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Range
...mitive function. "Range" refers to [[Unique]] in K and [[Index Generator]] in BQN.'' ...enerator]] for creating a range of numbers. Range is currently implemented in [[NARS2000]] (using the digraph <syntaxhighlight lang=apl inline>..</syntax

3 KB (282 words) - 22:18, 10 September 2022
Commute
...lt-in|Commute|⍨}}, or <syntaxhighlight lang=apl inline>⊂</syntaxhighlight> in [[SHARP APL]], is a [[monadic operator]] that takes a [[dyadic function]] a {{Works in|[[Dyalog APL]], [[dzaima/APL]], [[NARS2000]]}}

3 KB (376 words) - 16:56, 16 March 2024
APL Farm
In addition to these, the Discord server has rooms for self-promotion, code ch ...'' executes codeblocks starting with <code>bqn)</code> in CBQN. Only works in the rooms bridged to Matrix.

3 KB (393 words) - 12:53, 31 August 2023
Binomial
{{Built-in|Binomial|!}} is a [[dyadic]] [[scalar function]] which gives the [[wikipedi </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

3 KB (320 words) - 21:50, 10 September 2022
LCM
...same results on [[Boolean]] arguments and the same [[identity element]] 1, in the same way that [[GCD]] extends [[Or]]. </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

2 KB (230 words) - 21:28, 10 September 2022
Pair
...o dyadic Pair primitive). Dyadic Pair is similar to the [[Link]] primitive in [[SHARP APL]] and [[J]], but Link has an asymmetric definition that adds it ...rators. SATN-41, 1981-06-20.</ref> Pair aids in constructing nested arrays in [[tacit programming]], where [[stranding]] by juxtaposition is not availabl

3 KB (486 words) - 17:16, 6 March 2024
Case
...ite Item <syntaxhighlight lang=j inline>}</syntaxhighlight>, which differs in that the right argument is an array whose [[major cell]]s are mixed togethe {{Works in|[[dzaima/APL]]}}

1 KB (235 words) - 02:25, 9 March 2024
Format
{{Built-in|Format|⍕}} is an [[ambivalent]] [[primitive function]] which formats the Format in its [[monadic]] form allows the user to convert [[Array model|arrays]] of a

3 KB (292 words) - 21:02, 10 September 2022
Logarithm
{{Built-in|Logarithm|⍟}}, or '''Log''', is a [[dyadic]] [[scalar function]] which co ...used to determine how many digits are needed to write a positive integer Y in base X:

3 KB (287 words) - 22:06, 10 September 2022
Derived function
...s a [[function]], it can then be applied to [[argument]] arrays, resulting in other arrays. ...he derived function <syntaxhighlight lang=apl inline>⌈/</syntaxhighlight>. In most modern APLs this function can be manipulated like any other function,

1 KB (201 words) - 22:18, 10 September 2022
Function axis
...ich adhere to [[leading axis theory]] reject the use of axis specification in favor of the [[Rank operator]] because it is a fully general operator while ...list of axes to specify where the axes of argument elements will be placed in the result.

6 KB (878 words) - 05:12, 11 November 2022
RANK ERROR
...]] or [[scalar]], so giving it a higher-rank array as [[argument]] results in a RANK ERROR: ...RROR may be caused when argument ranks are incompatible in some other way. In languages with [[major cell search]] such as [[Dyalog APL]] and [[J]], the

1 KB (190 words) - 23:30, 10 March 2024
Type
...rmation about the type and structure of its argument array's [[element]]s. In normal cases, the result is identical to the argument, with all numbers rep ...ement'') was repurposed for [[Enlist]]. Thus, Dyalog left the Type meaning in place only when [[migration level]] is 0, while setting it to 1 or higher f

5 KB (491 words) - 14:28, 13 February 2023
APL.jl
...s returns Julia data. Dfns defined using APl.jl can hence be used directly in Julia code like ordinary functions. ...l""</code> string macro parses and evaluates an APL expression. The parser works on the reverse of the APL code, using the help of concatenation rules to re

3 KB (393 words) - 08:25, 23 September 2022
Function-operator overloading
...lyphs themselves, or to their values and derivations as well: for example, in [[Dyalog APL]] the assignments <syntaxhighlight lang=apl inline>r←/</synt ...nts, but dialects with overloading always choose the first interpretation, in which the overloaded value is treated as an operator.

6 KB (797 words) - 12:53, 13 February 2024
Dot
* In all dialects, it is used as [[wikipedia:decimal separator|decimal separator * In all dialects, it is a [[dyadic operator]] with function [[operand]]s, deriv

3 KB (322 words) - 22:12, 10 September 2022
From
...ted]] left argument, which varies from one language to another. It appears in [[SAX]] (as <syntaxhighlight lang=apl inline>@</syntaxhighlight>), [[Extend </syntaxhighlight>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}

6 KB (853 words) - 15:55, 19 February 2024
Unique
...hich do not [[match]] an earlier distinct cell) in the order they appeared in the array. It works on nested arrays as well:

9 KB (1,243 words) - 12:57, 23 November 2023
Drop
...and a detailed description of those extensions and their history is given in that article rather than this one. Unlike Take, Drop never uses [[fill elem {{Works in|[[Dyalog APL]], [[ngn/apl]]}}

4 KB (605 words) - 21:23, 10 September 2022
Indices
...o [[Replicate]], and may be seen as an index-based equivalent to Replicate in the same way that [[Grade]] is an index-based equivalent of sorting. ...st language to include the primitive, it is called Where (<code>&</code>). In [[J]], it is called Indices (<syntaxhighlight lang=j inline>I.</syntaxhighl

8 KB (1,126 words) - 20:03, 14 April 2024
GCD
...same results on [[Boolean]] arguments and the same [[identity element]] 0, in the same way that [[LCM]] extends [[And]]. </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

4 KB (497 words) - 21:37, 17 February 2024
Empty array
In the APL [[array model]], an '''empty''' array is one with a [[bound]] of ze ...axhighlight>. These arrays have different prototypes, and do not [[match]] in most APLs.

5 KB (810 words) - 22:29, 10 September 2022
Frame agreement
...if one frame is empty. The latter case corresponds to pairing one argument in its entirety with each of the [[cells]] of the other argument. {{Works in|[[Dyalog APL]]}}

7 KB (779 words) - 14:23, 26 August 2023
Defined function (traditional)
...ll forms; in particular [[dfn]]s are considered a type of defined function in [[Dyalog APL]] and [[GNU APL]].'' ...ctions]] have appeared, with [[J]] and [[K]] rejecting function definition in favor of [[anonymous function]] description.

11 KB (1,470 words) - 22:13, 10 September 2022
Raze
...e outer vector's axis with the first axis of each element. Raze is present in [[SHARP APL]], [[A+]], [[J]], and [[BQN]]. {{Works in|[[A+]]}}

6 KB (812 words) - 23:25, 29 January 2024
Membership
...ment. Membership derives from the traditional mathematical notation <math>\in</math> (''Element of'') and therefore uses that [[glyph]] (lunate epsilon). ...ch as [[J]] (spelled <syntaxhighlight lang=j inline>e.</syntaxhighlight>). In this case, if the right argument is a higher-[[rank]] array, the [[cell|cel

2 KB (324 words) - 15:33, 11 January 2024
Main Page
...remember]] APL with little effort. There is plenty of material to help you in the process. ...user groups|user groups]] all around the globe, many of these hold regular in-person meet-ups. There are also multiple online [[chat rooms and forums]].

5 KB (707 words) - 22:15, 10 September 2022
Roll
...cts allow <syntaxhighlight lang=apl inline>n</syntaxhighlight> to be zero, in which case Roll chooses a floating-point number between 0 and 1. Roll share {{Works in|[[Dyalog APL]], [[NARS2000]], [[dzaima/APL]]}}

3 KB (373 words) - 22:14, 10 September 2022
Scalar extension
...]s, so it's unclear when scalar extension as a unified concept was adopted in [[Iverson notation]]. ...ve been a [[RANK ERROR]] into a valid application. Second, the application works by conceptually extending the scalar to function as though it were an array

8 KB (947 words) - 03:06, 20 February 2024
Rotate
...ault one. In the [[leading axis model]], specifying an axis is discouraged in favor of using <syntaxhighlight lang=apl inline>⊖</syntaxhighlight> with </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

5 KB (626 words) - 22:15, 10 September 2022
Comment
In fact, the [[right]] function (<syntaxhighlight lang=apl inline>⊢</syntaxh </syntaxhighlight>{{Works in|[[APL64]]}}

2 KB (292 words) - 14:22, 20 May 2024
Depth
...ber of levels of [[Nested array model|nesting]] or [[box]]ing it exhibits. In some languages, Depth returns a negative result to indicate that not all pa Nested APLs vary in their definition of depth. They may take into account the array's [[prototy

3 KB (549 words) - 21:14, 10 September 2022
Atop (operator)
{{Built-in|Atop|⍤}} is a [[primitive operator|primitive]] [[dyadic operator]] which ...for the close form and <code>@:</code> for the rankless form that appears in modern APLs.

3 KB (410 words) - 19:05, 16 March 2024
Reshape
...right argument. Elements are copied from the right argument to the result in [[ravel order]], truncating if the result has smaller [[bound]] than the ri In fact it repeats an argument of any length, singleton or otherwise. This rep

6 KB (891 words) - 22:26, 10 September 2022
Ceiling
{{Built-in|Ceiling|⌈}} is a [[monadic]] [[scalar function]] that gives the [[wikiped </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

2 KB (269 words) - 21:57, 28 November 2022
Circular
{{Built-in|Circular|○}}, or '''Circle Function''', is a [[dyadic]] [[scalar function The Circular function, as found in today's APL implementations, was designed by [[Gene McDonnell]], based on

7 KB (900 words) - 22:28, 10 September 2022
Fast Fourier transform
...as early as 1970, with an 8-line implementation by Alan R. Jones published in [[APL Quote-Quad]].<ref>Jones, Alan R. ([[IBM]]). "Fast Fourier transform". A Fourier Transform (FFT) is a method of calculating the frequency components in a data set — and the inverse FFT converts back from the frequency domain

4 KB (552 words) - 21:06, 10 September 2022
Replicate
...|/|⌿}}, or '''Copy''' (<syntaxhighlight lang=j inline>#</syntaxhighlight>) in [[J]], is a [[dyadic function]] or [[monadic operator]] that copies each [[ ...s the right argument, returning only those elements which correspond to 1s in the provided mask.

16 KB (2,092 words) - 19:15, 16 March 2024
Partitioned Enclose
:''In the [[APL2]] family and many related dialects, <syntaxhighlight lang=apl in ...determined by the left argument. It was introduced by [[NARS]] and appears in [[Dyalog APL]] and some newer dialects influenced by it.

4 KB (424 words) - 21:33, 28 January 2024
Simple examples
...n definition. It can be assigned a name for use later, or used anonymously in a more complex expression. ...e [[tally]] function, which returns here the length of (number of elements in) the argument <syntaxhighlight lang=apl inline>⍵</syntaxhighlight>. The d

11 KB (1,379 words) - 01:32, 10 March 2024
Reciprocal
{{Built-in|Reciprocal|÷}} is a [[monadic]] [[scalar function]] which gives the [[wiki </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

2 KB (235 words) - 21:56, 10 September 2022
Interval Index
...) and the major cell at the following index (first word on the next page). In general computer science, this problem is known as a '''predecessor search' ...grouped together. A few APL developers want to know which section they are in. Interval Index is a perfect fit for this task. The left argument should be

9 KB (1,337 words) - 23:27, 10 March 2024
Windowed Reduce
...derives a [[dyadic function]] which [[reduce]]s each overlapping "window" in its right [[argument]] of the size given by its left argument. ...o windows of size <syntaxhighlight lang=apl inline>n</syntaxhighlight>. It works like [[Reduce]], except applied on overlapping segments of an array, and bo

3 KB (392 words) - 21:47, 18 May 2024
Residue
{{Built-in|Residue|<nowiki>|</nowiki>}}, '''Remainder''', or '''Modulus''' is a [[dyad For negative arguments, one may decide to return non-negative numbers in all cases or follow the sign of the dividend or the divisor. For complex ar

2 KB (311 words) - 21:10, 10 September 2022
Take
...t the left argument length match the right argument rank, and was extended in [[SHARP APL]] 19.0 to allow short left arguments. It is closely related to {{Works in|[[Dyalog APL]], [[ngn/apl]]}}

13 KB (1,829 words) - 01:23, 2 March 2024
Index Generator
...array of [[index|indices]] with [[shape]] given by the right [[argument]]. In the result, the [[element]] at each [[index]] is that index. ...h 1. In [[A+]] and [[J]] Iota of a vector returns an array which counts up in [[ravel order]], that is, it matches Iota of its [[bound]], [[reshape]]d. A

11 KB (1,493 words) - 21:44, 25 February 2024
Complex (function)
...hlight> together with initial support for complex numbers, and was adopted in [[Extended Dyalog APL]] using the [[glyph]] <syntaxhighlight lang=apl inlin ...]. [https://www.jsoftware.com/papers/APLDesignExercises.htm Some Exercises in APL Language Design]. §8 Imaginary/Complex and sample answer. Jsoftware. 2

4 KB (508 words) - 22:25, 10 September 2022
Index (function)
{{Built-in|Index|⌷}}, also called '''Squad Indexing''' after the name of the [[glyph ...right argument Y. The result is identical to that of [[bracket indexing]] in that <syntaxhighlight lang=apl inline>Y[X1;X2;…;Xn] ≡ X1 X2 … Xn⌷Y<

3 KB (398 words) - 22:04, 10 September 2022
Ravel
...odel]], an array's ravel is the [[vector]] containing all its [[elements]] in [[ravel order]]. It is equivalent to [[Reshape|reshaping]] an array using i In some APLs an [[Function axis|axis]] may be specified for Ravel in order to combine only some [[Axis|axes]] of an array, or insert a length-1

4 KB (533 words) - 08:56, 14 February 2024
Hook
...r (<code>⟜</code>), which also serve the purpose of the [[Bind]] operator. In [[J]], a 2-[[train]] is a hook, while [[I]] adds the mirror image to give t ...ef>, proposed hook as the meaning of a 2-train, and this was soon included in [[J]]. This definition specifies that <syntaxhighlight lang=j inline>(F G)

4 KB (585 words) - 06:48, 28 February 2024

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