J (programming language)

TheJprogramming language,developed in the early 1990s byKenneth E. IversonandRoger Hui,is anarray programminglanguage based primarily onAPL(also by Iverson).

J

Paradigm	Array,functional,object-oriented(class-based,prototype-based),function-level,tacit
Designed by	Kenneth E. Iverson,Roger Hui
Developer	JSoftware
First appeared	1990(1990)
Stable release	J9.5 / 20 December 2023(2023-12-20)
Typing discipline	dynamic
OS	Cross-platform:Windows,Linux,macOS,Android,iOS,Raspberry Pi
License	GPLv3
Website	www.jsoftware.com
Majorimplementations
J
Influenced by
APL
Influenced
NumPy,SuperCollider

To avoid repeating the APL special-character problem, J uses only the basicASCIIcharacter set, resorting to the use of the dot and colon asinflectionsto form short words similar todigraphs.Most suchprimary(orprimitive) J words serve as mathematical symbols, with the dot or colon extending the meaning of the basic characters available. Also, many characters which in other languages often must be paired (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 tersearray programming language,and is most suited tomathematicalandstatisticalprogramming, especially when performing operations onmatrices.It has also been used inextreme programmingandnetwork performanceanalysis.

LikeJohn Backus's languagesFPandFL,J supportsfunction-level programmingvia itstacit programmingfeatures.

Unlike most languages that supportobject-oriented programming,J's flexible hierarchicalnamespacescheme (where every name exists in a specificlocale) can be effectively used as a framework for bothclass-basedandprototype-basedobject-oriented programming.

Since March 2011, J isfree and open-source softwareunder theGNU General Public Licenseversion 3 (GPLv3).One may also purchase source under a negotiated license.

Examples

J permitspoint-free styleandfunction composition.Thus, its programs can be very terse and are considered difficult to read by some programmers.

The"Hello, World!" programin 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 aUnixsystem:

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

(Note that current j implementations install eitherjconsoleor (because jconsole is used by java),ijconsoleand likely install this to /usr/bin or some other directory (perhaps the Application directory on OSX). So, there's a system dependency here which the user would have to solve.)

Historically, APL used/to indicate thefold,so+/1 2 3was equivalent to1+2+3.Meanwhile, division was represented with the mathematicaldivision symbol(÷).

Because ASCII does not include a division symbolper 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.)

Defining a J function namedavgto calculate the average of a list of numbers yields:

avg=:+/%#

• +/sums the items of the array.
• #counts the number of items in the array.
• %divides the sum by the number of items.

This is a test execution of the function:

avg1234
2.5

Above,avgis defined using a train of three verbs (+/,%,and#) termed afork.Specifically,(V0 V1 V2) Nyis 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 usingavg:

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

4avg\vNB. 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=:?.45$50NB. 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"1mNB. apply avg to each rank 1 subarray (each row) of m
17.2 22 21.2 26.4

Rankis a crucial concept in J. Its significance in J is similar to the significance ofselectinSQLand ofwhileinC.

Implementingquicksort,from the J Dictionary yields:

sel=:adverbdef'u # ['

quicksort=:verbdefine
if.1>:#ydo.y
else.
(quicksorty<sele),(y=sele),quicksorty>sele=.y{~?#y
end.
)

The following is an implementation of quicksort demonstratingtacit programming.The latter involves composing functions together and not referring explicitly to any variables. J's support forforksandhooksdictates 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 example demonstrates the usage of the self-reference verb$:to recursively calculate fibonacci numbers:

1:`($:@-&2+$:@<:)@.(>&2)

This recursion can also be accomplished by referring to the verb by name, although this is of course only possible if the verb is named:

fibonacci=:1:`(fibonacci@-&2+fibonacci@<:)@.(>&2)

The following expression exhibitspiwith n digits and demonstrates the extended precision abilities of J:

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

Verbs and Modifiers

A program or routine - something that takes data as input and produces data as output - is called averb.J has a rich set of predefined verbs, all of which work on multiple data types automatically: for example, the verbi.searches within arrays of any size to find matches:

314159i.31NB. find the index of the first occurrence of 3, and of 1
01
314159i:31NB. find the index of the last occurrence of 3, and of 1
03

User programs can be named and used wherever primitives are allowed.

The power of J comes largely from itsmodifiers:symbols that take nounsand verbsas operands and apply the operands in a specified way. For example, the modifier/takes one operand, a verb to its left, and produces a verb that applies that verb between each item of its argument. That is,+/is a verb, defined as 'apply+between the items of your argument' Thus, the sentence

+/12345

produces the effect of

1+2+3+4+5

+/12345
15

J has roughly two dozen of these modifiers. All of them can apply to any verb, even a user-written verb, and users may write their own modifiers. While modifiers are powerful individually, allowing

• repeated execution, i. e.do-while
• conditional execution, i. e.if
• execution of regular or irregular subsets of arguments

some of the modifiers control the order in which components are executed, allowing modifiers to be combined in any order to produce the unlimited variety of operations needed for practical programming.

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 thebit.There are two bit values:0,and1.Also, bits can be formed into lists. For example,1 0 1 0 1 1 0 0is a list of eight bits. Syntactically, the J parser treats that as one word. (The space character is recognized as a word-forming character between what would otherwise be numeric words.) Lists of arbitrary length are supported.

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

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

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

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 are never tokens alone, unless preceded bywhitespace characters.)

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 is a boxed data type. Typically, data is put in a box using the<operation (with no left argument; if there's a left argument, this would be theless thanoperation). This is analogous toC's&operation (with no 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 boxand allows working with an array of boxes (it can be assembled with other boxes or more 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 list1 2 3is a list of integers despite1being a bit. For the most part, these sorts of type issues are transparent to programmers. Only certain specialized operations reveal differences in type. For example, the list1.0 0.0 1.0 0.0would be treated exactly the same, by most operations, as the list1 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. 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.

Debugging

Dissecting the Collatz sequence starting from 6

J has the usual facilities for stopping on error or at specified places within verbs. It also has a unique visual debugger, calledDissect,that gives a 2-D interactive display of the execution of a single J sentence. Because a single sentence of J performs as much computation as an entire subroutine in lower-level languages, the visual display is quite helpful.

Documentation

J's documentation includes adictionary,with words in J identified asnouns,verbs,modifiers,and so on. Primary words are listed in thevocabulary,in which their respectiveparts of speechare indicated using markup. Note that verbs have two forms:monadic(arguments only on the right) anddyadic(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

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

External links

• Official website– JSoftware, creators of J
• jsourceonGitHub– Repository of source
• J Wiki
• Learning J– An Introduction to the J Programming Language by Roger Stokes