II. Notes on Data Structuring * - Cornell University

158 c.A.R. HOARE
individual sessions, and do not mention the timetable at all. This suggests
that the program can be structured as an inner part which selects a suitable
session satisfying (4) (5) and (6), and an outer loop which constructs the
timetable out of such suitable sessions.
The objective of the outer loop is to achieve satisfaction of conditions (2)
and (3) on its completion. We therefore choose one of these conditions as a
terminating condition of the loop, and design the body of the loop in such a
way that is preserves the truth of the other condition (that is, the invariant
of the loop); furthermore we ensure that the invariant is true before starting
the loop.
The obvious choice of invariant is exclusiveness (condition (3)), leaving
exhaustiveness as the terminating condition towards which each execution
of the body of the loop will progress. The empty timetable obviously satisfies
the invariant. This leads to an algorithm of the following structure"
timetable: = { };
while timetable does not satisfy (2) do
begin select a session satisfying (4), (5), (6);
end;
add the session to the timetable
print timetable.
In order for the addition of a new session to preserve the truth of the
invariant, it is necessary that the exams of the session shall be selected from
exams which do not yet appear in the timetable. We therefore introduce a
new variable to hold these remaining exams:
remaining: powerset exam;
which is defined by the invariant relation"
remaining = exam. all- ~ s.
s in timetable
The structure of the program as a whole now takes the form:
timetable: = { };
remaining" = exam. all;
while remaining 4: { } do
begin s'= suitable;
end;
print timetable.
timetable: v {s };
i
remaining'- s