The Executable Mathematical Notation called J is the latest form of Iverson Notation and APL. Copies of some early papers on J are available here for historical interest.

       Picture of Ken Iverson visiting Pomona College, c. 1985

Ken Iverson
on a visit to Pomona College

Click on the picture for a
Tribute to Ken Iverson
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To download a free copy of J and for more information about this elegant and powerful language click on: J Forum

The following papers relating to J are reproduced here with permission of the copyright holders.
(Donald McIntyre is no longer at the address given in these papers.)

The files are mostly in PDF (Portable Document Format) and can be read with Adobe Reader 7. Adobe Reader is free, and freely distributable. Older versions are slower and may be unable to read the compressed files. To download a copy click on Adobe Reader 7.0

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0. APL91 Stanford, CA: Mastering J: a challenge posed in 1990

This paper illustrates some of the features – and occasionally difficulties – inherent in the earliest versions of the language. Eugene McDonnell shepherded the paper in time for it to be included in the APL91 Proceedings Volume. Jan Karman, Middelburg, Netherlands, provided photocopies of the relevant pages.

1. Language as an intellectual tool: from hieroglyphics to APL, IBM Systems Journal, vol.30, No.4, 1991, p.554-581. This was Special Issue of the Journal celebrating the 25th Anniversary of APL (J’s predecessor), where it was immediately followed by K.E. Iverson's A personal view of APL, the authoritative account of the history of APL as the roots of the J dialect. Both papers are cited by Hui and Iverson in the J Dictionary.

As this 4MB paper takes significant time to download, it may be helpful to provide the Abstract here:

"We learn elementary mathematics before understanding the source of its symbols and procedures, which therefore appear, incorrectly, to have been decreed ready-made. Language and reason are intimately related, and the embodiment of an idea in a symbol may be essential to its comprehension. APL unifies algebra into a single consistent notation; it allows us to exploit the powerful concepts of functions and operators; and it helps us to escape from the tyranny of scalars by giving us the tools to think in terms of arrays, or multiple quantity, as J.J. Sylvester so eloquently urged us to do a century ago. APL has an intellectual consistency that is a source of satisfaction and pleasure. This paper traces the history of symbols from hieroglyphics to APL."

For an evaluation of this paper see John C. McPherson's letter

For information about John McPherson see John C. McPherson & his role in IBM

Click to download all 29 pages (4MB) of the 1991 paper (IBM Systems Journal)

If your connection is a slow one you can sample an individual page by clicking on the desired page below (from 72KB to 185KB)

p.553,   p.554,   p.555,   p.556,   p.557,   p.558,   p.559,   p.560,   p.561,   p.562,   p.563,   p.564,   p.565,   p.566,   p.567,   p.568,   p.569,   p.570,   p.571,   p.572,   p.573,   p.574,   p.575,   p.576,   p.577,   p.578,   p.579,   p.580,   p.581

3. Vector Vol.9, No.3, 1992 p.125-133 Jacobi's Method for Eigenvalues: an illustration of J   (247KB).

4. Vector Vol.11, No.4, April 1995, p.93-103 Perils of Subtraction   (362KB)

5. APL95 San Antonio, TX: Composition of Functions   (125KB)

6. Tribute to Roger Hui:   Kenneth E. Iverson Award, 1996 (31KB)

------ The Story of J ------

For some landmarks in the history of APL & J go to The Story of J   (20KB)

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