Editing APL (programming language) (section)

=== Mathematical notation===
A [[mathematical notation]] for manipulating arrays was developed by [[Kenneth E. Iverson]], starting in 1957 at [[Harvard University]]. In 1960, he began work for [[IBM]] where he developed this notation with [[Adin Falkoff]] and published it in his book ''A Programming Language'' in 1962.<ref name="aplbook"/> The preface states its premise:
{{blockquote|Applied mathematics is largely concerned with the design and analysis of explicit procedures for calculating the exact or approximate values of various functions. Such explicit procedures are called algorithms or ''programs''. Because an effective notation for the description of programs exhibits considerable syntactic structure, it is called a ''programming language''.
}}

This notation was used inside IBM for short research reports on computer systems, such as the [[Burroughs B5000]] and its stack mechanism when [[stack machine]]s versus [[register machine]]s were being evaluated by IBM for upcoming computers.

Iverson also used his notation in a draft of the chapter ''A Programming Language'', written for a book he was writing with [[Fred Brooks]], ''Automatic Data Processing'', which would be published in 1963.<ref>Iverson, Kenneth E., [http://www.softwarepreservation.org/projects/apl/Books/Iverson-AutomaticDataProcessing-bilevel.pdf/view "Automatic Data Processing: Chapter 6: A programming language"] {{webarchive|url=https://web.archive.org/web/20090604091847/http://www.softwarepreservation.org/projects/apl/Books/Iverson-AutomaticDataProcessing-bilevel.pdf/view |date=June 4, 2009}}, 1960, Draft copy for Brooks and Iverson 1963 book, ''Automatic Data Processing''.</ref><ref>[[Fred Brooks|Brooks, Fred]]; Iverson, Kenneth, (1963), ''Automatic Data Processing'', John Wiley & Sons Inc.</ref>

In 1979, Iverson received the [[Turing Award]] for his work on APL.<ref>{{cite web |url=http://awards.acm.org/citation.cfm?id=9147499&srt=all&aw=140&ao=AMTURING |title=Turing Award Citation 1979 |publisher=Awards.acm.org |access-date=February 3, 2010 |archive-url=https://web.archive.org/web/20091223064709/http://awards.acm.org/citation.cfm?id=9147499&srt=all&aw=140&ao=AMTURING |archive-date=2009-12-23 |url-status=dead}}</ref>