EWD249 - 64

A second example of step-wise program composition.

With a picture of program structure as a layered hierarchy of machines emerging, my fingers are itching to play with it, i.e. to make another program. The notational techniques employed should not be regarded as a well-considered proposal: they have been chosen to suit my fancy and should be regarded as part of the experiment.

The problem is the following one. There is given a line printer which is controlled by two commands "NLCR" (New Line Carriage Return) which defines the utmost left position of the next line as the "currently printable position", and the command "PRSYM(n)" which prints a character identified by the value of the integer parameter n on the currently printable position and defines the position immediately to the right of the printed position as the new currently printable position. (For our discussion we can regard lines of infinite length as permissible.) We shall only make use of two specific values of n, called "space" and "mark" respectively. "PRSYM(space)" causes the currently printable position to remain blank, "PRSYM(mark)" will print a given, visible character, some sort of asterisk say.

Furthermore two integer function of an integer argument are given, satisfying

      for 0 ≤ i < 1000  :     0 ≤ fx(i) < 100    and    0 ≤ fy(i) < 50  .

Now we have to make a program printing 50 lines, numbered from top to bottom by a y-co-ordinate running from 49 through 0, the positions on a line being numbered from left to right by an x-co-ordinate running from 0 through 99. On the thousand positions (or less in the case of coincidence) given by

            x = fx(i) and y = fy(i) for some i satisfying  0 ≤ i < 1000

a mark has to be printed; all other positions on the paper have to remain blank. In other words: a curve is given in a discrete parameter representation and we wish to use the line printer as a digital plotter.

I have used this problem extensively in viva voce examinations and the majority of the students quickly discover that, due to the absence of OLCR (Old