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.... For example, consider a function which expects one or more English words in uppercase and counts the words that include the letter E. </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

...ument is already an array, it is returned unmodified. It is only available in [[Dyalog APL]], which supports classes and .NET objects. Materialise shares </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

{{Built-in|Link|⊃}}, or <syntaxhighlight lang=j inline>;</syntaxhighlight> in [[J]], is a [[dyadic]] [[primitive function]] which builds a [[nested]] [[v </syntaxhighlight>{{Works in|[[SHARP APL]]}}

...length with each element in the left argument corresponding to an element in the right argument. Partition begins a new '''division''' of its right argu {{Works in|[[Dyalog APL]]}}

{{Built-in|Exponential|*}} is a [[monadic]] [[scalar function]] which computes the [[w </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

{{Built-in|Without|~}}, '''Set Difference''', '''Excluding''', or '''Less''', is a [[d ...line>(~X∊Y)/X</syntaxhighlight>. This preserves the order and multiplicity in the left argument. Both arguments can be [[nested array|nested arrays]].

...ure of its [[element]]s. It is derived from the first element of the array in [[ravel order]], or, if the array is [[Empty array|empty]], from informatio ...type is used when an array is expanded or when empty elements are inserted in some other way. [[Take]] and [[Expand]] on a [[character]] array produce an

{{Built-in|Factorial|!}} is a [[monadic]] [[scalar function]] which gives the [[wikipe In multiple implementations, this function has an extended definition using th

...The shape of the result is that of the [[argument]] with higher [[rank]]. In J, since all functions, including dyadic scalar functions, have [[function A scalar dyadic function works when the two arrays have the same shape:

...ntaxhighlight> as a monadic counterpart of [[Complex (function)|Complex]]. In other APL implementations that support complex numbers, [[Circular]] with t </syntaxhighlight>{{Works in|[[Extended Dyalog APL]]}}

{{Built-in|Intersection|∩}} is a [[dyadic]] [[set function]] which computes the [[wi ...line>(X∊Y)/X</syntaxhighlight>, which preserves the order and multiplicity in the left argument. Both arguments can be [[nested array|nested arrays]].

...the concept of a function being defined in terms of the [[simple scalar]]s in [[nested array]]s. It is a feature of [[Nested array model|nested]] array l ...ntaxhighlight> to reach the simple scalars at the deepest point of nesting in any argument.

{{Built-in|Union|∪}} is a [[dyadic]] [[set function]] which computes the [[wikipedia ...ne>X,(~Y∊X)/Y</syntaxhighlight>. This preserves the order and multiplicity in both arguments, the left one taking precedence. Both arguments can be [[nes

...nded Dyalog APL]], sharing its [[glyph]] with [[Commute]], and was adopted in [[Dyalog APL 18.0]] as an alternative to the constant [[dfn]] such as <synt ...d for Constant arises in various contexts, such as at the rightmost branch in a [[train]] and mapping over an array to create a constant-filled one. The

...m]. [[APL Quote Quad]], Volume 18, Number 1, 1987-09.</ref>) and '''Fit''' in [[J]], is a special [[dyadic operator]] which takes a function as its left ...r]] when the feature was added, a system operator alternative was provided in form of <syntaxhighlight lang=apl inline>⎕OPT</syntaxhighlight>.

{{Built-in|Natural Logarithm|⍟}}, or '''Natural Log''', is a [[monadic]] [[scalar fu </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

...r whose length along one [[axis]] would exceed the maximum allowed length. In [[Dyalog APL]], the maximum rank is 15, so taking an [[Outer Product]] of t {{Works in|[[Dyalog APL]]}}

{{Built-in|Magnitude|<nowiki>|</nowiki>}}, or '''Absolute Value''', is a [[monadic]] [ </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

{{Built-in|Spawn|&}} is a [[monadic operator]] which applies its [[operand]] in a new [[wikipedia:green thread]]. Rather that returning the result of its o ...xhighlight lang=apl inline>¨</syntaxhighlight>) to launch multiple threads in parallel.

...nition matches the [[hook]] function Before, represented as <code>⊸</code> in [[BQN]]. ...xhighlight>{{←→}}<syntaxhighlight lang=apl inline>g⍨∘f⍨</syntaxhighlight>. In [[dzaima/APL]] the monadic case is simply an error.

...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

...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]]}}

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.

{{Built-in|Binomial|!}} is a [[dyadic]] [[scalar function]] which gives the [[wikipedi </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

...same results on [[Boolean]] arguments and the same [[identity element]] 1, in the same way that [[GCD]] extends [[Or]]. </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

...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

...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]]}}

{{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

{{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:

...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,

...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.

...]] 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

...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

...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

...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.

* 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

...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]]}}

...hich do not [[match]] an earlier distinct cell) in the order they appeared in the array. It works on nested arrays as well:

...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]]}}

...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

...same results on [[Boolean]] arguments and the same [[identity element]] 0, in the same way that [[LCM]] extends [[And]]. </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

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.

...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]]}}

...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.

...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+]]}}

...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

...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]].

...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]]}}

...]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

In fact, the [[right]] function (<syntaxhighlight lang=apl inline>⊢</syntaxh </syntaxhighlight>{{Works in|[[APL64]]}}

...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]]}}

...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

{{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.

...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

{{Built-in|Ceiling|⌈}} is a [[monadic]] [[scalar function]] that gives the [[wikiped </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

{{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

...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

...|/|⌿}}, 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.

:''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.

...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

{{Built-in|Reciprocal|÷}} is a [[monadic]] [[scalar function]] which gives the [[wiki </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

...) 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

{{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

...of the size of its left [[argument]], and evaluates it into a single array in right-to-left order. ...o windows of size <syntaxhighlight lang=apl inline>n</syntaxhighlight>. It works like [[Reduce]], except applied on overlapping segments of an array, and bo

...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]]}}

...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

...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

{{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<

...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

...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)

...ht> with the dyadic function [[Drop]]. Split is the [[inverse]] of [[Mix]] in the sense that the latter undoes the enclosing that Split introduced. </syntaxhighlight>{{Works in|[[Dyalog APL]]}}

</syntaxhighlight>{{Works in|[[Dyalog APL]]}} ...e argument is placed in a [[box]], and the result is this box as a scalar. In the [[nested array model]] it can simply be viewed as creating a new array.

...array theory]], the elements should be tolerantly [[equal to]] each other; in [[nested array theory]], the definition is recursive with the base case of Arrays match if they are equal in all the characteristics defined by APL's [[array model]]:

{{Built-in|Negate|-}}, or '''Minus''', is a [[monadic]] [[scalar function]] which retu Negate works on every type of number present, including [[complex number]]s.

...ph, '''Diamond''', allows placing multiple statements on a single line. It works both inside a function and directly within the interpreter. Empty statement ...the system goes immediately to the line whose number is the first element in that expression."<ref>[[Paul Berry|Berry, Paul]]. [https://archive.org/deta

If the right argument is a [[vector]], the number of positive values in the left argument must match the length of the right argument. Each positiv Expand works along a particular [[axis]], which can be specified in languages with [[function axis]] and otherwise is the first axis for <synta

...ray of [[index|indices]] where each item in the right [[argument]] appears in the left argument. If some item is not found, the corresponding index retur ...cates at which index the corresponding item is found (or not found at all) in the left argument.

...xtracting items from an array. See [[Index]] for the concept of a location in an array. See [[Bracket indexing]], [[Index (function)]], [[Pick]], and [[S ...[[index|indices]]. All indexing operations are subject to [[index origin]] in languages which have such a concept.

...(relative to APL) and two-dimensional structure of the notation presented in ''A Programming Language''. * While [[scalar extension]] is not defined in general, a scalar can be multiplied by an array as a "scalar multiple".

...eal'' comes from the analogy of [[wikipedia:card game#Deal|dealing cards]] in a card game such as Poker. Both [[argument|arguments]] of <syntaxhighlight ...d to generate multiple permutations at once. This behavior can be mimicked in other APLs by writing <syntaxhighlight lang=apl inline>?⍤0</syntaxhighlig

...ohn Scholes]] explains his own implementation of [[Conway's Game of Life]] in [[Dyalog APL]], where he, one step at a time, develops the following [[dfn] ...in his [[dfns workspace]]. The workspace includes a function which differs in a few small details.

...vector. A partition contains all the original [[element]]s of the vector, in the same order, but at one greater [[depth]]. ...called dividers: we do not name the two outermost edges, which must exist in any partition.

...imitive function]] which computes the representation of the right argument in the radix system defined by the left argument. Some implementations add [[m Encode works by finding the "digits" one by one from the rightmost digit. Let's consider

{{Built-in|Outer Product|<nowiki>∘.</nowiki>}}, or '''Table''' is a [[monadic operat ...operation, which collapses two dimensions in an inner product, is not used in the outer product. The notation for outer product reflects this by canonica

...to its semantics, that is, the meaning of the actual operations performed. In part because of APL's [[Comparison with traditional mathematics|close relat ...ent. While such individual statements may be enough for simple programming in a [[session]], larger programs are constructed by defining functions, with

...mpress]] and [[Expand]]. A related function also named Mesh is implemented in [[NARS]] and [[NARS2000]] as a case of [[Bind|Compose]]: <syntaxhighlight l == In Iverson notation ==

...his idea to [[dyadic function]]s, allowing various patterns of application in addition to the simple application of one [[monadic function]] to the resul [[Reverse Compose]] and [[Beside]] treat their arguments in an asymmetric way. They can be seen as using a [[monadic function]] to pre-

...ed keys group the indices or major cells of an argument. It was introduced in [[Dyalog APL]] version 14.0 and is commonly compared to SQL's [[wikipedia:G In the [[dyadic]] case, Key applies the function to collections of major cells

The term '''idioms''' is used in the [[community]] to mean either of two distinct (but overlapping) groups o ...gnises as a whole, directly computing a result rather than evaluating each in turn.

{{Built-in|Transpose|⍉}} is an [[ambivalent]] [[primitive function]] which reorders ...of Y. This means that, given a multi-dimensional [[index]] V of an element in the resulting array, <syntaxhighlight lang=apl inline>V⌷X⍉Y</syntaxhigh

{{Built-in|Inner Product|<nowiki>.</nowiki>}} is a [[dyadic operator]] that produces a ...y vectors, there is only one rank-1 cell in each argument, so this results in the following application pattern:

{{Built-in|Floor|⌊}} is a [[monadic]] [[scalar function]] that gives the [[wikipedia ...method present here has issues dealing with larger values due to the loss in precision because of the ⍎ operator.

...e because it encodes not only which cells are unique but where they appear in the argument. This means it can be used for tasks such as filtering seconda Nub Sieve returns a 1 for each [[major cell]] in the argument that is unique, and a 0 if it's a duplicate:

...nk (operator)|Rank operator]]. It was initially developed in [[SHARP APL]] in the early 1980s and is now a major feature of [[J]] and [[Dyalog APL]], as ...sliterates to APL <syntaxhighlight lang=apl inline>,⍤¯1</syntaxhighlight>) in both valences.

⍝ Note that the order of two 10s are preserved in both cases ...ys]] of possibly different [[shape]] and [[type]]. Grade is the only built-in function which can perform comparisons between arbitrary arrays of previous

{{Built-in|Rank|⍤}} is a [[primitive operator|primitive]] [[dyadic operator]] which Reverse order of rows in matrices of a 3D array:

| platforms = JVM, Native Linux, In-browser, [[wikipedia:Node.js|Node.js]] ...f standard APL, along with additional features. Much of standard APL works in Kap, although if an APL feature does not fit with Kap's design, those featu

On the other hand, installing user commands in a different folder, such as <syntaxhighlight lang=apl inline>MyUCMDs/</synt * Anything installed into this folder will be available in all installed versions of Dyalog APL

...x. However, for a uniform appearance, the font should be designed with APL in mind.<ref>Phil Chastney: ''[https://web.archive.org/web/20161005120746/http ...rogramming font optimized for coziness. (In Dyalog Windows IDE, works best in sizes divisble by 13) || [[File:Cozette.png|none]]

...s on usage and is [https://github.com/abrudz/logos/tree/main/apl available in vector and bitmap formats]. Many kinds of [[APL merchandise|merchandise]] f The logo can be experienced in various realistic web contexts, including as favicons:

Employment of wit and puns has a long history in the APL [[community]]. In particular, [[John Scholes]] was known for [[wikipedia:John_M._Scholes#Wit| * Many APL glyphs have popular humorous names in addition to their official names. This includes ''splat'' for the [[Logarit

...://chat.stackexchange.com/transcript/message/52389201#52389201 "52389201"] in ''The Nineteenth Byte'' chat room. Stack Exchange network, 2019-10-31 23:57 ...s the computer system itself. APL has no reserved words. Rather, all built-in constants, variables, functions and operators have the prefix <syntaxhighli

...WD215.html EWD 215: A Case against the GO TO Statement]</ref>. He is known in array programming for his consistent complaints against the APL language an ...asked a question of Iverson:<ref>[[Ken Iverson|Iverson, K.E.]] ''Formalism in Programming Languages'' ([https://www.jsoftware.com/papers/FPL.htm transcri

...ge variety of tasks. It was first presented at the 1984 [[APL conference]] in Helsinki, Finland. The huge contribution of the Finnish APL Association is ...all of the below library, updated to use the latest language features, and in an easily searchable format that includes modern day synonyms.

...that year, it was seen as part of a sequence with the 2000 conference also in Berlin, but this sequence was not extended to 2020. | APL in Action