Lecture 06

Q&A session for homeworks and quiz.

Otherwise, you can try to solve this problem as an exercise:

For the next code fragment, do the following

transform the loop into guarded command language
construct a formula F(x, x') for the loop body
write down the loop invariant and show it is inductive with respect to the given pre- and postcondition.

$\begin{equation*} P: n> 0\wedge \forall i. (0 \le i\le n-1) \to (a[i] = a_0[i]) \end{equation*}$

$\begin{equation*} Q: \forall i. (0 \le i\le n-2) \to (a[i] = a_0[i+1]) \wedge \forall i. (i = n-1) \to (a[i] = a_0[0]) \end{equation*}$

e = a[0];
i = 0;
while(i <= n-2) {
  a[i] = a[i+1];
  i = i + 1;
}
a[n-1] = e