EWD249 - 49

Note. In the refinement of 2b4(4)d, when mult[n] is compared with the current value of j, mult[n] is increased as much as possible; this could have been done in steps of 2 * p[n], because we only submit odd values of j and therefore are only interested in odd multiples of p[n]. (The value of mult[1] remains, once set, equal to 4.)

The refinement of 2c "print p[k] for k from 1 through 1000" is left to the reader. I suggest that the table should be printed on five lages, each page containing four columns with fifty consecutive prime numbers.

* * *

Here I have completed what I announced at the beginning of this section, viz. "to describe in very great detail the composition process of such a [well-structured] program". I would like to end this section with some comments.

The most striking observation is that our treatment of a very simple program has become very long, too long indeed to my taste and wishes, even if I take into account that essentially we did two things: we made a program and we discussed extensively the kind of considerations leading to it. It is not so much the length of the latter part that bothers me (writers fill whole novels with the description of human behaviour); what bothers me is the length of the texts at the various levels. Therefore we may expect that notational technique will be one of our main concerns.

But we have also had encouraging experiences. Giving full recognition to the fact that the poor programmer cannot decide all at once, we succeeded to a large extent in building up this program one decision at a time, and in our example quite a lot of programming was already done in its definite form while major decisions were still left open: irrespective of whether the final decisions are taken this way or that way, the coding of the earlier levels remains valid. In view of the requirement of program manageability, this is very encouraging.