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Content derived from Wikipedia article on J Programming Language

J (programming language)

From Wikipedia, the free encyclopedia

Not to be confused with the J++ or J# programming languages.

J Paradigm: array, functional, function-level, tacit

Appeared in: 1990

Developer: JSoftware

Typing discipline: strong

Major implementations: J

Influenced by: APL, FP, FL

The J programming language, developed in the early 1990s by Ken Iverson and Roger Hui, is a synthesis of APL (also by Iverson) and the FP and FL functional programming languages created by John Backus (of FORTRAN, ALGOL, and BNF fame).

To avoid the problems faced by the special character set of APL, J requires only the basic ASCII character set, resorting to the use of dot and colon characters to extend the meaning of the basic characters available.

Being an array programming language, J is very terse and powerful, and is often found to be useful for mathematical and statistical programming, especially when performing operations on matrices.

Like the original FP/FL languages, J supports function-level programming (also known as higher-order functional 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 hierarchichal 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.

J is a non-von Neumann programming language that nevertheless allows the programmer to use von Neumann programming style when desired.

Contents

1 Examples

2 Data Types and Structures

3 Dictionary

3.1 Vocabulary

4 See also

5 External links

Examples

J is an extremely powerful language, and its programs can be very terse but even more cryptic.

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, but the mechanisms for associating a script with the interpreter are system dependent. Here's how this might look on a unix system:

#!/bin/jc

echo 'Hello, world!'

exit ''

But many accomplished J programmers never resort to such mechanisms.

Here's a J program to calculate the average of a list of numbers:

avg =. +/ % #

avg 1 2 3 4

2.5

'#' - counts the number of elements in the string. '+/' - adds up all the elements in the string. '%' - divides the sum of the elements by the number of elements.

Now let's generate some random numbers and find the average:

a =. ?20$100

31 16 60 64 64 71 13 3 76 26 25 77 68 48 42 91 99 97 99 9

avg a

53.95

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

quicksort =: ($:@(}.#~{.>:}.),{.,[:$:}.#~{.<}.)`]@.(2:>#)

The following expression (thanks to Roger Hui) computes n digits of pi 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

Also have a look at Cliff Reiter's implementation of Conway's game of life at http://ww2.lafayette.edu/~reiterc/j/vector/vlife_index.html

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. And, syntactically, the J parser treats that as a single word (space characters are recognized as a word forming character when they're 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 (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. (And, when parsing J, . and : are word forming characters. They're never tokens by themselves unless preceded by a space.)

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). Boxed data is displayed by J, somewhat after the fashion some SQL interpreters decorate table results from select statements.

<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 homogenously 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.

Dictionary

J's documentation is organized as a dictionary, with words in J identified as nouns, verbs, adverbs, conjunctions, and so on. Here's an overview (with external links into the corresponding definitions,). Parts of speech are indicated using markup: nouns verbs, and miscellaneous adverbs, and conjunctions. Note that verbs have two forms -- monads (arguments only on the right) and dyads (arguments on the left and on the right). For example, in '-1' the hyphen is a monad, and in '3-2' the hyphen is a dyad. The monad definition is mostly independent of the dyad definition, regardless of whether the verb is a primitive verb or a derived verb.

Vocabulary

Constants

Controls

Foreigns

Parts of Speech

= Self-Classify ? Equal =. Is (Local) =: Is (Global)

< Box ? Less Than <. Floor ? Lesser Of (Min) <: Decrement ? Less Or Equal

> Open ? Larger Than >. Ceiling ? Larger of (Max) >: Increment ? Larger Or Equal

_ Negative Sign / Infinity _. Indeterminate _: Infinity

+ Conjugate ? Plus +. Real / Imaginary ? GCD (Or) +: Double ? Not-Or

* Signum ? Times *. Length/Angle ? LCM (And) *: Square ? Not-And

- Negate ? Minus -. Not ? Less -: Halve ? Match

% Reciprocal ? Divide %. Matrix Inverse ? Matrix Divide %: Square Root ? Root

^ Exponential ? Power ^. Natural Log ? Logarithm ^: Power

$ Shape Of ? Shape $. Sparse $: Self-Reference

~ Reflex ? Passive / EVOKE ~. Nub ? ~: Nub Sieve ? Not-Equal

| Magnitude ? Residue |. Reverse ? Rotate (Shift) |: Transpose

. Determinant ? Dot Product .. Even .: Odd

: Explicit / Monad-Dyad :. Obverse :: Adverse

, Ravel ? Append ,. Ravel Items ? Stitch ,: Itemize ? Laminate

; Raze ? Link ;. Cut ;: Word Formation ?

# Tally ? Copy #. Base 2 ? Base #: Antibase 2 ? Antibase

! Factorial ? Out Of !. Fit (Customize) !: Foreign

/ Insert ? Table /. Oblique ? Key /: Grade Up ? Sort

\ Prefix ? Infix \. Suffix ? Outfix \: Grade Down ? Sort

[ Same ? Left [: Cap

] Same ? Right

{ Catalogue ? From {. Head ? Take {: Tail ? {:: Map ? Fetch

} Item Amend ? Amend }. Behead ? Drop }: Curtail ?

" Rank ". Do ? Numbers ": Default Format ? Format

` Tie (Gerund) `: Evoke Gerund

@ Atop @. Agenda @: At

& Bond / Compose &. Under (Dual) &: Appose

&.: Under

? Roll ? Deal ?. Roll ? Deal (fixed seed)

a. Alphabet a: Ace (Boxed Empty) A. Anagram Index ? Anagram

b. Boolean / Basic c. Characteristic Values C. Cycle-Direct ? Permute

d. Derivative D. Derivative D: Secant Slope

e. Raze In ? Member (In) E. ? Member of Interval f. Fix

H. Hypergeometric i. Integers ? Index Of i: Integers ? Index Of Last

j. Imaginary ? Complex L. Level Of L: Level At

NB. Comment o. Pi Times ? Circle Function

p. Polynomial p.. Poly. Deriv. ? Poly. Integral p: Primes ?

q: Prime Factors ? Prime Exponents r. Angle ? Polar s: Symbol

S: Spread t. Taylor Coefficient t: Weighted Taylor

T. Taylor Approximation u: Unicode

x: Extended Precision _9: to 9: Constant Functions

See also

K, another programming language influenced by APL

External links

JSoftware- Creators of J (currently free for all uses)

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

J Forum Archives- Discussion of the language

Retrieved from http://en.wikipedia.org/wiki/J_%28programming_language%29

End of Wikipedia content, http://en.wikipedia.org/wiki/J_programming_language

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