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'''Operators and Functions''' is a research report published by [[Ken Iverson]] in 1978, collecting a set of [[operator]]s and [[function]]s he had developed over the preceding years. Released two years before Iverson left [[IBM]] for [[I.P. Sharp]] over differences regarding the direction of APL, it offers precursors for many of the ideas later developed in [[SHARP APL]]. Its primitives were used more directly in [[NARS]], which influenced [[Dyalog APL]] and in this way shaped much of present-day APL development. | '''Operators and Functions''' is a research report published by [[Ken Iverson]] in 1978, collecting a set of [[operator]]s and [[function]]s he had developed over the preceding years. Released two years before Iverson left [[IBM]] for [[I.P. Sharp]] over differences regarding the direction of APL, it offers precursors for many of the ideas later developed in [[SHARP APL]]. Its primitives were used more directly in [[NARS]], which influenced [[Dyalog APL]] and in this way shaped much of present-day APL development. | ||
Functions: | |||
{|class=wikitable | |||
! Glyph !! Monadic !! Dyadic | |||
|- | |||
| <syntaxhighlight lang=apl inline><</syntaxhighlight> || [[Enclose]] || | |||
|- | |||
| <syntaxhighlight lang=apl inline>></syntaxhighlight> || [[Disclose]] || | |||
|- | |||
| <syntaxhighlight lang=apl inline>∪</syntaxhighlight> || [[Nub]] || [[Union]] | |||
|- | |||
| <syntaxhighlight lang=apl inline>∩</syntaxhighlight> || Ordered Nub || [[Intersection]] | |||
|- | |||
| <math>\cup\!\!\!\!-</math> || Distribution || | |||
|- | |||
| <math>\cap\!\!\!\!-</math> || Ordered Distribution || | |||
|- | |||
| <syntaxhighlight lang=apl inline>~</syntaxhighlight> || || [[Set Difference]] | |||
|- | |||
| <syntaxhighlight lang=apl inline>⊆</syntaxhighlight> || Inclusion || | |||
|- | |||
| <syntaxhighlight lang=apl inline>⊇</syntaxhighlight> || Inclusion || | |||
|- | |||
| <syntaxhighlight lang=apl inline>⊂</syntaxhighlight> || Strict inclusion || | |||
|- | |||
| <syntaxhighlight lang=apl inline>⊃</syntaxhighlight> || Strict inclusion || | |||
|- | |||
| <syntaxhighlight lang=apl inline>⌷</syntaxhighlight> || Indexing || | |||
|} | |||
Operators: | |||
{|class=wikitable | |||
! Syntax !! Monadic call !! Dyadic call | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⍣B</syntaxhighlight> || [[Power (operator)|Power]] || | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⍣∘</syntaxhighlight> || Identity function (e.g. <syntaxhighlight lang=apl inline>+</syntaxhighlight> to <syntaxhighlight lang=apl inline>×</syntaxhighlight>) || | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⍨</syntaxhighlight> || || [[Commute]] | |||
|- | |||
| <syntaxhighlight lang=apl inline>̈∆</syntaxhighlight> ||colspan=2| Domain | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⍤a</syntaxhighlight> ||colspan=2| Nuax | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⍥a</syntaxhighlight> ||colspan=2| Coax | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⍢g</syntaxhighlight> ||colspan=2| [[Dual]] | |||
|- | |||
| <syntaxhighlight lang=apl inline>f¨g</syntaxhighlight> ||colspan=2| [[Over|Composition]] | |||
|- | |||
| <syntaxhighlight lang=apl inline>f/</syntaxhighlight> || || (Windowed) [[Windowed Reduction|Reduction]] | |||
|- | |||
| <syntaxhighlight lang=apl inline>f\</syntaxhighlight> || || (Windowed) Scan | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⌿</syntaxhighlight> || || (Windowed) [[Windowed Reduction|Reduction]] | |||
|- | |||
| <syntaxhighlight lang=apl inline>f⍀</syntaxhighlight> || || (Windowed) Scan | |||
|- | |||
| <syntaxhighlight lang=apl inline>f∆</syntaxhighlight> || Derivative || Difference | |||
|- | |||
| <syntaxhighlight lang=apl inline>̄:</syntaxhighlight> ||colspan=2| [[Variant]] | |||
|- | |||
| <math>\vee\!\!\!\!\wedge</math> || || Boolean | |||
|} | |||
== External links == | == External links == | ||
* [[Jsoftware]]: [https://www.jsoftware.com/papers/opfns.htm Operators and Functions] (digitised) | * [[Jsoftware]]: [https://www.jsoftware.com/papers/opfns.htm Operators and Functions] (digitised) | ||
{{APL dialects}}[[Category:Iverson designs]] | {{APL dialects}}[[Category:Iverson designs]] | ||