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  • Roll
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
    3 KB (373 words) - 22:14, 10 September 2022
  • Not
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
    3 KB (385 words) - 22:18, 10 September 2022
  • Residue
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    2 KB (311 words) - 21:10, 10 September 2022
  • Conjugate
    ...-numeric argument and return it unchanged even though other monadic scalar functions give a [[DOMAIN ERROR]]: ...ps://dl.acm.org/doi/full/10.1145/586003.586007 Notation for complex "part" functions]. [[APL Quote Quad]] Volume 8, Issue 1. 1977-09.</ref> who noted that it ha
    5 KB (719 words) - 01:19, 18 March 2024
  • Hook
    ...while [[I]] adds the mirror image to give two functions (I has first-class functions but no operators) hook (<code>h</code>) and backhook (<code>H</code>).
    4 KB (585 words) - 06:48, 28 February 2024
  • Advanced examples
    ...anking poker hands]] — so they can be compared and ordered with normal APL functions
    814 bytes (114 words) - 11:24, 29 October 2021
  • Not Match
    {{APL built-ins}}[[Category:Primitive functions]]
    924 bytes (132 words) - 03:12, 3 February 2021
  • GCD
    ...]]. [https://doi.org/10.1145/800117.803810 "A Notation for the GCD and LCM Functions"] ([https://www.jsoftware.com/papers/eem/gcd.htm web]) at [[APL75]].</ref> {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    4 KB (497 words) - 21:37, 17 February 2024
  • Binomial
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    3 KB (320 words) - 21:50, 10 September 2022
  • LCM
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    2 KB (230 words) - 21:28, 10 September 2022
  • Commute
    ...adic function]] as operand and modifies how the argument(s) of its derived functions are used. If the derived function is used monadically, the argument is also ...ph <syntaxhighlight lang=apl inline>⍨</syntaxhighlight> in [[Operators and Functions]] in 1978, and taken up by [[NARS]] as a result. [[Dyalog]], influenced by
    3 KB (376 words) - 16:56, 16 March 2024
  • SAX
    == Primitive functions == All scalar functions have rank zero.
    16 KB (1,323 words) - 03:23, 11 May 2024
  • Lang5
    ...tures from the APL tradition: Most notably, it uses keywords for primitive functions, and uses reserved words for control flow and looping constructs. ...to [[K]] and [[RAD]]. Similar to those languages, it also allows usage of functions as data using Forth's quoting.
    3 KB (361 words) - 22:46, 24 January 2024
  • NARS2000
    Language ideas include new functions, operators, datatypes, and many other extensions. The project is free open === Functions ===
    10 KB (1,101 words) - 02:29, 9 March 2024
  • APLX
    ...character set, APLX is a bit more verbose, due to the prevalence of system functions with long names, and the use of structured-control keywords. The use of exp === Functions ===
    11 KB (959 words) - 13:25, 13 February 2024
  • Windowed Reduce
    Windowed reduce is used to apply functions on overlapping sections of array e.g. when you need the deltas of an array. ...operand between neighbouring elements, and especially so with [[comparison functions]]. For example, <syntaxhighlight lang=apl inline>1,2≠/v</syntaxhighlight>
    3 KB (392 words) - 21:47, 18 May 2024
  • Glyph
    ...t lang=apl inline>√</syntaxhighlight> for the [[Square Root]] and [[Root]] functions. ...ighlight>…<syntaxhighlight lang=j inline>}}</syntaxhighlight> for explicit functions, similar to the syntax of [[dfns]].
    4 KB (622 words) - 05:22, 26 February 2024
  • Function composition
    ...ore [[function]]s using a [[dyadic operator]] or a [[train]] such that the functions are applied to the [[argument]](s) as normal, but in a particular pattern. ...unction to the result(s) of one (for 2-trains) or two (for 3-trains) other functions. These patterns are also called Atop and Fork, and can be visualised as fol
    8 KB (1,071 words) - 17:07, 29 May 2024
  • Major cell search
    The dyadic functions [[Index Of]] (<syntaxhighlight lang=apl inline>⍳</syntaxhighlight>), [[In ...4. The more recent array languages [[BQN]] and [[Uiua]] also define search functions to work on major cells.
    3 KB (388 words) - 06:58, 11 March 2024
  • Dfn
    ...rooms/52405/conversation/lesson-2-diving-into-functions-in-apl Diving Into Functions in APL] {{APL syntax}}[[Category:Kinds of functions]][[Category:Defining functions]]
    4 KB (545 words) - 22:11, 10 September 2022
  • Variant
    ...tive function|primitive]] and [[system function]]s, and [[derived function|functions derived]] from [[primitive operator|primitive]] and [[system operator]]s, h
    5 KB (626 words) - 10:43, 11 September 2022
  • Defined function (traditional)
    ...mainstream APLs. Since the 1990s other ways to [[Function styles|describe functions]] have appeared, with [[J]] and [[K]] rejecting function definition in favo In many dialects the function header syntax of defined functions is adapted to allow user-defined [[operator]]s as well. A tradfn operator c
    11 KB (1,470 words) - 22:13, 10 September 2022
  • Axis
    ...x origin]]. Axis indices are used to specify [[function axis]] and in some functions such as dyadic [[Transpose]]. ...ice to put lower-order places at higher indices in the base representation functions [[Decode]] and [[Encode]]. This is known in the wider programming world as
    3 KB (444 words) - 22:29, 10 September 2022
  • Comparison with traditional mathematics
    ...[Ken_Iverson#Iverson_bracket|Iverson bracket]] is implied and [[Precedence|functions have long right scope]]. In APL, all functions that only take a single argument are placed to the immediate left of their
    11 KB (1,523 words) - 22:22, 10 September 2022
  • Q
    ...to which it bears great resemblance, but keywords replace most [[monadic]] functions.
    1 KB (135 words) - 19:07, 20 February 2024
  • Timeline of APL primitives
    ...APL/700]] || [[Union]], [[Intersection]], [[Set Difference]] (but these functions only return unique elements), [[modified assignment]] (scalar dyadics only) ...g=apl inline>⍣</syntaxhighlight>), [[Windowed Reduction]] ([[Operators and Functions]] 1978)
    8 KB (788 words) - 17:11, 31 May 2024
  • Matrix Inverse
    ...often called ''Domino'') with the dyadic function [[Matrix Divide]]. These functions were added to [[APL\360]] in 1970<ref>"Report of the APL SHARE conference" {{APL built-ins}}[[Category:Primitive functions]]
    3 KB (344 words) - 01:39, 18 March 2024
  • Over
    ...Ken Iverson]]. [https://www.jsoftware.com/papers/opfns.htm ''Operators and Functions''], §8 Composition and Duality. IBM Research Report #RC7091. 1978-04-26.</
    3 KB (428 words) - 21:33, 28 January 2024
  • Under
    In dialects that support user-defined operators and invertible functions, it can be defined as (or similar): ...Ken Iverson]]. [https://www.jsoftware.com/papers/opfns.htm ''Operators and Functions''], §8 Composition and Duality. IBM Research Report #RC7091. 1978-04-26.</
    5 KB (664 words) - 13:35, 17 February 2024
  • APL.SV
    ...[system function]]s. APL.SV also introduced the [[Format]] and [[Execute]] functions, and the [[Scan]] operator. === Functions ===
    8 KB (747 words) - 01:28, 26 February 2024
  • Kap
    * First class functions === Functions ===
    11 KB (1,055 words) - 14:37, 11 March 2024
  • APL2C
    ...lang=apl inline>⎕FX</syntaxhighlight>, and can't pass arrays (rather than functions) as [[operand]]s to user-defined operators.
    4 KB (556 words) - 14:59, 10 March 2024
  • Minimum
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    3 KB (415 words) - 22:23, 10 September 2022
  • Semantic density
    * most primitive functions have Roman-alphabet names
    3 KB (414 words) - 06:10, 25 September 2020
  • Tacit programming
    ...tradfn]]s (which have named arguments). Some APL dialects allow to combine functions into [[train]]s following a small set of rules. This allows creating comple All [[primitive functions]] are tacit. Some APLs allow primitive functions to be named.
    13 KB (1,347 words) - 21:28, 6 March 2024
  • Train
    A '''function train''' is a compound function made up of a series of functions. It's written as an isolated expression (surrounded by parentheses or named ...axhighlight>, and <syntaxhighlight lang=apl inline>h</syntaxhighlight> are functions (which themselves can be tacit or not), and <syntaxhighlight lang=apl inlin
    8 KB (1,165 words) - 15:43, 8 March 2024
  • Glee
    * There are no [[tradfn]]s and no [[dfn]]s. All functions are declared using blocks, which take their arguments via variable referenc ...rved words which all start with a <code>#</code>. These provide additional functions and values outside the symbolic primitives included.
    3 KB (394 words) - 22:43, 24 January 2024
  • Rotate
    ...ght> and <syntaxhighlight lang=apl inline>⊖</syntaxhighlight> with monadic functions [[Reverse]] and Reverse First, respectively. {{APL built-ins}}[[Category:Primitive functions]][[Category:Functions with first- and last-axis forms]]
    5 KB (626 words) - 22:15, 10 September 2022
  • Pick
    {{APL built-ins}}[[Category:Primitive functions]]
    2 KB (144 words) - 15:20, 8 November 2022
  • Floor
    ...monadic]] [[scalar function]] that gives the [[wikipedia:floor and ceiling functions|floor]] of a real number, that is, the greatest integer tolerantly<ref>[[Ro {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
    5 KB (582 words) - 16:27, 24 December 2023
  • Classify
    {{APL built-ins}}[[Category:Primitive functions]]
    1 KB (169 words) - 17:01, 27 January 2024
  • Klong
    4 KB (511 words) - 20:15, 31 January 2024
  • Matrix Divide
    ...ten called ''Domino'') with the monadic function [[Matrix Inverse]]. These functions were added to [[APL\360]] in 1970<ref>"Report of the APL SHARE conference" {{APL built-ins}}[[Category:Primitive functions]]
    4 KB (453 words) - 01:40, 18 March 2024
  • Nub in
    {{APL built-ins}}[[Category:Primitive functions]]
    1 KB (182 words) - 16:42, 27 January 2024
  • Complex (function)
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    4 KB (508 words) - 22:25, 10 September 2022
  • Inverse
    ...as <syntaxhighlight lang=apl inline>(f⍣¯1) x</syntaxhighlight>. While some functions such as [[Reverse]] have an obvious exact inverse, others might have no val
    2 KB (216 words) - 23:23, 29 January 2024
  • Negate
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
    3 KB (502 words) - 22:05, 10 September 2022
  • Subtract
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    4 KB (452 words) - 10:58, 11 September 2022
  • Control structure
    ...1145/800136.804483 On the locus of program flow within and among secondary functions] at [[APL79]].</ref><ref>Edward V. Eusebi. [https://dl.acm.org/doi/10.1145/ ...also does not include pre-defined control structures, but its first-class functions and list literals allow a similar syntax to be achieved without extending t
    7 KB (1,008 words) - 14:57, 10 March 2024
  • Equal to
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Comparison functions]]
    4 KB (500 words) - 21:57, 28 November 2022
  • Unique
    ...Iverson|Iverson]]'s 1978 [[Operators and Functions]] along with other set functions including [[Union]], [[Intersection]], and [[Difference]]. There it had the ...P APL]] successor [[SAX]]. [[J]] uses similar definitions: its Nub-related functions are Nub (<syntaxhighlight lang=j inline>~.</syntaxhighlight>), [[Nub Sieve]
    9 KB (1,243 words) - 12:57, 23 November 2023
  • IVSYS/7090
    ...Iverson]] to prepare an answer book for the problems in Ken's ''Elementary Functions''. IVSYS was only available in this way for a short time, as the TSM projec
    7 KB (773 words) - 17:37, 19 March 2024
  • Pair
    By 1982, [[Nial]] had defined four infix functions to join two arrays, enclosing any combination of them.<ref>Fl. Schmidt and {{APL built-ins}}[[Category:Primitive functions]]
    3 KB (486 words) - 17:16, 6 March 2024
  • Raze
    ...s which partition major cells along the first axis, although few partition functions do this. {{APL built-ins}}[[Category:Primitive functions]]
    6 KB (812 words) - 23:25, 29 January 2024
  • Bind
    2 KB (215 words) - 10:57, 6 October 2022
  • First
    {{APL built-ins}}[[Category:Primitive functions]]
    1 KB (200 words) - 21:59, 10 September 2022
  • Cut (K)
    [[Category:Primitive functions]]
    1 KB (201 words) - 07:01, 8 September 2022
  • Group (K)
    {{APL built-ins}}[[Category:Primitive functions]]
    1 KB (199 words) - 23:29, 17 March 2024
  • Quad name
    ...er all syntactic classes of such built-ins; constants, variables, objects, functions and operators. It is common to call these ''system constants'', ''system va * System functions are various utility functions, like <syntaxhighlight lang=apl inline>⎕FX</syntaxhighlight> to define ("
    6 KB (871 words) - 00:01, 16 April 2024
  • Jay Foad
    ...ter in Dyalog 16.0"].</ref> Foad worked not only on speeding up particular functions but also optimising the interpreter as a whole, for instance implementing s ...s for [[system function]]s that previously lacked any result (as no-result functions are difficult to use in [[dfn]]s). Foad was involved in designing several e
    6 KB (887 words) - 14:50, 4 March 2024
  • Complex floor
    ...hlight> and <syntaxhighlight lang=apl inline>im</syntaxhighlight> refer to functions that return the real and imaginary part of the given complex number respect {{APL features}}[[Category:Scalar monadic functions]]
    5 KB (632 words) - 22:14, 10 September 2022
  • Add
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
    4 KB (525 words) - 22:11, 10 September 2022
  • Promote
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Leading axis theory]]
    2 KB (244 words) - 01:22, 6 February 2024
  • Nested array
    [[Scalar functions]] descend into nested arrays one element at a time. Arrays can be nested at
    1 KB (208 words) - 22:01, 10 September 2022
  • A+
    ...t based on [[APL 90 (dialect)]] and presented at [[APL90]], which replaced functions with first-class blocks, see [[A+ (Girardot)]].'' ...|| [[Assignment]] or [[Selective Assignment]] || Result (returns from functions)
    9 KB (859 words) - 02:29, 5 March 2024
  • Element
    1 KB (197 words) - 07:16, 29 June 2020
  • Group (BQN)
    {{APL built-ins}}[[Category:Primitive functions]]
    1 KB (206 words) - 20:15, 31 January 2024
  • Close composition
    ...E. Iverson]]. [https://www.jsoftware.com/papers/opfns1.htm#8 Operators and Functions. §8 ''Composition and Duality''.] Research Report RC-7091. [[IBM]] Watson
    2 KB (258 words) - 02:12, 27 August 2023
  • Nib
    ...a pair type, the removal of overloaded and [[Ambivalent function|variadic functions]], and the modification of [[trains]]' syntax to allow assignment and loose
    2 KB (203 words) - 22:46, 24 January 2024
  • Bob Smith
    * [https://doi.org/10.1145/800142.805376 "Nested arrays, operators, and functions"] at [[APL81]].
    1 KB (198 words) - 16:42, 14 February 2024
  • Pometo
    ...''Rappel'', during development, the purpose of Pometo is to create library functions for use in Erlang and Elixir applications.
    2 KB (190 words) - 11:28, 20 April 2021
  • Each
    The Each operator has no effect on [[scalar function]]s, since these functions already map over each array element. For example, both expressions below ha
    5 KB (488 words) - 22:16, 10 September 2022
  • Case
    {{APL built-ins}}[[Category:Primitive functions]]
    1 KB (235 words) - 02:25, 9 March 2024
  • Cartesian Product
    {{APL built-ins}}[[Category:Primitive functions]]
    1 KB (188 words) - 02:15, 5 March 2024
  • Futhark
    ...s}}[[Category:Typed array languages]][[Category:Languages with first-class functions]][[Category:Ahead-of-time compilers]]
    2 KB (213 words) - 23:06, 24 January 2024
  • Type
    {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
    5 KB (491 words) - 14:28, 13 February 2023
  • Lil
    ...Category:List-based array languages]][[Category:Languages with first-class functions]][[Category:ASCII languages]][[Category:IR compilers]]
    2 KB (212 words) - 23:27, 24 January 2024
  • APL\iv
    ...es parsing by omitting user-defined operators while requiring user-defined functions to use lowercase names and arrays to use uppercase names. Despite these sim
    2 KB (209 words) - 14:08, 12 April 2021
  • Personalized Array Translator
    ...re.com/wiki/Doc/Elementary_Functions_An_Algorithmic_Treatment ''Elementary Functions An Algorithmic Treatment'']. ...hs]], PAT used letters prefixed by the <code>@</code> symbol. [[Comparison functions]] were denoted by <code>@</code> followed by three digits 0 or 1, indicatin
    7 KB (986 words) - 22:42, 24 January 2024
  • BQN
    === Functions === ...s}}[[Category:Based array languages]][[Category:Languages with first-class functions]][[Category:IR compilers]][[Category:Leading axis languages]][[Category:Lan
    11 KB (1,330 words) - 15:35, 6 March 2024
  • Scalar extension
    Dyadic [[scalar functions]] and the [[Each]] operator use scalar extension to pair their arguments:
    8 KB (947 words) - 03:06, 20 February 2024
  • Uiua
    ...first-class to facilitate features that depend on the number of arguments functions take. ...]]s is removed. Because of this, Uiua often splits APL primitives into two functions. Its primitives use [[Unicode]] glyphs including many not found in other la
    16 KB (2,314 words) - 20:02, 14 April 2024
  • String
    2 KB (281 words) - 10:52, 11 September 2022
  • Partition
    * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-7-apl-functions-#41436171 APL Cultivation] {{APL built-ins}}[[Category:Primitive functions]]
    3 KB (319 words) - 22:18, 10 September 2022
  • Operator valence
    ...nds while the derived function's valence counts [[argument]]s. Unlike with functions, there is no possibility for a [[niladic]] or [[ambivalent]] operator.
    2 KB (270 words) - 22:16, 10 September 2022
  • Beside
    ⍝ same as this, because operators are left-associative, unlike functions which are right-associative
    3 KB (310 words) - 06:20, 28 February 2024
  • Materialise
    {{APL built-ins}}[[Category:Primitive functions]]
    2 KB (233 words) - 21:51, 10 September 2022
  • Nest
    {{APL built-ins}}[[Category:Primitive functions]]
    2 KB (259 words) - 22:22, 10 September 2022
  • Find
    ...ments and not the prototype. [[Adin Falkoff]] presented code for Find-like functions using <syntaxhighlight lang=apl inline>∧.=</syntaxhighlight> at [[APL79]] {{APL built-ins}}[[Category:Primitive functions]]
    5 KB (595 words) - 21:36, 10 September 2022
  • Grade
    ...ins|Grade|⍋|⍒}} is a pair of [[ambivalent]] [[primitive function|primitive functions]] related to [[wikipedia:sorting#sorting information or data|sorting]]. Ins ...sort the [[major cell]]s of its argument, and introduced the dyadic Grade functions,<ref>Peter Wooster. "Extended Upgrade and Downgrade". SATN-35. 1980-09-15.<
    8 KB (962 words) - 16:23, 16 March 2024
  • One-liner
    2 KB (283 words) - 01:30, 10 March 2024
  • KamilaLisp
    ...Category:List-based array languages]][[Category:Languages with first-class functions]][[Category:Languages with tacit programming]]
    2 KB (232 words) - 17:39, 2 March 2024
  • Comparison of APL dialects
    ...programming|tacit function]]s, which are created by manipulating existing functions with no reference to [[argument]]s. ...operator]] in [[NARS]] and a library to translate this notation to defined functions in [[SHARP APL]]. [[Function assignment]], a necessary feature for tacit pr
    21 KB (1,991 words) - 06:36, 17 March 2024
  • Iverson notation
    ...icit procedures for calculating the exact or approximate values of various functions. Such explicit procedures are called algorithms or programs. Because an eff
    2 KB (278 words) - 15:45, 30 April 2020
  • Introductions
    ...ngle consistent notation; it allows us to exploit the powerful concepts of functions and operators; and it helps us to escape from the tyranny of scalars by giv
    2 KB (352 words) - 15:01, 5 February 2024
  • Dyalog APL Vision
    All scalar functions support [[leading axis agreement]]. * All set functions support arguments of any rank.
    9 KB (1,087 words) - 15:09, 6 March 2024
  • Shape
    * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-10-apl-functions-- APL Cultivation] {{APL built-ins}}[[Category:Primitive functions]][[Category:Array characteristics]]
    2 KB (340 words) - 22:05, 10 September 2022
  • Link
    {{APL built-ins}}[[Category:Primitive functions]]
    3 KB (267 words) - 21:02, 10 September 2022
  • Major cell
    ...ighlight lang=apl inline>¯1</syntaxhighlight> using the [[Rank operator]]. Functions designed to follow leading axis theory often manipulate the major cells of
    2 KB (306 words) - 23:27, 10 March 2024
  • SHARP APL
    == Primitive functions == All scalar functions have rank zero.
    22 KB (2,017 words) - 03:25, 11 May 2024

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