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...[[enclose]]d array, and an array of boxes (a "boxed array") to a [[nested array]]. ...arrays which contain both numbers and characters, as well as arrays with a nested structure.

:''This article is about the items of an array. For the set function, see [[Membership]]. ...y theory]] each element of an array is another array, and an element of an array can be retrieved using the [[Pick]] function. [[Stranding]] forms a [[vecto

{{Infobox array language | array model = [[flat array model|flat]] arrays with nested lists

The following array family programming languages, and papers describing languages, have had a major influence on commonly-used APLs. ...on of APL", [[Jim Brown]]'s Ph.D. thesis, describes a [[Nested array model|nested]] APL which later becomes the basis of [[APL2]]

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[nested array model|nested]]

...ed simple in most contexts, although they may have depth greater than 1 in languages that use the [[prototype]] to determine depth. ...ke numbers and characters. Arrays which would not be representable in flat array theory—those which contain a mixture of simple scalar types, or contain b

:''This page is about array depth, a number associated with every array. For the operator that applies a function at a given depth, see [[Depth (op ...Depth returns a negative result to indicate that not all paths through the array have the same depth.

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[List model|Lists]]

{{Infobox array language | array model = [[nested array model|nested]]

{{DISPLAYTITLE:dzaima/APL}}{{Infobox array language | array model = [[nested array model|nested]] or [[flat array model|flat]]

{{Infobox array language | array model = [[Nested array model|nested]]

{{Infobox array language | array model = [[based array model|based]]

...Pervasion can be seen as and modelled by [[recursion|recursing]] into all nested elements until the function can be applied to all simple scalars.

{{Infobox array language | array model = [[List model|Lists]] compiled to [[Flat array model|flat]]

...ment]] or another relevant array is used. The fill element is usually that array's [[prototype]]. [[J]] allows the fill to be specified using the fit conjun Fills are one way to convert an [[empty array]] into a non-empty array. [[Reduction]] along an empty [[axis]] also produces such a transition, but

{{Infobox array language | array model = [[nested]]

...them until reaching [[simple scalars]]; in [[Flat array model|flat]] array languages they usually do not apply inside [[boxes]]. Functions which are not scalar,

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[Flat array model|flat]] statically typed

...utside of APL, such one-dimensional data might also be called a "list" or "array". ...lang=apl inline>A ≡ (⍴A)⍴,A</syntaxhighlight>), the multidimensional APL [[array model]] can be built up from only an understanding of vectors.

{{DISPLAYTITLE:ngn/apl}}{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[nested]]

{{Infobox array language | array model = [[nested]]

{{Infobox array language | array model = [[List model|lists]]

...ement]]s) or rank to fit a common shape. In all APLs Mix allows a [[simple array]] argument, and returns it unchanged. Mix is a left inverse to both [[Enclo ⍴x ⍝ x is a nested array, i.e. array of array

{{Infobox array language | array model = [[nested array model|nested]]

...efined by array languages. For the role of arrays in [[APL syntax]], see [[Array]].'' ...o restrictions at all: any kind of data can be treated as a [[scalar]], or array with rank 0!

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[nested array model|nested]]

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

...lt-in|Index Of|⍳}} is a [[dyadic]] [[primitive function]] which returns an array of [[index|indices]] where each item in the right [[argument]] appears in t ...is usually restricted to a [[vector]]. The result is a [[simple]] integer array with the shape of the right argument, and each cell indicates at which inde

:''This article is about one-liners in APL. For other languages, see [[wikipedia:One-liner program|Wikipedia]].'' ...like [[Each]] did not exist until the development of [[Nested array model|nested]] APLs. Once introduced, [[Execute]] became one possibility for performing

:''This page is about generating indices for an array of a given size. See [[Indexing]], [[Indices]], [[Index of]], and [[Interva ...yph]] '''Iota''', is a [[monadic]] [[primitive function]] which returns an array of [[index|indices]] with [[shape]] given by the right [[argument]]. In the

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[nested array model|nested]]

...lang=text inline>foldr1</syntaxhighlight>, in other functional programming languages such as Haskell. ...which forces it to [[enclose]] each non-[[simple]] result in the returned array. It can be modeled as <syntaxhighlight lang=apl inline>f¨/</syntaxhighligh

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[nested array model|nested]]

{{Infobox array language | array model = [[wikipedia:Julia (programming language)|Julia]]

{{Infobox array language | array model = [[nested array model|nested]]

{{Built-in|Reshape|⍴}} produces an array with [[shape]] given by the left argument and [[elements]] from the right a Reshape can be used to produce an array with a given shape and ravel:

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

{{DISPLAYTITLE:Extended Dyalog APL}}{{Infobox array language | array model = [[nested array model|nested]]

...tions focused partially or exclusively on performance. Currently-developed array-family implementations that advertise high performance include [[Dyalog APL ...or [[nested]] arrays, and compiled or GPU-based APLs may not fully support nested arrays.

...rn October 24, 1957) is the designer of [[A]], [[A+]], the [[K]] family of languages, and [[Q]], and cofounder of [[Kx Systems]]. Whitney was a major figure in ...APL session for him. Although Whitney was introduced to other programming languages in university (starting in 1974), he studied mathematics, focusing on set t

...ading axis" comes from the [[frame]], which consists of leading axes of an array, the related concept of [[leading axis agreement]], which extends [[scalar] ...ther they are part of leading axis theory or simply a decision made by two languages with a shared heritage. J introduced non-close compositions, and [[Dyalog A

{{Infobox array language | array model = [[flat array model|flat]] with [[boxes]]

...rst APL dialect to implement them, and previous definitions in other array languages or as proposals are indicated in parentheses. Because primitives tend to ha | [[Enclose]], [[Match]], [[Pick]], nested [[Index Generator]], [[stranded assignment]] (proposed [[Jim Brown|Brown]]

== Flat versus Nested == ...log APL]], [[NARS2000]], [[APL2]], [[GNU APL]], and others) use the nested array model.

{{Infobox array language | array model = [[List model|Lists]]

...omposition Operators. SATN-41, 1981-06-20.</ref> Pair aids in constructing nested arrays in [[tacit programming]], where [[stranding]] by juxtaposition is no ...<ref>Fl. Schmidt and M. A. Jenkins. [https://doi.org/10.1145/800071.802258 Array diagrams and the Nial approach] at [[APL82]].</ref> <code>link</code> enclo

...eveloped by [[Bob Smith]] and the first major language to use the [[nested array model]]. Many of its features would be incorporated in APL*PLUS II on its r

...APL\360]] in that it can be used to write arrays of rank greater than one. Array notation is supported in [[dzaima/APL]], [[BQN]] (using angle brackets <cod Array notation generally consists of a vector notation written with parentheses <

...also works in [[ngn/apl]], and other [[Nested array theory|nested]] array languages allow similar implementations: see [[#Translations]]. ...every element by scalar extension again. If the right argument were a flat array rather than being [[enclose]]d, we could obtain a similar, but flat, result

...ive]] [[dyadic function]] which shortens or extends the right [[argument]] array along zero or more [[Axis|axes]]. The [[vector]] left argument indicates th ...ins the same: if two different positive arguments are used to take from an array, the one which is closer to zero gives a [[prefix]] of the other result. If

{{Infobox array language | array model = [[nested array model|nested]]

...the Dyalog Forums. This design considerations page, and if necessary the [[Array notation#Specification|specification]], will be kept up to date as feedback The following requirements were proposed as objectives for an APL array notation:<ref>[[Adám Brudzewsky]]. Internal documents. [[Dyalog Ltd.]] 30

...ment array. It finds adjacent elements by [[Rotate|rotating]] the original array, causing elements at the edge to wrap around (giving a torus geometry). ...dexing]] with an array index, or [[Take]] to obtain the neighbors of every array element at once.

...[wikipedia:Burroughs Corporation|Burroughs]], and others, and some non-APL languages. IBM's promotion of [[VS APL]] as a platform became another source of deman ...ed to many other systems. The choice to make Dyalog a [[Nested array model|nested]] APL like [[NARS]] and the in-process [[APL2]] would also have a major eff

...Christensen's first APL application, [[APL conference]]s, the [[boxed]]/[[nested]] split, [[Ken Iverson]]'s [[Rationalized APL]] and [[J]], the [[Rank opera ...inline>⌹</syntaxhighlight>), Disjoined arrays using a dedicated Disjoined Array Computer (DAC), hardware [[APL machine]]s/processors, [[shared variable]]s.

...hen instantiated (for instance by taking the [[First]] element of an empty array), a prototype object would be created using the class's [[niladic]] constru ...arison]]s [[Equal]] and [[Not Equal]] (but not [[array ordering]]: [[total array ordering]] including ordering of complex numbers was added in [[#17.0|17.0]

While many [[conferences]] and sequences of conferences have been held by the array language community, the term '''APL conference''' refers to a sequence of c | Applied Programming Languages

...conference]] held by [[Dyalog Ltd.]] for users of [[Dyalog APL]] and other array programmers. It is approximately a week long and features presentations bot * '''Array languages at Morgan Stanley''', David Crossley