Consider the problem of finding the smallest number in a list L, of n numbers and the following algorithm for its solution.

Precondition:

PositionOfMin(L)

1) position := 1

2) i := 2

3) WHILE i n DO

4) IF A[i] < A[position]

5) THEN position := i

6) i := i + 1

7) RETURN position

Postcondition:

1. Using precise mathematical language, write reasonable preconditions and postconditions for this problem.

2. Using precise mathematical language, determine reasonable and useful loop-entry, loop-exit, loop-invariant statements.

3. Prove that your loop-exit condition and your loop-invariant together imply your post condition.

4. Prove that with your pre and post conditions, every instance terminates and meets its post condition.