Definition talk:Real Interval/Notation/Wirth

Niklaus Wirth may also deserve attribution
Although Knuth explicitly mentions Lyle Ramshaw in his 1990 paper in the tribute book Beauty Is Our Business, in the references he only mentions Hoare's 1972 BIT article. In this paper it is also explicitly mentioned that the notation is inspired directly by Pascal syntax (by Niklaus Wirth).

In Concrete Mathematics: A Foundation for Computer Science Knuth (et al) mention both C.A.R. Hoare and Lyle Ramshaw [p. 73, both editions], but there is no reference in the bibliography for this mention. I would not take this book's mention in passing of this notation as authoritative in any way.

In his BIT article [Vol. 12, No. 3, p. 334-341, 1972] Hoare says "we introduce the following notations for open and closed intervals:". He makes no mention of who "we" includes, though the only other authors mentioned in the references section of that paper are Niklaus Wirth, A. van Wijngarden, and R. W. Floyd. Directly above the introduction of the new interval notation Hoare discusses Wirth's innovation in Pascal with the new subrange type. Wirth of course used .. as the subrange notation (operator) in Pascal while Hoare used a full three-dot ellipse in this BIT article. The references mention Wirth's first publication about Pascal, dated 1971.

So I don't see any direct connection anywhere whatsoever between Hoare and Ramshaw (except somewhat later, and implicitly not explicitly, through Knuth; and through the fact that Ramshaw's thesis was to expand on Floyd's and Hoare's earlier work).

Wirth probably chose the double-dot representation instead of the colon (":") used previously in Algol (the creation of which both he and Hoare were involved in, e.g. as evidenced in their joint paper A contribution to the development of ALGOL in the June 1966 issue of C.A.C.M.) because he had already used the ":" in Pascal in declarations where it is also necessary to be able to indicate subranges. It's not a full ellipse ("..."), but looks like a colon laying on its side. In any case ".." avoids any possible confusion with a minus sign or a comma.

So far as I can find Ramshaw did not publish anything before his PhD thesis in 1979. It is interesting to note that his supervisor for this thesis was none other than Donald E. Knuth. I only skimmed through this thesis, but I did not find any use of, let alone a full description of, any form of interval notation resembling Hoare's notation.

Note I have read at least the related portions of all the books and papers I mention.

So, I think the attribution for this notation should be given to Wirth and Hoare (invention, first published mention of, and inspiration by Wirth; details and full publication by Hoare).

Maybe R.W. Floyd deserves some mention too, but that's not yet shown in what I've read.

I sort of trust Knuth to know something about Ramshaw's influence given he was his supervisor, but I'd like to see it in a publication and until then I'd suggest that perhaps Knuth is giving Ramshaw some unconscious favouritism. The dates of Wirth and Hoare's work and publications together are definitely not in Ramshaw's favour.

Robohack (talk) 03:47, 25 May 2017 (EDT)


 * Interesting thesis which (appropriately edited) merits inclusion as a historical note.


 * Once I'm not needing to concentrate on the day job I will do some research into the sources you cited. We may end up needing to rename this entry. --prime mover (talk) 04:02, 25 May 2017 (EDT)