For the rare languages that support invariants (or has a library that implements invariants) you would write it as code rather than a comment and the compiler will compile time error if the compiled code is capable of violating the invariant.

Another place to use this is if you're designing a new bit of code and want to write the design out before you write the code, rather than code first (or as the code is being produced, where at times it's non-executable because you have holes in the program that are filled with these textual descriptions).

You could put some of these into asserts or similar. Like for the three way partition. Create an assert that at each iteration the array[:low] values are all less than p, array[high:] values are each greater than p, and array[low:mid] values are each equal to p. If it doesn't hold then you know your code is wrong. This does induce a performance hit, but asserts can be turned off for deployed code.