II. Notes on Data Structuring * - Cornell University

122 c.A.R. HOARE
and on receipt of a newpage character, this should be output to a display
device by the instruction
outpage.
The display device does not recognise the characters newline or newpage;
consequently the ends of Iines and pages have to be filled up with spaces.
Write a program in a suitable language to perform this operation, using a
selection of representations for the display page, e.g.
unpacked
loosely packed
tightly packed
indirect.
Rewrite the program, using different representations. Compare the lengths
and speeds of the code and data involved in the different representations.
Write the corresponding programs to read a page from the display, and
output the individual characters, taking care to eliminate redundant spaces
at the ends of each line and blank lines at the end of each page wherever
possible.
7. THE POWERSET
The powerset of a given set is defined as the set of all subsets of that set;
and a powerset type is a type whose values are sets of values selected from
some other type known as the base of the powerset. For example, the primary
colours have been defined by enumeration as red, yellow and blue. The
other main colours are made up as a mixture of two or three of these colours:
orange is a mixture of red and yellow; brown is a mixture of all three primary
colours. Thus each main colour (including the primary colours) can be
specified as that subset of the primary colours out of which it can be mixed.
For example, orange may be regarded as the set with just two members,
red and yellow. Using the traditional notation for sets defined by enumeration,
this may be written: {red, yellow}. The pure colour red may be regarded as
the set whose only member is the primary colour red, i.e. {red }. In this way it
is possible to represent the seven main colours, red, orange, yellow, green,
blue, purple and brown. When no primary colour is present (i.e. the null or
empty set) this may be regarded as denoting the absence of colour, i.e.
perhaps white. The type whose values range over the colours may be declared
as the power set of the type primary colour:
type colour = powerset primary colour.
A second example is provided by considering a data structure required to
represent the status of the request buttons in a lift. A simple variable of type