Assignment 3 has been graded.  It will be handed back tomorrow.

Each question worths 10 marks.  Total = 50.

General comments:

1. Please pay attention to the lectures and read the lecture notes
   carefully.

2. Please read the assignment questions carefully.

3. Did I say please read the assignment questions carefully?  What is
   the business with discussing what would happen to your programs for
   n<0, when n is stated in the questions to be natural?

4. You should exercise extreme care when you deal with the sequential
   composition operator (the semicolon).  Please do not deviate from
   the exact definition and the substitution law.

Detailed marking scheme:

1. If attempt to prove, at most 6 marks.
   If disproof is weak (e.g., counterexample not concrete enough, or
   counterexample not proved to be a counterexample), at most 7 marks.

2. proof of first refinement = 3 marks
   proof of second refinement = 7 marks

3. program = 4 marks
   time claims = 2 marks
   proof = 4 marks

4. state refinements (s' has the right value) = 5 marks
   time refinements (t'-t has the right upper bound) = 5 marks

   Both require stating *all* specifications, including intermediate ones.

5. Putting in t:=t+1's = 1 mark
   Exponential time claim = 4 marks
   Proof = 5 marks

-- Albert