Lambda the Ultimate

But I'm being selfish. I wish to extend my condolences to Dr. Iverson's family, who have of course not lost a leader in their field, but their father, husband, and friend.

We need to post one. If someone wants to take it upon himself to write an obit for Iverson, please do.

Click here to see LtU threads that mentioned and discussed Iverson.

APL used to have quite a following, and APL die-hards still see it as one of the most elegant programming languages ever designed, if not the most elegant. However, APL did have some quirks, most notable among them, of course, is the reliance on an extended character set not available on most keyboards, and until recently requiring special facilities to display, print and edit.

Iverson's later work on J implemented his more recent thinking about programming (including things like support for richer phrasal forms, tacit programming, and verb rank). J uses regular ASCII characters, but continues APL's tradition by providing a large set of cryptic but very powerful built-in array operators. Deciding which of the two languages is more readable, is a matter of personal taste.

Iverson enjoyed language and words, and is reported to have read dictionaries "like people read novels." The J language is defined and explained in The J Dictionary.

Iverson was awarded the Turing Award in 1979 [f]or his pioneering effort in programming languages and mathematical 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.

His Turing Award lecture is titled Notation as a Tool of Thought a phrase that has become associated with him, and perhaps best summarizes his interests and contributions. The lecture is still worth reading by anyone interested in programming languages and notation design.

I conclude with a couple of quotes from Iverson, and a brief explanation of some J terminology.

The thesis ... is that the advantages of executability and universality found in programming languages can be effectively combined, in a single coherent language, with the advantages offered by mathematical notation. -- Notation as a Tool Of Thought, CACM, 23:8, 1980.

[T]he initial motive for developing APL was to provide a tool for writing and teaching. Although APL has been exploited mostly in commercial programming, I continue to believe that its most important use remains to be exploited: as a simple, precise, executable notation for the teaching of a wide range of subjects. -- A Personal View of APL, IBM Sys. Journal, 30:4, 1991.

Rank

An central concept in J, unifying and simplifying the handling of array functions (verbs).

A rank-k cell of A is a subarray of A along k contigous final axes. Primitive functions have intrinsic rank, and operate on arrays as collections of cells of the appropriate rank. For example, matrix inverse has rank 2. When applied to an array of shape 5 4 3, it treats it as a collection of five 4X3 matrices and produces a result of shape 5 3 4.

J allows the programmer to specify the rank of cells a verb should operate on. Rank coercion works for built-in verbs and user written verbs alike.

Tacit Programming

Iverson used the term tacit programming to refer to function definitions which make no explicit mention of the function arguments. The classic example is the average funcion.

sum=. +/       NB. reduce the argument using +
avg=. sum % #  NB. (sum x)%(# x) 
               NB. [this is the fork phrasal form]

Iverson was one of the pioneers in the field of programming language design, and his contributions and ideas influenced the thinking of many, be it directly or indirectly.