J (Programming language)

J is an array programming language, claiming itself an APL successor.

Basics

'hello, worms'
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "'hello, worms'", :position {:start {:line 17, :column 1, :offset 388}, :end {:line 17, :column 17, :offset 404}}}

Terminology

verb

A function. Verbs only come in two varieties, monadic (unary) and dyadic (binary).

operator

A higher-order function that computes functions from functions.

Adverb

A monadic operator.

monad

A unary verb.

dyad

A binary verb.

rank

The number of dimensions an array has. A scalar is rank-0, an array of scalars is rank-1, an XƗY table is rank-2, an XƗYƗZ table is rank-3, ...

shape

The list of an array's dimensions. 0 0 0 has shape 3, 2 3$0 has shape 2 3, etc. The shape of an object x is equal to #$x.

Syntax and evaluation order

J, like other array languages, only evaluates right-to-left ā€” entirely homogeneous operator precedence. Every monad extends as far to the right as possible, and every dyad is right-associative. 

2*3+4
(2*3)+4
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "14\n10", :position {:start {:line 43, :column 1, :offset 1336}, :end {:line 44, :column 5, :offset 1345}}}

This tradition starts with APL.

Basic operations

Most basic verbs (functions) in J are overloaded to apply between scalars, map over arrays, and apply pointwise between arrays. 

2*3
2*1 2 3
1 0 1*1 2 3
0 1*1 2 3
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "6\n2 4 6\n1 0 3\nlength error, executing dyad *", :position {:start {:line 60, :column 1, :offset 1602}, :end {:line 63, :column 33, :offset 1654}}}

Some other verbs: 

2<1 2 3 4
*:4       NB. Square function
25%5      NB. Division
#1 0 1 0  NB. "Tally" (length/count)
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "0 0 1 1\n16\n5\n4", :position {:start {:line 75, :column 1, :offset 1811}, :end {:line 78, :column 4, :offset 1833}}}

/

/ is an adverb, akin to a fold or reduce operator. J people call it insert. 

*/1 2 3
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "6", :position {:start {:line 89, :column 1, :offset 1970}, :end {:line 89, :column 4, :offset 1973}}}

Example: array equality

Comparing arrays lifts the test pointwise: 

x=:1 2 3 4
y=:1 2 7 4
x=y
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "1 1 0 1", :position {:start {:line 102, :column 1, :offset 2110}, :end {:line 102, :column 10, :offset 2119}}}

One could reduce this to a single boolean with a fold: 

x=:1 2 3 4
y=:1 2 7 4
x=y
=/x=y
x=x
=/x=x
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "1 1 0 1\n0\n1 1 1 1\n1", :position {:start {:line 116, :column 1, :offset 2255}, :end {:line 119, :column 4, :offset 2282}}}

Assignments

x=:2 3 4
x
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "2 3 4", :position {:start {:line 129, :column 1, :offset 2347}, :end {:line 129, :column 8, :offset 2354}}}

A terse reference list of basic verbs

The names listed are not those commonly-accepted. This is for my own personal recollection. }:3

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" (" [:code "table-row"] ")")] [:samp {:style {:overflow "scroll", :display "block", :white-space "pre"}} "{:type \"table-row\",\n :row-type \"standard\",\n :contents-begin 2908,\n :contents-end 2958,\n :position\n {:start {:line 143, :column 1, :offset 2907},\n :end {:line 143, :column 52, :offset 2958}},\n :children\n ([:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 2909,\\n :contents-end 2912,\\n :position\\n {:start {:line 143, :column 2, :offset 2908},\\n :end {:line 143, :column 9, :offset 2915}},\\n :children ([:code \\\";\\\"])}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 2929,\\n :contents-end 2929,\\n :position\\n {:start {:line 143, :column 9, :offset 2915},\\n :end {:line 143, :column 24, :offset 2930}},\\n :children nil}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 2931,\\n :contents-end 2935,\\n :position\\n {:start {:line 143, :column 24, :offset 2930},\\n :end {:line 143, :column 52, :offset 2958}},\\n :children (\\\"link\\\")}\\n\"]])}\n"]] [:details [:summary {:style {:font-family "IBM Plex Sans"}} ("unimplemented!" " (" [:code "table-row"] ")")] [:samp {:style {:overflow "scroll", :display "block", :white-space "pre"}} "{:type \"table-row\",\n :row-type \"standard\",\n :contents-begin 2960,\n :contents-end 3010,\n :position\n {:start {:line 144, :column 1, :offset 2959},\n :end {:line 144, :column 52, :offset 3010}},\n :children\n ([:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 2961,\\n :contents-end 2964,\\n :position\\n {:start {:line 144, :column 2, :offset 2960},\\n :end {:line 144, :column 9, :offset 2967}},\\n :children ([:code \\\"=\\\"])}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 2981,\\n :contents-end 2981,\\n :position\\n {:start {:line 144, :column 9, :offset 2967},\\n :end {:line 144, :column 24, :offset 2982}},\\n :children nil}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 2983,\\n :contents-end 3008,\\n :position\\n {:start {:line 144, :column 24, :offset 2982},\\n :end {:line 144, :column 52, :offset 3010}},\\n :children (\\\"pointwise/scalar equality\\\")}\\n\"]])}\n"]] [:details [:summary {:style {:font-family "IBM Plex Sans"}} ("unimplemented!" " (" [:code "table-row"] ")")] [:samp {:style {:overflow "scroll", :display "block", :white-space "pre"}} "{:type \"table-row\",\n :row-type \"standard\",\n :contents-begin 3012,\n :contents-end 3062,\n :position\n {:start {:line 145, :column 1, :offset 3011},\n :end {:line 145, :column 52, :offset 3062}},\n :children\n ([:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3013,\\n :contents-end 3017,\\n :position\\n {:start {:line 145, :column 2, :offset 3012},\\n :end {:line 145, :column 9, :offset 3019}},\\n :children ([:code \\\":*\\\"])}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3020,\\n :contents-end 3026,\\n :position\\n {:start {:line 145, :column 9, :offset 3019},\\n :end {:line 145, :column 24, :offset 3034}},\\n :children (\\\"square\\\")}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3061,\\n :contents-end 3061,\\n :position\\n {:start {:line 145, :column 24, :offset 3034},\\n :end {:line 145, :column 52, :offset 3062}},\\n :children nil}\\n\"]])}\n"]] [:details [:summary {:style {:font-family "IBM Plex Sans"}} ("unimplemented!" " (" [:code "table-row"] ")")] [:samp {:style {:overflow "scroll", :display "block", :white-space "pre"}} "{:type \"table-row\",\n :row-type \"standard\",\n :contents-begin 3064,\n :contents-end 3114,\n :position\n {:start {:line 146, :column 1, :offset 3063},\n :end {:line 146, :column 52, :offset 3114}},\n :children\n ([:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3065,\\n :contents-end 3069,\\n :position\\n {:start {:line 146, :column 2, :offset 3064},\\n :end {:line 146, :column 9, :offset 3071}},\\n :children ([:code \\\"-:\\\"])}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3085,\\n :contents-end 3085,\\n :position\\n {:start {:line 146, :column 9, :offset 3071},\\n :end {:line 146, :column 24, :offset 3086}},\\n :children nil}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3087,\\n :contents-end 3106,\\n :position\\n {:start {:line 146, :column 24, :offset 3086},\\n :end {:line 146, :column 52, :offset 3114}},\\n :children (\\\"structural equality\\\")}\\n\"]])}\n"]] [:details [:summary {:style {:font-family "IBM Plex Sans"}} ("unimplemented!" " (" [:code "table-row"] ")")] [:samp {:style {:overflow "scroll", :display "block", :white-space "pre"}} "{:type \"table-row\",\n :row-type \"standard\",\n :contents-begin 3116,\n :contents-end 3166,\n :position\n {:start {:line 147, :column 1, :offset 3115},\n :end {:line 147, :column 52, :offset 3166}},\n :children\n ([:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3117,\\n :contents-end 3121,\\n :position\\n {:start {:line 147, :column 2, :offset 3116},\\n :end {:line 147, :column 9, :offset 3123}},\\n :children ([:code \\\">:\\\"])}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3124,\\n :contents-end 3133,\\n :position\\n {:start {:line 147, :column 9, :offset 3123},\\n :end {:line 147, :column 24, :offset 3138}},\\n :children (\\\"successor\\\")}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3139,\\n :contents-end 3142,\\n :position\\n {:start {:line 147, :column 24, :offset 3138},\\n :end {:line 147, :column 52, :offset 3166}},\\n :children (\\\"GTE\\\")}\\n\"]])}\n"]] [:details [:summary {:style {:font-family "IBM Plex Sans"}} ("unimplemented!" " (" [:code "table-row"] ")")] [:samp {:style {:overflow "scroll", :display "block", :white-space "pre"}} "{:type \"table-row\",\n :row-type \"standard\",\n :contents-begin 3168,\n :contents-end 3218,\n :position\n {:start {:line 148, :column 1, :offset 3167},\n :end {:line 148, :column 52, :offset 3218}},\n :children\n ([:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3169,\\n :contents-end 3172,\\n :position\\n {:start {:line 148, :column 2, :offset 3168},\\n :end {:line 148, :column 9, :offset 3175}},\\n :children ([:code \\\"#\\\"])}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3176,\\n :contents-end 3181,\\n :position\\n {:start {:line 148, :column 9, :offset 3175},\\n :end {:line 148, :column 24, :offset 3190}},\\n :children (\\\"tally\\\")}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3217,\\n :contents-end 3217,\\n :position\\n {:start {:line 148, :column 24, :offset 3190},\\n :end {:line 148, :column 52, :offset 3218}},\\n :children nil}\\n\"]])}\n"]] [:details [:summary {:style {:font-family "IBM Plex Sans"}} ("unimplemented!" " (" [:code "table-row"] ")")] [:samp {:style {:overflow "scroll", :display "block", :white-space "pre"}} "{:type \"table-row\",\n :row-type \"standard\",\n :contents-begin 3220,\n :contents-end 3270,\n :position\n {:start {:line 149, :column 1, :offset 3219},\n :end {:line 149, :column 52, :offset 3270}},\n :children\n ([:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3221,\\n :contents-end 3224,\\n :position\\n {:start {:line 149, :column 2, :offset 3220},\\n :end {:line 149, :column 9, :offset 3227}},\\n :children ([:code \\\">\\\"])}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3228,\\n :contents-end 3233,\\n :position\\n {:start {:line 149, :column 9, :offset 3227},\\n :end {:line 149, :column 24, :offset 3242}},\\n :children (\\\"unbox\\\")}\\n\"]]\n [:details\n [:summary\n {:style {:font-family \"IBM Plex Sans\"}}\n (\"unimplemented!\" \" (\" [:code \"table-cell\"] \")\")]\n [:samp\n {:style {:overflow \"scroll\", :display \"block\", :white-space \"pre\"}}\n \"{:type \\\"table-cell\\\",\\n :contents-begin 3243,\\n :contents-end 3245,\\n :position\\n {:start {:line 149, :column 24, :offset 3242},\\n :end {:line 149, :column 52, :offset 3270}},\\n :children (\\\"GT\\\")}\\n\"]])}\n"]])}

On the naming of primitive verbs

Almost all of J's built-in verbs have names one or two characters long. If there is a second character, it is always (:) or (.). The colon or dot suffix is intended to imply some connection to the one-character name. E.g., square (*:) bears an obvious connection to multiplication (*).

Presented are some examples intended to illustrate the loose connection between uses of similarly-named verbs.

>

1>2          NB. Greater-than
3>.12        NB. Maximum
>.0.5        NB. Ceiling
>:3          NB. Increment
5>:4 5 6     NB. Greater-than or equal
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "0\n12\n1\n4\n1 1 0", :position {:start {:line 168, :column 1, :offset 3907}, :end {:line 172, :column 8, :offset 3931}}}

Tables

Constructing a 2Ɨ3 table

Excess will be truncated: 

2 3$0 1 2 3 4 5 6 7
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "0 1 2\n3 4 5", :position {:start {:line 185, :column 1, :offset 4057}, :end {:line 186, :column 8, :offset 4072}}}

Insufficiency will be coped with by cycling: 

2 3$0 1
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "0 1 0\n1 0 1", :position {:start {:line 195, :column 1, :offset 4164}, :end {:line 196, :column 8, :offset 4179}}}

Tally

Tally counts the number of rows a table has: 

#2 5$0
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "2", :position {:start {:line 207, :column 1, :offset 4281}, :end {:line 207, :column 4, :offset 4284}}}

Bonding

double =: * & 2
double 2
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "4", :position {:start {:line 217, :column 1, :offset 4359}, :end {:line 217, :column 4, :offset 4362}}} 

    (f & k) y    means    y f k
    (k & f) y    means    k f y

Addons (libraries)

There are a number of official J libraries living under the jsoftware Github org.

Use on NixOS

J makes a lot of FHS-based assumptions that make packaging for Nix non-trivial. Perhaps I'll be the one to deal with that if I continue using J }:3.

In the meantime, the workaround isn't too bad [cite:@young2021workaround]:

1. Figure out where your J startup file is

The startup file is called startup.ijs, and lives in the directory returned by the following expression: 

jpath'~config'
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "/home/crumb/j9.5-user/config", :position {:start {:line 243, :column 1, :offset 5048}, :end {:line 243, :column 31, :offset 5078}}}

It is okay if the startup file doesn't yet exist; just create it!

2. Tell J where to find addons

Append this to your startup file: 

SystemFolders_j_=:('addons';jpath'~user/addons'),SystemFolders_j_

3. Install your desired addons

Simply ā€” though inelegantly ā€” all that is left is to manually clone addons into the addons directory. E.g., for graphics/plot: 

$ cd "$(jconsole <<< "jpath'~addons'")"
$ mkdir graphics
$ git clone git@github.com:jsoftware/graphics_plot.git graphics/plot

And load the library in jconsole like so: 

load'plot'
unimplemented! (fixed-width){:type "fixed-width", :affiliated {:results ""}, :value "not found: /home/crumb/j9.5-user/addons/graphics/bmp/bmp.ijs\n|file name error in script, executing monad 0!:0\n|nonexistent file or invalid filename\n| 0!:0 y[4!:55<'y'\n|[-2] /home/crumb/j9.5-user/addons/graphics/plot/jzplot.ijs", :position {:start {:line 272, :column 1, :offset 5724}, :end {:line 276, :column 62, :offset 5966}}}

Oops ā€” we need to manually install each dependency }:P. It's not fun, but it isn't so bad. So far, I've only had to install 3ā€“4 dependencies (transitives included) for new addons.

Graphics

It appears many graphics-related things are only avaiable in the JQT IDE. Namely, wd and OpenGL.

References