Kenneth Eugene Iverson (17 December 1920 – 19 October 2004) was a Canadiancomputer scientist noted for the development of theprogramming languageAPL. He was honored with theTuring Award in 1979 "for his pioneering effort in programming languages andmathematical notation resulting in what the computing field now knows as APL; for his contributions to the implementation of interactive systems, to educational uses of APL, and to programming language theory and practice".[1]
Ken Iverson was born on 17 December 1920 nearCamrose, a town in centralAlberta, Canada.[2] His parents were farmers who came to Alberta fromNorth Dakota; his ancestors came fromTrondheim,Norway.[3]
Iverson began school on 1 April 1926 in aone-room school,[4] initially in Grade 1, promoted to Grade 2 after 3 months and to Grade 4 by the end of June 1927.He left school after Grade 9 because it was the depths of theGreat Depression and there was work to do on thefamily farm, and because he thought further schooling only led to becoming a schoolteacher and he had no desire to become one. At age 17, while still out of school, he enrolled in a correspondence course on radios withDe Forest Training in Chicago, and learned calculus by self-study from a textbook.[4][6]DuringWorld War II, while serving in theRoyal Canadian Air Force, he took correspondence courses toward a high school diploma.
After the war, Iverson enrolled inQueen's University inKingston, Ontario, taking advantage of government support for ex-servicemen and under threat from an Air Force buddy who said he would "beat his brains out if he did not grasp the opportunity".[4] He graduated in 1950 as the top student with aBachelor's degree inmathematics andphysics.[3]
Continuing his education atHarvard University, he began in the Department of Mathematics and received aMaster's degree in 1951. He then switched to the Department of Engineering and Applied Physics, working withHoward Aiken andWassily Leontief.
Kenneth Iverson has recalled graduate study under Aiken as "like an apprenticeship" in which the student "learned the tools of the scholarship trade". Every topic was "used more as a focus for the development of skills such as clarity of thought and expression than as an end in itself". Once admitted to the program, a graduate student underwent a rite of "adoption into the fold". He was given a desk (or a share of a desk) among a group of other graduate students, the permanent staff, or visiting scholars, "most of whom were engaged in some aspect of the design and building of computers". A student was thus "made to feel part of a scholarly enterprise" and was provided, "often for the first time, with easy and intimate access to others more experienced in his chosen field".
— I. Bernard Cohen,Howard Aiken: Portrait of a Computer Pioneer, MIT Press, 1999, page 215.[7]
When interviewing Aiken, I had asked him whether Tropp and I might see his lecture notes; Aiken replied that he had always destroyed his lecture notes at the end of each year, so that he would not be tempted to repeat his lectures.
— I. Bernard Cohen and Gregory W. Welch, editors,Makin' Numbers, MIT Press, 1999, page xvi.[8]
Howard Aiken had developed theHarvard Mark I, one of the first large-scale digital computers, whileWassily Leontief was an economist who was developing theinput–output model of economic analysis, work for which he would later receive theNobel Prize. Leontief's model required large matrices and Iverson worked on programs that could evaluate these matrices on theHarvard Mark IV computer. Iverson received aPh.D. inapplied mathematics in 1954 with a dissertation based on this work.[9][10]
At Harvard, Iverson met Eoin Whitney, a 2-timePutnam Fellow and fellow graduate student from Alberta.[11][12] This had future ramifications.
Iverson stayed on at Harvard as anassistant professor to implement the world's first graduate program in "automatic data processing".[15][16][17]
Many people think that Aiken was interested only inscientific computers. This was simply not so. During one coffee hour, Aiken turned to Ken Iverson, who had just finished his Ph.D., and said: "These machines are going to be immensely important for business, and I want you to prepare and teach a course in business data processing next fall." There had never been such a course anywhere in the world. Ken was qualified only because he was a mathematician. I was so excited by the prospect that I immediately volunteered to be Ken's graduate teaching assistant.
— Frederick Brooks Jr., Aiken and the Harvard "Comp Lab", in I. Bernard Cohen and Gregory W. Welch, editors,Makin' Numbers, MIT Press, 1999, page 141.[8]
It was in this period that Iverson developed notation for describing and analyzing various topics in data processing, for teaching classes, and for writing (with Brooks)Automatic Data Processing.[18] He was "appalled" to find that conventional mathematical notation failed to fill his needs, and began work on extensions to the notation that were more suitable. In particular, he adopted the matrix algebra used in his thesis work, the systematic use of matrices and higher-dimensional arrays intensor analysis, and operators in the sense ofHeaviside in his treatment ofMaxwell's equations,higher-order functions on function argument(s) with a function result.[4] The notation was also field-tested in the business world in 1957 during a 6-month sabbatical spent atMcKinsey & Company.[4][19] The first published paper using the notation wasThe Description of Finite Sequential Processes, initially Report Number 23 toBell Labs and later revised and presented at the Fourth London Symposium on Information Theory in August 1960.[13][20]
Iverson stayed at Harvard for five years but failed to get tenure, because "[he hadn't] published anything but the one little book".[3]
Iverson joinedIBM Research in 1960 (and doubled his salary).[4] He was preceded to IBM byFred Brooks, who advised him to "stick to whatever [he] really wanted to do, because management was so starved for ideas that anything not clearly crazy would find support." In particular, he was allowed to finish and publishA Programming Language[20][21] and (with Brooks)Automatic Data Processing,[18] two books that described and used the notation developed at Harvard. (Automatic Data Processing andA Programming Language began as one book "but the material grew in both magnitude and level until a separation proved wise".[18][21])
At IBM, Iverson soon metAdin Falkoff, and they worked together for the next twenty years. Chapter 2 ofA Programming Language used Iverson's notation to describe theIBM 7090 computer.[20][21] In early 1963 Falkoff, later joined by Iverson andEd Sussenguth, proceeded to use the notation to produce a formal description of theIBM System/360 computer then under design.[22] The result was published in 1964 in a double issue of the IBM Systems Journal,[23] thereafter known as the "grey book" or "grey manual". The book was used in a course on computer systems design at the IBM Systems Research Institute.[23] A consequence of the formal description was that it attracted the interest of bright young minds.[4][24] One hotbed of interest was atStanford University which includedLarry Breed,Phil Abrams,Roger Moore,Charles Brenner,[25] and Mike Jenkins,[26][27] all of whom later made contributions to APL. Donald McIntyre, head of geology atPomona College which had the first general customer installation of a 360 system, used the formal description to become more expert than the IBM systems engineer assigned to Pomona.[4][28]
With the completion of the formal description Falkoff and Iverson turned their attention to implementation. This work was brought to rapid fruition in 1965 whenLarry Breed andPhil Abrams joined the project. They produced a FORTRAN-based implementation on the 7090 called IVSYS (for Iverson system) by autumn 1965, first in batch mode and later, in early 1966, in time-shared interactive mode.[25][29][30] Subsequently, Breed,Dick Lathwell (exUniversity of Alberta), and Roger Moore (ofI. P. Sharp Associates) produced the System/360 implementation;[31] the three received theGrace Murray Hopper Award in 1973 "for their work in the design and implementation of APL\360, setting new standards in simplicity, efficiency, reliability and response time for interactive systems."[32] While the 360 implementation work was underway "Iverson notation"[30][33] was renamed "APL", by Falkoff.[34] The workspace "1 cleanspace" was saved at 1966-11-27 22.53.58UTC.[24] APL\360 service began within IBM several weeks before that[35] and outside IBM in 1968.[29] Additional information on the implementation of APL\360 can be found in the Acknowledgements of theAPL\360 User's Manual[36] and in "Appendix. Chronology of APL development" ofThe Design of APL.[22]
APL expression for the depth of parentheses nesting[37][38]
The formal description and especially the implementation drove the evolution of the language, a process of consolidation and regularization in typography, linearization, syntax, and function definition described inAPL\360 History,[39]The Design of APL,[22] andThe Evolution of APL.[19] Two treatises from this period,Conventions Governing the Order of Evaluation[40] andAlgebra as a Language,[41] are apologias of APL notation.
The notation was used by Falkoff and Iverson to teach various topics at various universities and at the IBM Systems Research Institute.[22][39] In 1964 Iverson used the notation in a one-semester course for seniors at theFox Lane High School,[34][42] and later inSwarthmore High School.[4] After APL became available its first application was to teach formal methods in systems design atNASA Goddard.[39][43] It was also used at theHotchkiss School,[25]Lower Canada College,[44]Scotch Plains High School,[45] Atlanta public schools,[46][47] among others. In one school the students became so eager that they broke into the school after hours to get more APL computer time;[24][48] in another the APL enthusiasts steered newbies toBASIC so as to maximize their own APL time.[25]
In 1969, Iverson and the APL group inaugurated the IBM Philadelphia Scientific Center.[29][39] In 1970 he was namedIBM Fellow.[49] He used the funding that came with being an IBM Fellow to bring in visiting teachers and professors from various fields, including Donald McIntyre from Pomona[28] andJeff Shallit as a summer student.[24] For a period of several months the visitors would start using APL for expositions in their own fields, and the hope was that later they would continue their use of APL at their home institutions.[50] Iverson's work at this time centered in several disciplines, including collaborative projects in circuit theory, genetics, geology, and calculus.[51][52][53][54] When the PSC closed in 1974,[29][34] some of the group transferred to California while others including Iverson remained in the East, later transferring back to IBM Research. He received theTuring Award in 1979.[1]
(L to R) Dick Lathwell, Ken Iverson, Roger Moore, Adin Falkoff, Phil Abrams, and Larry Breed. On the extreme left in the background: Jon McGrew. Taken in the I.P. Sharp Associates hospitality suite during the 1978 APL Users Meeting in Toronto, Ontario.
The following table lists the publications which Iverson authored or co-authored while he was at IBM. They reflect the two main strands of his work.
In 1980, Iverson left IBM forI. P. Sharp Associates,[79][80] an APLtime-sharing company. He was preceded there by his IBM colleagues Paul Berry, Joey Tuttle,Dick Lathwell, andEugene McDonnell. At IPSA, the APL language and systems group was managed by Eric Iverson (Ken Iverson's son);Roger Moore, one of the APL\360 implementers, was a vice president.
Iverson worked to develop and extend APL on the lines presented inOperators and Functions.[73][81] The language work gained impetus in 1981 whenArthur Whitney and Iverson produced a model of APL written in APL[82][83] at the same time they were working on IPSA'sOAG database.[3][12][84] (Iverson introduced Arthur Whitney, son of Eoin Whitney, to APL when he was 11-years-old[12] and in 1974 recommended him for a summer student position at IPSACalgary.[24]) In the model, the APL syntax was driven by an 11-by-5 table. Whitney also invented therank operator in the process.[85] The language design was further simplified and extended inRationalized APL[86] in January 1983, multiple editions ofA Dictionary of the APL Language between 1984 and 1987, andA Dictionary of APL[87] in September 1987. Within IPSA, the phrase "dictionary APL" came into use to denote the APL specified byA Dictionary of APL, itself referred to as "the dictionary". In the dictionary, APL syntax is controlled by a 9-by-6 table and the parsing process was precisely and succinctly described in Table 2, and there is a primitive (monadic ⊥, modeled in APL) for word formation (lexing).
In the 1970s and 1980s, the main APL vendors wereIBM,STSC, andIPSA, and all three were active in developing and extending the language. IBM had APL2, based on the work ofJim Brown.[88][89][90] Work on APL2 proceeded intermittently for 15 years,[29] with actual coding starting in 1971 and APL2 becoming available as an IUP (Installed User Program, an IBM product classification) in 1982. STSC had an experimental APL system called NARS, designed and implemented by Bob Smith.[91][92] NARS and APL2 differed in fundamental respects from dictionary APL,[93] and differed from each other.
I.P. Sharp implemented the new APL ideas in stages: complex numbers,[94] enclosed (boxed) arrays, match, and composition operators in 1981,[95] the determinant operator in 1982,[96] and the rank operator, link, and the left and right identity functions in 1983.[97] However, the domains of operators were still restricted to the primitive functions or subsets thereof. In 1986, IPSA developed SAX,[77][98] SHARP APL/Unix, written in C and based on an implementation bySTSC. The language was as specified in the dictionary with no restrictions on the domains of operators. An alpha version of SAX became available within I.P. Sharp around December 1986 or early 1987.
In education, Iverson developedA SHARP APL Minicourse[99][100] used to teach IPSA clients in the use of APL, andApplied Mathematics for Programmers[101] andMathematics and Programming[102] which were used in computer science courses atT.H. Twente.
Ken Iverson and Arthur Whitney, 1989
Publications which Iverson authored or co-authored while he was atI. P. Sharp Associates:
Iverson retired from I. P. Sharp Associates in 1987. He kept busy while "between jobs". Regarding language design, the most significant of his activities in this period was the invention of "fork" in 1988.[111] For years, he had struggled to find a way to write f+g as in calculus, from the "scalar operators" in 1978,[73] through the "til" operator in 1982,[82][86] the catenation and reshape operators in 1984,[106] the union and intersection operators in 1987,[87] "yoke" in 1988,[112] and finally forks in 1988. Forks are defined as follows:
(f g h) y
←→
(f y) g (h y)
x (f g h) y
←→
(x f y) g (x h y)
Moreover, (f g p q r) ←→ (f g (p q r)). Thus to write f+g as in calculus, one can write f+g in APL. Iverson andEugene McDonnell worked out the details on the long plane rides to the APL88 conference in Sydney, Australia, with Iverson coming up with the initial idea on waking up from a nap.[85][113][81]: §1.3, §3.8
Iverson presented the rationale for his work post 1987 as follows:[16]
When I retired from paid employment, I turned my attention back to this matter [the use of APL for teaching] and soon concluded that the essential tool required was a dialect of APL that:
• Is available as "shareware", and is inexpensive enough to be acquired by students as well as by schools
• Can be printed on standard printers
• Runs on a wide variety of computers
• Provides the simplicity and the generality of the latest thinking in APL
The result has beenJ, first reported in [theAPL 90 Conference Proceedings].[114]
Roger Hui described the final impetus that got J started in Appendix A ofAn Implementation of J:[115]
One summer weekend in 1989,Arthur Whitney visited Ken Iverson at Kiln Farm and produced—on one page and in one afternoon—an interpreter fragment on theAT&T 3B1 computer. I studied this interpreter for about a week for its organization and programming style; and on Sunday, August 27, 1989, at about four o'clock in the afternoon, wrote the first line of code that became the implementation described in this document.Arthur's one-page interpreter fragment is as follows: ...
Hui, a classmate of Whitney at theUniversity of Alberta, had studiedA Dictionary of the APL Language whenhe was between jobs,[4] modelled the parsing process in at least two different ways,[85] and investigated uses of dictionary APL in diverse applications.[116] As well, from January 1987 to August 1989 he had access to SAX,[77] and in the later part of that period used it on a daily basis.[85]
J initially tookA Dictionary of APL[87] as the specification, and the J interpreter was built around Table 2 of the dictionary. The C data and program structures were designed so that the parse table in C corresponded directly to the parse table in the dictionary.[85] In retrospect, Iverson's APL87 paperAPL87,[107] in five pages, prescribed all the essential steps in writing an APL interpreter, in particular the sections on word formation and parsing.Arthur Whitney, in addition to the "one-page thing", contributed to J development by suggesting that primitives be oriented on the leading axis, that agreement (a generalization of scalar extension) should be prefix instead of suffix,[117] and that a total array ordering be defined.[118]
One of the objectives was to implement fork. This turned out to be rather straightforward, by the inclusion of one additional row in the parse table. The choice to implement forks was fortuitous and fortunate. It was realized only later[119][120] that forks madetacit expressions (operator expressions) complete in the following sense: any sentence involving one or two arguments that did not use its arguments as an operand, can be written tacitly with fork, compose, the left and right identity functions, and constant functions.
Two obvious differences between J and other APL dialects are: (a) its use of terms from natural languages instead of from mathematics or computer science (the practice began withA Dictionary of APL): noun, verb, adverbs, alphabet, word formation, sentence, ... instead of array, function, operator, character set, lexing, expression, ... ; and (b) its use of 7-bit ASCII characters instead of special symbols. Other differences between J and APL are described inJ for the APL Programmer[121] andAPL and J.[122]
The J source code is available from Jsoftware under theGNU General Public License version 3 (GPL3), or a commercial alternative.[123]
Eric Iverson founded Iverson Software Inc., in February 1990 to provide an improved SHARP APL/PC product. It quickly became obvious that there were shared interests and goals, and in May 1990 Iverson and Hui joined Iverson Software Inc.; later joined by Chris Burke. The company soon became J only. The name was changed to Jsoftware Inc., in April 2000.[85]
Ken Iverson (right) and Roger Hui, 1996
Publications which Iverson authored or co-authored while he was at Iverson Software Inc. and Jsoftware Inc.:
^Iverson, Kenneth E. (June 1954). Jacobson, Arvid W. (ed.)."Graduate Instruction and Research".Proceedings of the First Conference on Training Personnel for the Computing Machine Field. Wayne State University. Retrieved9 April 2016.
^Jenkins, Michael A. (June 1970). "The Solution of Linear Systems of Equations and Linear Least Squares Problems in APL".Technical Report Number 320-2989. IBM Corp.
^Jenkins, Michael A. (10 February 1972). "Domino – An APL Primitive Function for Matrix Inverse – Its Implementation and Applications".APL Quote Quad.3 (4). Reprinted inJenkins, M. A. (1972). "DOMINO: An APL Primitive Function for Matrix Inversion – – Its Implementation and Applications".ACM SIGPLAN Notices.7 (4):29–40.doi:10.1145/1115910.1115911.
^Biancuzzi, Federico; Warden, Shane (March 2009).Masterminds of Programming. O'Reilly Media. Archived fromthe original on 5 July 2018. Retrieved13 April 2016.
^Berry, Paul;Falkoff, Adin D.; Iverson, Kenneth E. (24 August 1970). "Using the Computer to Compute: A Direct but Neglected Approach to Teaching Mathematics".IFIP World Conference on Computer Education.
^Iverson, Kenneth E. (1972).Algebra: An Algorithmic Treatment. Addison-Wesley.
^Iverson, Kenneth E. (January 1972)."APL in Exposition"(PDF).Technical Report Number RC 320-3010. IBM Philadelphia Scientific Center. Retrieved9 April 2016.
^Iverson, Kenneth E. (July 1972)."Introducing APL to Teachers".Technical Report Number RC 320-3014. IBM Philadelphia Scientific Center. Retrieved9 April 2016.
^Iverson, Kenneth E. (1976).Elementary Analysis. APL Press.
^Iverson, Kenneth E. (May 1962)."A Programming Language".Proceedings of the AFIPS Spring Joint Computer Conference, San Francisco. Retrieved13 April 2016.
^Iverson, Kenneth E. (September 1976). "Two combinatoric operators".Proceedings of the eighth international conference on APL - APL '76. pp. 233–237.doi:10.1145/800114.803681.S2CID20408139.
^abcIverson, Kenneth E. (26 April 1978)."Operators and Functions".Research Report #RC7091. IBM. Retrieved9 April 2016.
^Iverson, Kenneth E. (June 1979). "The derivative operator".Proceedings of the international conference on APL: Part 1 - APL '79. pp. 347–354.doi:10.1145/800136.804486.
^Brown, James A. (1971).A Generalization of APL (Ph.D. thesis). Department of Computer and Information Sciences, Syracuse University.
^Brown, James A. (1984). "The Principles of APL2".Technical Report 03.247. IBM Santa Teresa Laboratory.
^Brown, James A. (1988). "APL2 Programming: Language Reference".Sh20-9227. IBM Corporation.
^Smith, Bob (1981). "Nested arrays, operators, and functions".Proceedings of the international conference on APL - APL '81. pp. 286–290.doi:10.1145/800142.805376.ISBN0-89791-035-4.
^Bernecky, Robert; Iverson, Kenneth E. (6 October 1980)."Operators and Enclosed Arrays".1980 APL Users Meeting Proceedings. Retrieved10 April 2016.
^Iverson, Kenneth E. (October 1980). "Direct Definition".SHARP APL Technical Note.36.
^Iverson, Kenneth E.; Wooster, Peter K. (September 1981). "A function definition operator".APL Quote Quad.12:142–145.doi:10.1145/390007.805349.
^abIverson, Kenneth E.; Pesch, Roland H.; Schueler, J. Henri (June 1984)."An Operator Calculus".APL 84 Conference Proceedings. Retrieved10 April 2016.
^abIverson, Kenneth E. (May 1987)."APL87".APL 87 Conference Proceedings. Retrieved10 April 2016.
^Hagamen, W.D.; Berry, P.C.; Iverson, K.E.; Weber, J.C. (August 1989). "Processing natural language syntactic and semantic mechanisms". Conference Proceedings on APL as a Tool of Thought, APL 1989, New York City, NY, USA, August 7–10, 1989.APL Quote Quad.19 (4):184–189.doi:10.1145/75144.75170.ISBN0897913272.S2CID14004227.
^Hui, Roger; Iverson, Kenneth E. (January 1998). "Mathematical roots of J".Proceedings of the conference on Share knowledge share success - APL '97. pp. 21–30.doi:10.1145/316689.316698.S2CID2317632.
Ken Iverson Quotations and Anecdotes illustrations of what Iverson was like as a person, what he was like to work with, the milieu in which he studied and worked, his outlook on life, his sense of humor, etc.
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