Search results

{{Built-in|Compose|∘}} or '''Composition''' is the most common name for the [[primitive operator|primitive]] [[dyadi {{quote|Composition assembles functions and arguments to form derived functions. This provides

...t 1. [[I.P. Sharp Associates]]. 1983-04-04.</ref> In SHARP all composition operators follow this pattern, while in J, both close and non-close forms (with a res {{APL features}}[[Category:Composition operators]]

== Close composition == In [[SHARP APL]] and [[J]], Over is implemented as a [[close composition]], meaning that (using SHARP syntax) <syntaxhighlight lang=apl inline>f⍤g

...behaviour as if the [[Atop]] 2-train or any of the [[Beside]] or [[Over]] operators had been used: == Close composition ==

In dialects that support user-defined operators and invertible functions, it can be defined as (or similar): == Close composition ==

...hlight>, and <syntaxhighlight lang=apl inline>h</syntaxhighlight>, a split composition on arguments <syntaxhighlight lang=apl inline>x</syntaxhighlight> and <synt ...hlight> which also represents the [[Over]] operator - as it too is a split composition with identical outer operands.

...=apl inline>∘</syntaxhighlight>) with [[Beside]]; in many dialects the two operators share the name [[Compose]]. <syntaxhighlight lang=apl inline>∘</syntaxhig * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-4-more-apl-operators--#41029677 APL Cultivation]

'''Operators and Functions''' is a research report published by [[Ken Iverson]] in 1978, Operators:

...he rank of their right operand—the [[derived function]] produced by such a composition has ranks derived from that function's ranks. ...ghlight>".<ref>K.E. Iverson. [https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"]. SATN 41, 1981-06-20.</ref> The concept of function rank wa

...l81">[[Bob Smith]]. [https://doi.org/10.1145/800142.805376 "Nested arrays, operators, and functions"] at [[APL81]].</ref> | influenced by = [[APL*PLUS]], [[Operators and Functions]], [[Iverson notation]]

⍝ same as this, because operators are left-associative, unlike functions which are right-associative * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-4-more-apl-operators--#41029677 APL Cultivation]

{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]

...fined with glyph <syntaxhighlight lang=apl inline>⍨</syntaxhighlight> in [[Operators and Functions]] in 1978, and taken up by [[NARS]] as a result. [[Dyalog]], * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-3-some-apl-operators-----#40900200 APL Cultivation]

...n a particular pattern. The term [[wikipedia:function composition|function composition]] comes from [[traditional mathematics]] where it is used for a function <m ...yalog.tv/Dyalog19/?v=czWC4tjwzOQ Tacit Techniques with Dyalog version 18.0 Operators]

...the mirror image to give two functions (I has first-class functions but no operators) hook (<code>h</code>) and backhook (<code>H</code>). [[File:Hooks.png|thumb|right|Hook operators in [[BQN]]]]

{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]

...jsoftware.com/papers/satn41.htm "Composition and Enclosure"] § Composition Operators. SATN-41, 1981-06-20.</ref> Pair aids in constructing nested arrays in [[ta

Language ideas include new functions, operators, datatypes, and many other extensions. The project is free open source sof ...feature of NARS2000 is its heavy use of experimental primitive functions & operators. In the table below, symbols which are unknown or obscure in the APL world

...xhighlight lang=apl inline>⍣</syntaxhighlight>), [[Windowed Reduction]] ([[Operators and Functions]] 1978) ...ght>), [[Under]] (<syntaxhighlight lang=apl inline>¨</syntaxhighlight>) ([[Operators and Functions]] 1978; not widely adopted) <br/> [[complex]] extensions: [[C

[[File:Function compositions.png|thumb|right|Diagrams of [[function composition]]s, an important part of tacit programming.]] == Derived operators ==

...obtain analogous functionality by using an [[Under]] operator with [[close composition]] along with the [[Function rank|rank]]-0 function [[Disclose]] (or Unbox). * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-3-some-apl-operators-----#message-40899092 APL Cultivation]

'''New primitive operators''' ...ned%20Functions%20and%20Operators/DynamicFunctions/Dynamic%20Operators.htm Operators]

| Compositional operators ''(see [[Function composition]])'' || Kompositions-Operatoren | [[Function composition|(Function) composition]] || Komposition<ref>German wikipedia: [https://de.wikipedia.org/wiki/Kompo

...light>), [[Match]] (<syntaxhighlight lang=apl inline>≡</syntaxhighlight>); operators [[Atop|Over]] (<syntaxhighlight lang=apl inline>⍥</syntaxhighlight>), [[O == Primitive Operators ==

.... In this way it unifies APL's pairs of first- and last-axis functions and operators including [[Reverse]], [[Rotate]], [[Replicate]], [[Expand]], [[Reduce]], a ...k 0 as they apply only to [[scalar]]s. J and SHARP APL also define [[close composition]]s, which compose two functions while retaining the rank of the first one a

...syntaxhighlight lang=j inline>@.</syntaxhighlight> for agenda, non-[[close composition]]s | 7.0 || 1993-11-14 || [[wikipedia:Taylor series|Taylor series]] operators <syntaxhighlight lang=j inline>t.</syntaxhighlight> and <syntaxhighlight la

...lowed a long history of attempts to define train-like behavior in terms of operators.<ref>[[Roger Hui]] and [[Morten Kromberg]]. [https://dl.acm.org/doi/abs/10. ...v]], [[dzaima/APL]], [[April]], and [[BQN]], and also matches the function composition featured in [[I]] in 2012.

...ange of [[glyphs|special graphic symbols]] to represent most functions and operators. While keyboard mappings become [[mnemonics|memorized]] over time, entering ...d>AltGr</kbd> as shifting key, <kbd>`</kbd> as prefix key, or ASCII symbol composition.

...rator)|Rank operator]], [[trains]], and [[Function composition|composition operators]], namely [[Atop]] and [[Over]], from J to APL. | 4.0 || 1986 || October || User-defined operators, [[function assignment]] (including for [[derived function]]s), <syntaxhigh

...Sharp APL]] were to exchange the glyphs, and remove the concept of [[close composition]]). dzaima/APL has adopted Extended Dyalog's [[Pair]] (<syntaxhighlight lan * [https://dyalog.tv/Webinar/?v=jBxQZemmA1w User-Defined Operators]

* '''10: An Investigation into Higher Level Operators''', [[John Scholes]] * '''G09: Co-operators''', [[Phil Last]], Independent Consultant ([https://www.dyalog.com/uploads/

* '''APL unary matrix operators as represented by the eighth order Dihedral group'''. John H. Crayton. [htt * '''Uses of general arrays and operators'''. J. E. Mezei. [https://doi.org/10.1145/800269.810828].