About 65 participants, including Dijkstra, attended the "Advanced Course on Functional Programming and its Applications" at the University upon Tyne (20-31 July 1981). The following points are of general interest because they seem to have recurred throughout Dijkstra's career:
Dijkstra's Structured Programming abided by a top-down presentation of his programs. In the Spring of 1981, Van Gasteren and Dijkstra recommended a similar presentation style for mathematical arguments. For instance, they advocated using lemmata before giving their proofs:
Though unusual, this seems entirely correct. The statement of a lemma is a logical firewall between its usage and its proof; the use of a lemma is independent of how the lemma can be proved and, during study of its use, knowledge of its proof is therefore an unnecessary burden. [AvG5/EWD788 - 5]
Using the right notation is key to proving theorems elegantly. To get this message across, Van Gasteren and Dijkstra explained why they were dissatisfied with the notation that Courant and Robbins had used in a particular proof concerning the prime decomposition of a natural number m. The notation under scrutiny was:
In the Spring of 1981, A.J.M. van Gasteren and E.W. Dijkstra wanted to understand "how to tame the complexity of artefacts such as proofs and programs". In hindsight it is no surprise that Dijkstra's rallying cry for generalization in programming of the early 1960s is reflected in his work of the early 1980s with regards to proving mathematical theorems. Some examples below will illustrate this, based on AvG5/EWD788.
On 19 May 1981, Dijkstra spent the day in Munich with Bauer, Broy and Partsch in order to select the participants for the NATO Summer School in Marktoberdorf [EWD790]. It is interesting to note how close Dijkstra and Bauer had become by 1981.
Given a specific function, called lambo, how do you prove that it is equal to its own inverse? Dijkstra's answer: by massaging a program that computes lambo. That is, by gradually transforming an original program that computes lambo into a symmetric program that is rather useless to the programmer but useful to the mathematician!
Dijkstra went on a trip to California, visiting universities and research centers. While doing so, he got annoyed by the many researchers who viewed the difficulties underlying multi-person software projects as "communication problems" and who, therefore, advocated new specification languages.