diaries

Top-down presentation of mathematical arguments

Dated: 

21 May 1981

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]

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Overspecifying a mathematical argument

Dated: 

21 May 1981

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:

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A Cry for Generalization in Mathematics

Dated: 

21 May 1981

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.

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Trip to Munich

Dated: 

19 May 1981

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.

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Influence of ALGOL 60 on Hardware Design in the USA

Dated: 

9-11 May 1961

Among Dijkstra's possessions is the booklet of the 1961 Western Joint Computer Conference which was held in Los Angeles. The booklet contains the abstracts of the presented lectures, including:

  • J. McCarthy's `A Basis for a Mathematical Theory of Computation' and
  • R.S. Barton's `A New Approach to the Functional Design of a Digital Computer'.

The abstract of the latter paper is briefly discussed here because it may help us understand how ALGOL 60 influenced hardware design in the USA during the early 1960s.

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David N. Freeman contacts Dijkstra for a sabbatical

Dated: 

5 May 1971

David N. Freeman, director of Computing Activities at the University of Pennsylvania, contacted Dijkstra in order to express his interest in taking a sabbatical leave at Eindhoven between September 1972 and September 1973. As future posts on this blog will show, he was not the only one to do so. In fact, several American researchers in computing wanted to visit the Netherlands and Eindhoven in particular. Presumably, this was due to Dijkstra's presence at the University of Eindhoven.

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The peer group

Dated: 

15 March 1981

Though Dijkstra's own research publications were cited a lot, he himself did not want to judge the quality of one's work in terms of number of citations, nor in terms of number of papers.

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