J (programming language)

J

Paradigm	Array, functional, function-level, tacit
Designed by	Ken Iverson, Roger Hui
Developer	JSoftware
First appeared	1990 (1990)
Stable release	J803 / 9 December 2014 (2014-12-09)
Typing discipline	dynamic
OS	Cross-platform (Windows, Linux, Mac OS X)
License	GPLv3
Website	www.jsoftware.com
Major implementations
J
Influenced by
APL, FP, FL
Influenced
NumPy, SuperCollider

The J programming language, developed in the early 1990s by Kenneth E. Iverson and Roger Hui, is a synthesis of APL (also by Iverson) and the FP and FL function-level languages created by John Backus.

To avoid repeating the APL special-character problem, J requires only the basic ASCII character set, resorting to the use of the dot and colon as "inflections" to form short words similar to digraphs. Most such "primary" (or "primitive") J words serve as mathematical symbols, with the dot or colon extending the meaning of the basic characters available. Additionally, many characters which might need to be balanced in other languages (such as [] {} "" `` or <>) are treated by J as stand-alone words or, when inflected, as single-character roots of multi-character words.

J is a very terse array programming language, and is most suited to mathematical and statistical programming, especially when performing operations on matrices. It has also been used in Extreme Programming and network performance analysis.

Like the original FP/FL languages, J supports function-level programming via its tacit programming features (note that function-level programming is not the same as functional programming).

Unlike most languages that support object-oriented programming, J's flexible hierarchical namespace scheme (where every name exists in a particular locale) can be effectively used as a framework for both class-based and prototype-based object-oriented programming.

Since March 2011, J is free and open source software under the GPLv3 license. One may also purchase source for commercial use under a negotiated license.

Examples

J permits point-free style and function composition. Thus, its programs can be very terse and are considered difficult to read by some programmers.

The hello world program in J is

  'Hello, world!'

This implementation of hello world reflects the traditional use of J – programs are entered into a J interpreter session, and the results of expressions are displayed. It's also possible to arrange for J scripts to be executed as standalone programs. Here's how this might look on a UNIX system:

   #!/bin/jc
   echo 'Hello, world!'
   exit ''

Historically, APL used / to indicate the fold, so +/1 2 3 was equivalent to 1+2+3. Meanwhile, division was represented with the classic mathematical division symbol (the obelus, ÷), which was implemented by overstriking a minus sign and a colon (on both EBCDIC and ASCII paper terminals). Because ASCII in general does not support overstrikes in a device-independent way, and does not include a division symbol per se, J uses % to represent division, as a visual approximation or reminder. (This illustrates something of the mnemonic character of J's tokens, and some of the quandaries imposed by the use of ASCII.)

The following defines a J function named "avg" to calculate the average of a list of numbers:

  avg=: +/ % #

This is a test execution of the function:

  avg 1 2 3 4
2.5

# counts the number of items in the array. +/ sums the items of the array. % divides the sum by the number of items. Note: avg is defined above using a train of three verbs ("+/", "%", and "#") known as a fork. Specifically (V0 V1 V2) Ny is the same as (V0(Ny)) V1 (V2(Ny)) which shows some of the power of J. (Here V0, V1, and V2 denote verbs and Ny denotes a noun.)

Some examples of using avg :

  v=: ?. 20 $100     NB. a random vector
  v
46 55 79 52 54 39 60 57 60 94 46 78 13 18 51 92 78 60 90 62
  avg v
59.2

  4 avg\ v            NB. moving average on periods of size 4
58 60 56 51.25 52.5 54 67.75 64.25 69.5 57.75 38.75 40 43.5 59.75 70.25 80 72.5

  m=: ?. 4 5 $50     NB. a random matrix
  m
46  5 29  2  4
39 10  7 10 44
46 28 13 18  1
42 28 10 40 12

  avg"1 m             NB. apply avg to each rank 1 subarray (each row) of m
17.2 22 21.2 26.4

Rank is a crucial concept in J. Its significance in J is similar to the significance of "select" in SQL and of "while" in C.

Here is an implementation of quicksort, from the J Dictionary:

   sel=: adverb def 'u # ['
   
   quicksort=: verb define
    if. 1 >: #y do. y
    else.
     (quicksort y <sel e),(y =sel e),quicksort y >sel e=.y{~?#y
    end.
   )

The following is an implementation of quicksort demonstrating tacit programming. Tacit programming involves composing functions together and not referring explicitly to any variables. J's support for forks and hooks dictates rules on how arguments applied to this function will be applied to its component functions.

   quicksort=: (($:@(<#[), (=#[), $:@(>#[)) ({~ ?@#)) ^: (1<#)

Sorting in J is usually accomplished using the built-in (primitive) verbs /: (Sort Up) and \: (Sort Down). User-defined sorts such as quicksort, above, typically are for illustration only.

The following expression exhibits pi with n digits and demonstrates the extended precision capabilities of J:

  n=: 50                      NB. set n as the number of digits required
  <.@o. 10x^n                 NB. extended precision 10 to the nth * pi
314159265358979323846264338327950288419716939937510

Data types and structures

J supports three simple types:

• Numeric
• Literal (Character)
• Boxed

Of these, numeric has the most variants.

One of J's numeric types is the bit. There are two bit values: 0, and 1. Additionally, bits can be formed into lists. For example, 1 0 1 0 1 1 0 0 is a list of eight bits. Syntactically, the J parser treats that as a single word. (The space character is recognized as a word-forming character between what would otherwise be numeric words.) Lists of arbitrary length are supported.

Furthermore, J supports all the usual binary operations on these lists, such as and, or, exclusive or, rotate, shift, not, etc. For example,

  1 0 0 1 0 0 1 0 +. 0 1 0 1 1 0 1 0     NB. or
1 1 0 1 1 0 1 0

  3 |. 1 0 1 1 0 0 1 1 1 1 1             NB. rotate
1 0 0 1 1 1 1 1 1 0 1

Note that J also supports higher order arrays of bits—they can be formed into two-dimensional, three-dimensional, etc. arrays. The above operations perform equally well on these arrays.

Other numeric types include integer (e.g. 3, 42), floating point (3.14, 8.8e22), complex (0j1, 2.5j3e88), extended precision integer (12345678901234567890x), and (extended precision) rational fraction (1r2, 3r4). As with bits, these can be formed into lists or arbitrarily dimensioned arrays. As with bits, operations are performed on all numbers in an array.

Lists of bits can be converted to integer using the #. verb. Integers can be converted to lists of bits using the #: verb. (When parsing J, . (period) and : (colon) are word-forming characters. They're never tokens by themselves unless preceded by whitespace.)

J also supports the literal (character) type. Literals are enclosed in quotes, for example, 'a' or 'b'. Lists of literals are also supported using the usual convention of putting multiple characters in quotes, such as 'abcdefg'. Typically, individual literals are 8-bits wide (ASCII), but J also supports other literals (Unicode). Numeric and boolean operations are not supported on literals, but collection-oriented operations (such as rotate) are supported.

Finally, there's the boxed data type. Typically, data is put in a box using the < operation (without any left argument—if there's a left argument, this would be the 'less than' operation). This is analogous to C's & operation (without any left argument). However, where the result of C's & has reference semantics, the result of J's < has value semantics. In other words, < is a function and it produces a result. The result has 0 dimensions, regardless of the structure of the contained data. From the viewpoint of a J programmer, < 'puts the data into a box' and lets the programmer work with an array of boxes (it can be assembled with other boxes, and/or additional copies can be made of the box).

  <1 0 0 1 0
+---------+
|1 0 0 1 0|
+---------+

The only collection type offered by J is the arbitrarily dimensioned array. Most algorithms can be expressed very concisely using operations on these arrays.

J's arrays are homogeneously typed, for example the list 1 2 3 is a list of integers despite the fact that 1 is a bit. For the most part, these sorts of type issues are transparent to the programmer. Only certain specialized operations reveal differences in type. For example, the list 1.0 0.0 1.0 0.0 would be treated exactly the same, by most operations, as the list 1 0 1 0 .

J also supports sparse numeric arrays where non-zero values are stored with their indices. This is an efficient mechanism where relatively few values are non-zero.

J also supports objects and classes, but these are an artifact of the way things are named, and are not data types in and of themselves. Instead, boxed literals are used to refer to objects (and classes). J data has value semantics, but objects and classes need reference semantics.

Another pseudo-type—associated with name, rather than value—is the memory mapped file.

Documentation

J's documentation includes a dictionary, with words in J identified as nouns, verbs, adverbs, conjunctions, and so on. Primary words are listed in the vocabulary, in which their respective parts of speech are indicated using markup. Note that verbs have two forms: monadic (arguments only on the right) and dyadic (arguments on the left and on the right). For example, in '-1' the hyphen is a monadic verb, and in '3-2' the hyphen is a dyadic verb. The monadic definition is mostly independent of the dyadic definition, regardless of whether the verb is a primitive verb or a derived verb.

Control structures

J provides control structures (details here) similar to other procedural languages. Prominent control words in each category include:

• assert.
• break.
• continue.
• for.
• goto_label.
• if. else. elseif.
• return.
• select. case.
• throw.
• try. catch.
• while. whilst.

See also

• A+ (programming language) - an APL dialect
• K (programming language) - another APL-influenced language
• Q - The language of KDB+ and a new merged version of K and KSQL.

External links

• JSoftware - Creators of J
• Learning J - An Introduction to the J Programming Language by Roger Stokes
• J Wiki - Showcase, documentation, articles, etc.
• J Forum Archives - Discussion of the language
• Cliff Reiter - Chaos, fractals, and mathematical symmetries, in J
• Ewart Shaw - Bayesian inference, medical statistics, and numerical methods, using J
• Keith Smillie - Statistical applications of array programming languages, especially J
• John Howland - Research on parallelization of array programming languages, especially J

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