Archived Notes on Grading: HW6

The code "A1" is shorthand for "missing base case (-2)."

The code "A4" is shorthand for "no explanation/work shown (-2)."

The code "A2" is shorthand for "missing base case (-3)."

The code "A3" is shorthand for "no inductive hypothesis stated (-3)."

The bold-face T in the initial assertion is a propositional constant (defined on p. 17). It is not a variable.

The final assertion that you (most naturally) get from the if-then-else inference rule is...

(x < y /\ min = x) \/ (x >= y /\ min = y)    Q

...a postcondition which is slightly different from the one that the exercise asks you to verify:

(x <= y /\ min = x) \/ (x > y /\ min = y)    Q'

The solution argues that Q and Q' are logically equivalent, but many people overlooked this fact / step, resulting in several incidents of the following errors:

• falsely claiming that the algorithm is not correct with respect to Q'
• incorrectly stating Q' as the result of a straightforward application of the if-then-else inference rule
  [nit: it is possible to get Q' from the if-then-else rule, but doing so requires additional justification, most notably an extra case split--"x = y" vs. "x > y"--in the else branch of the argument]
• implicitly assuming that !(x < y) is equivalent to x > y
• proving the x < y and x > y cases but neglecting to address the x = y case

[If you simply see "-5" on your paper, then you made one of the above errors (or an error closely related to the above).]