Dafny verifies insertion sort using swap

Question

I'm working on how to use dafny to verify an insertion sort using "swap" adjacent elements but I can't find a reasonable invariant for the while loop, can anyone help me fix it? Here is the link: http://rise4fun.com/Dafny/wmYME

Answer 1

There are a few problems here.

First, your inner loop is not correct, because the temp variable is never updated. I recommend removing temp and using the loop condition down >= 0 && a[down+1] < a[down] instead.

Second, you have several issues with the inner loop invariant being ill formed (index out of range, violating precondition of sorted). However, instead of fixing these, I recommend throwing out both inner loop invariants and trying again.

My preferred invariant for the inner loop of insertion sort is "a[0..up+1] is sorted except possibly at down + 1". You can state this as

invariant forall j,k | 0 <= j < k < up+1 && k != down+1 :: a[j]<=a[k]

The resulting file verifies.