you formally verified the comparison function and it's correct.